{"id":19099,"date":"2022-01-06T15:33:44","date_gmt":"2022-01-06T07:33:44","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=19099"},"modified":"2025-10-21T17:43:26","modified_gmt":"2025-10-21T09:43:26","slug":"publications","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/xccai\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"19099\" class=\"elementor elementor-19099\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-e38af62 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e38af62\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-65f1bc4\" data-id=\"65f1bc4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d27358a elementor-widget elementor-widget-text-editor\" data-id=\"d27358a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul style=\"list-style-type: disc\"><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Xu, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/xulei_ccp2025.pdf\">A parallel fully implicit unstructured finite volume Lattice Boltzmann method for incompressible flows<\/a>, Communications in Computational Physics, 37 (2025), p. 547-574.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Yan, R. Chen, F. Qi, and X.-C.Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/yzz_IEEE2025.pdf\">A functional region-based approach for the numerical simulation of patient-specific cerebral blood flows with clinical validation<\/a>, IEEE Transactions on Biomedical Engineering, (2025).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F. Qi, Y. Liu, Y. Gong, J.-Y. Wang, R. Chen, P. Hu, L. Luo, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/qff_metacom2025.pdf\">Towards a digital twin of the human kidney for diagnosis of renal diseases<\/a>, IEEE International Conference on Metaverse Computing, Networking and Applications, (2025), p. 173-180.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J.-Y. Wang, Y. Gong, Y. Shan,F. Qi, Y. Liu, Z. Yan, Z. Cheng, R. Chen, X. Wang, L. Luo, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/wjy_metacom2025.pdf\">Offline modeling and mixed reality based remote diagnosis system for patient-specific cardiovascular diseases<\/a>, IEEE International Conference on Metaverse Computing, Networking and Applications, (2025), p. 189-196.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Zhang, L. Luo, Y. Li, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/zxd_jcp2025.pdf\">A fully implicit method for numerical simulation of blood flows with incompressible Navier-Stokes equations with slip and penetration boundary conditions<\/a>, Journal of Computational Physics, (2025), p. 114267.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Chen and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/cxd_jcp2025.pdf\">A preconditioning method with the Generalized\u2212\u03b1 time discretization for dynamic crack propagations based on XFEM<\/a>, Journal of Computational Physics, 533 (2025), p. 113992.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Yan, D. Shang, R. Chen, and X.-C. Cai, \u00a0<a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/yzz_cmpb2025.pdf\">A computational study of the connection between coronary revascularization and cardio-cerebral hemodynamics<\/a>, Computer Methods and Programs in Biomedicine, 263 (2025), p. 108667.<\/span><\/li><li><span style=\"font-size: 14pt;font-family: 'times new roman', times, serif\">S. Li, L. Xu, and X.-C. Cai,\u00a0<a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/lss_NLAA2025.pdf\">Multilevel additive Schwarz preconditioners for high-order block implicit methods for parabolic equations<\/a>, Numerical Linear Algebra with Applications, 32 (2025), p. \u00a0e70014.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Li, J.-Y. Wang and X.-C.Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/lss_BIT2025.pdf\">Block implicit methods with L-stability for parabolic problems<\/a>, BIT Numerical Mathematics, 65 (2025), p. 12.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen and X.-C.Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2025\/10\/rl_US12223626.pdf\">Method for denoising image, apparatus, and computer-readable storage medium<\/a>, US Patent, 12, 223,626, 2025.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F. Qi, Y. Liu, Y. Gong, J.-Y. Wang, J. Zhou, R. Chen, R.-S. Huang, X. Wang, L. Luo, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/11\/ffq_cai_2024.pdf\">Mixed reality visualization and interactive hemodynamic computation of the human brain<\/a>, IEEE International Conference on Metaverse Computing, Networking and Applications, (2024).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J.-Y. Wang, Y. Gong, J. Zhou, F. Qi, Y. Liu, Z. Cheng, R. Chen, X. Wang, L. Luo, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/11\/jyw_cai_2024.pdf\">A collaborative mixed reality platform for the planning of vascular surgery<\/a>, IEEE International Conference on Metaverse Computing, Networking and Applications, (2024).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Jiang, Z. Yan, X. Wang, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/11\/jiang_cai_2024.pdf\">A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model<\/a>, Journal of Computational Physics, 508 (2024), p. 113027.<\/span><\/span><\/li><li><span style=\"font-size: 14pt;font-family: 'times new roman', times, serif\">H. Yang, T.-H. Ma, F.-N. Huang, and <span style=\"font-size: 14pt\"><span style=\"font-family: 'times new roman', times, serif\">X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/11\/hjy_cai_2024.pdf\">Nonlinearly preconditioned semismooth Newton algorithms for nonlinear nonsmooth systems<\/a>, International Journal of Computer Mathematics, 101 (2024), p. 1-22.<\/span><\/span><\/span><\/li><li><span style=\"font-size: 14pt\"><span style=\"font-family: 'times new roman', times, serif\">Y. Liu, F. Qi, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/11\/yzl_cai_2024.pdf\">A one-dimensional coarse preconditioner for three-dimensional unsteady incompressible Navier-Stokes flows in patient-specific arteries<\/a>, SIAM Journal of Scientific Computing, 46 (2024), p. S1-S23.<\/span><\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J. Li and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2024\/01\/li_cai_2024.pdf\">Domain decomposed classification algorithms based on linear discriminant analysis: An optimality theory and applications<\/a>, Neurocomputing, (2024).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif\"><span style=\"font-size: 14pt\">Y. Liu, F. Qi, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/09\/lqc2023.pdf\">An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flow<\/a>, International Journal for Numerical Methods in Biomedical Engineering, (2023).<\/span><\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Gong, F. Qi, Y. Liu, J.-Y. Wang, T. Ma, Z. Cheng, Y. Jiang, R. Chen, X. Wang, L. Luo, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/meta2023_heart.pdf\">An interactive platform for a high performance digital twin of a human heart<\/a>, IEEE International Conference on Metaverse Computing, Networking and Applications, (2023).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Li, J. Wang, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/BIM_li2023.pdf\">A-stable high order block implicit methods for parabolic equations<\/a>, SIAM J. Num. Anal., (2023).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Liu and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/yingzhi2023.pdf\">Two-level additive Schwarz methods for three-dimensional unsteady Stokes flows in patient-specific arteries with parameterized one-dimensional central-line coarse preconditioner<\/a>, Journal of Computational Physics, 490 (2023), p. 112290.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/luo2023.pdf\">PIN_L: Preconditioned inexact Newton with learning capability for nonlinear system of equations<\/a>, SIAM J. Sci. Comput., 45 (2023), p. A849-A871.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Lin, B. Wu, S. Qin, X. Wang, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/lin_dd26.pdf\">Numerical calculation of the portal pressure gradient of the human liver with a domain decomposition method<\/a>, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 161-168.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Gu, W. Zhang, J. Liu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/gu_dd26.pdf\">Decomposition and preconditioning of deep convolutional neural networks for training acceleration<\/a>, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 153-160.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, X.-C. Cai, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/luo_dd26.pdf\">A parallel adaptive finite element method for modeling a deformable droplet travelling in air<\/a>, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 169-176.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Laudenschlager and X.-C. Cai, <\/span><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\"><a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/subastian2023.pdf\">An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations<\/a>, International Journal for Numerical Methods in Biomedical Engineering, 39 (2023), p. e3677.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Qin, R. Chen, B. Wu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/qin2023.pdf\">A highly parallel fully implicit domain decomposition method for the simulation of the hemodynamics of a patient-specific artery at the full-body scale<\/a>, J. Comput. Phys., 472 (2023), p. 111730.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Gu, W. Zhang, J. Liu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/12\/gu-2022.pdf\">Decomposition and composition of deep convolutional neural networks and training acceleration via sub-network transfer learning<\/a>, Electronic Transactions on Numerical Analysis, 56 (2022), pp. 157-186.<\/span><\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Yan, Z. Yao, W. Guo, D. Shang, R. Chen, J. Liu, X.-C. Cai, and J. Ge, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/11\/yzz2022_1.pdf\">Impact of the pressure wire on the measured fractional flow reserve and hemodynamics: A combined computational and clinical study<\/a>, IEEE Transactions on Biomedical Engineering, (2022).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Liu, F. Qi, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/11\/liusiam_2022.pdf\">A one-dimensional coarse preconditioner for three-dimensional unsteady incompressible Navier-Stokes flows in patient-specific arteries<\/a>, SIAM J. Sci. Comput., (2022).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Deng, Z.-J. Liao, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/xiaomao2022.pdf\">An efficient two-level overlapping domain decomposition method for recovering unsteady sources of 3D parabolic problems<\/a>, Computers &amp; Mathematics with Applications, 111 (2022), p. 98-108.<\/span><\/li><li><span style=\"font-size: 14pt;font-family: 'times new roman', times, serif\">X. Chen and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/xingding2022.pdf\">A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM<\/a>, Journal of Computational Physics, 452 (2022), p. 110910.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Liu, F.-N. Hwang, L. Luo, X.-C. Cai, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2023\/07\/lulu2022.pdf\">A nonlinear elimination preconditioned inexact Newton algorithm<\/a>, SIAM Journal on Scientific Computing, 44 (2022), p. A1579-A1605.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Lin, B. Wu, S. Qin, X. Wang, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/11\/lin_dd26.pdf\">Numerical calculation of the portal pressure gradient of the human liver with a domain decomposition method<\/a>, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, X.-C. Cai, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/11\/luo_dd26.pdf\">A parallel adaptive finite element method for modeling a deformable droplet travelling in air<\/a>, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Gu, W. Zhang, J. Liu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/11\/gu_dd26.pdf\">Decomposition and preconditioning of deep convolutional neural networks for training acceleration<\/a>, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z.-J. Liao, S. Qin, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lqcc2022.pdf\">A parallel domain decomposition method for large eddy simulation of blood flow in human artery with resistive boundary condition<\/a>, Computers and Fluids,\u00a0232 (2022), p. 105201.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J. Xie, Z. Cheng, L. Gu, B. Wu, G. Zhang, W. Shiu, R. Chen, Z. Wang, C. Liu, J. Tu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/xie22.pdf\">\u00a0Evaluation of cerebrovascular hemodynamics in vascular dementia patients with a new individual computational fluid dynamics algorithm<\/a>, Comput. Methods Programs Biomed., 213 (2022), p. 106497.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Yan,\u00a0R. Chen, and X.-C.\u00a0Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ycc22.pdf\">Large eddy simulation of the wind flow in a realistic full-scale urban community with a scalable parallel algorithm<\/a>, Comput. Phys. Commun.,\u00a0270\u00a0(2022), p. 108170.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Gu and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/gc2021.pdf\">Fusing 2D and 3D convolutional neural networks for the segmentation of aorta and coronary arteries from CT images<\/a>, Artif. Intell. Med., 121 (2021), pp. 102189.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Qin, B. Wu, J. Liu, W.-S. Shiu, Z. Yan, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/qin2021_cbm.pdf\">Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm<\/a>, Comput. Biol. Med., 136 (2021), p. 104652.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Deng, Z.-J. Liao, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/deng21.pdf\">A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations<\/a>, J. Comput. Appl. Math., 392 (2021), p. 113441.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Liu and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/Liu-Cai2021.pdf\">A central-line coarse preconditioner for Stokes flows in artery-like domains<\/a>, Numer. Algorithm, 1 (2021), pp. 137-160.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Lin, R. Chen, B. Gao, S. Qin, B. Wu, J. Liu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lin2021.pdf\">A highly parallel simulation of patient-specific hepatic flows<\/a>, Inter. J. Numer. Methods Biomed. Eng., (2021), p. e3451.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Xu, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/xu21.pdf\">Parallel finite-volume discrete Boltzmann method for inviscid compressible flows on unstructured grids<\/a>, Phys. Rev. E, 2 (2021), p. 023306.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Qin, R. Chen, B. Wu, W.-S. Shiu, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/Qin2021.pdf\">Numerical simulation of blood flows in patient-specific abdominal aorta with primary organs<\/a>, Biomech. Model. Mechanobiol., (2021), pp. 1-16.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, X.-C. Cai, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/Luo_sisc_2021.pdf\">Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method<\/a>, SIAM J. Sci. Comput., 0 (2021), pp. S317-S344.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J. Li and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/li21.pdf\">Summation pollution of principal component analysis and an improved algorithm for location sensitive data<\/a>, Numer. Linear Algebra Appl., (2021), p. e2370.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">W. Ma and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ma-cai-2020.pdf\">Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems<\/a>, Inter. J. High Perf. Comput. Appli., 2 (2020), pp. 121-135.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Jiang, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/Jiang2020.pdf\">A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes<\/a>, Comput. Mech., 6 (2020), pp. 1461-1475.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen, B. Wu, Z. Cheng, W.-S. Shiu, J. Liu, L. Liu, Y. Wang, X. Wang, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/chen20.pdf\">A parallel non-nested two-level domain decomposition method for simulating blood flows in cerebral artery of stroke patient<\/a>, Inter. J. Numer. Methods Biomed. Eng., 11 (2020), p. e3392.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, L. Liu, X.-C. Cai, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/llck2020.pdf\">Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids<\/a>, J. Comput. Phys., 409 (2020), p. 109312.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, X.-C. Cai, Z. Yan, L. Xu, and D.E. Keyes, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/Luo_Multilayer_SISC_2020.pdf\">A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions<\/a>, SIAM J. Sci. Comput., 6 (2020), pp. B1404-B1428.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, W.-S. Shiu, R. Chen, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lscc2019.pdf\">A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis<\/a>, J. Comput. Phys., 399 (2019), p. 108926.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F. Kong, V. Kheyfets, E. Finol, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/k2019A.pdf\">Simulation of unsteady blood flows in a patient-specific compliant pulmonary artery with a highly parallel monolithically coupled fluid-structure interaction algorithm<\/a>, Inter. J. Numer. Methods Biomed. Eng., 7 (2019), p. e3208.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Li, X. Shao, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lsc2019.pdf\">Highly parallel space-time domain decomposition methods for parabolic problems<\/a>, CCF Transactions on High Performance Computing, 1 (2019), pp. 25-34.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z.-J. Liao, R. Chen, Z. Yan, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lcyc2019.pdf\">A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes<\/a>. Inter. J. Numer. Methods Fluids, 9 (2019), pp. 343-361.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen, J. Huang, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/chc2019.pdf\">A parallel domain decomposition algorithm for large scale image denoising<\/a>, Inverse Probl. Imaging, 6 (2019), pp. 1259-1282.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Gong and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/gc2019.pdf\">A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity<\/a>, SIAM J. Sci. Comput., 5 (2019), pp. S390-S408.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen, Z. Yan, Y. Zhao, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cyzc2018.pdf\">Scalable domain decomposition algorithms for simulation of flows passing full size wind turbine<\/a>, Commun. Comput. Phys., 5 (2018), pp. 1503-1522.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Li, X. Shao, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lsc2018.pdf\">Multilevel space-time additive Schwarz methods for parabolic equations<\/a>, SIAM J. Sci. Comput., 40 (2018), pp. A3012-A3037.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, X.-P. Wang, and X.-C. Cai, <a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/lwc2017.pdf\">An efficient finite element method for simulation of droplet spreading on a topologically rough surface<\/a>, J. Comp. Phys., 349 (2017), pp. 233-252.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">J. Huang, C. Yang, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/hyc2015.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A fully implicit method for lattice Boltzmann equations<\/span><\/a>, SIAM J. Sci. Comput., (2015).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Deng, X.-C. Cai, and J. Zou,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dcz2015.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel space-time domain decomposition method for some unsteady source inversion problems<\/span><\/a>, Inverse Prob. Imaging, (2015).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">W.-S. Shiu, F.-N. Hwang, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/shc2015.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel domain decomposition method for finite element approximation of 3D non-Newtonian fluids<\/span><\/a>, Int. J. Numer. Methods in Fluids, 78 (2015), pp. 502-520.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang, Y.-C. Su, and X.-C. Cai,\u00a0<a href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/hsc2015.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\">A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation<\/span><\/a>, Computers and Fluids, 110 (2015), pp. 96-107.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Zheng, C. Yang, X.-C. Cai, and D. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/zyck2015.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel domain decomposition based implicit method for the Cahn-Hilliard-Cook phase-field equation with thermal fluctuation in 3D<\/span><\/a>, J. Comput. Phys., 285 (2015), pp. 55-70.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Cong, X.-C. Cai, and K. Gustafson,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/spde2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations<\/span><\/a>, SIAM J. Sci. Comput., 36 (2014), pp. C1-C24.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/euler2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows<\/span><\/a>, SIAM J. Sci. Comput., 36 (2014), S23-S47.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Wu and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/fsi2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A fully implicit domain decomposition based ALE framework for three-dimensional fluid-structure interaction with application in blood flow computation<\/span><\/a>, J. Comput. Phys., 258 (2014), pp. 524-537.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Z. Yan, R. Chen, Y. Zhao, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cicp14.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A scalable numerical method for simulating flows around high-speed train under crosswind conditions<\/span><\/a>, Comm. Comput. Phys., 15 (2014), pp. 944-958.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen, Y. Wu, Z. Yan, Y. Zhao, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jsc14.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel domain decomposition method for 3D unsteady incompressible flows at high Reynolds number<\/span><\/a>, J. Sci. Comput., 58 (2014), pp. 275-289.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F. Kong and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/kc2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A scalable Schwarz method for 3D linear elasticity problems on domains with complex geometry<\/span><\/a>, SC13, (2013).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ipdps2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A scalable implicit solver for phase field drystal simulations<\/span><\/a>, IEEE IPDPS Workshop (2013).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">H. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/control2012.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel fully implicit two-grid Lagrange-Newton-Krylov-Schwarz methods for distributed control of unsteady incompressible flows<\/span><\/a>, Intern. J. Numer. Methods in Fluids, 72 (2013), pp. 1-21.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang, X.-C. Cai, Y.-L. Cheng, and C.-W. Tsao,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/mixing2013.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D<\/span><\/a>, Intern. J. Comp. Math., 90 (2013), pp. 615-629.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Chen and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cc12.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel one-shot Lagrange-Newton-Krylov-Schwarz algorithms for shape optimization of steady incompressible flows<\/span><\/a>, SIAM J. Sci. Comput., 34 (2012), pp. B584-B605.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">H. Yang, E. Prudencio, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ypc12.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Fully implicit Lagrange-Newton-Krylov-Schwarz algorithms for boundary control of unsteady incompressible flows<\/span><\/a>, Int. J. Numer. Meth. Engin., 91 (2012), pp. 644-665.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Luo, C. Yang, Y. Zhao, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ly2c2011.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A scalable hybrid algorithm based on domain decomposition and algebraic multigrid for solving partial differential equations on a cluster of CPU\/GPUs<\/span><\/a>, Proceedings of 2nd International Workshop on GPUs and Scientific Applications. In conjunction with 2011 International Conference on Parallel Architectures and Compilation Techniques (PACT 2011).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Wu and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/wc11.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition<\/span><\/a>, Computers and Fluids, 45 (2011), pp. 92-102.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jcp2011.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on cubed-sphere<\/span><\/a>, J. Comput. Phys., 230 (2011), pp. 2523-2539.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and X. Li,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cl_sisc.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity<\/span><\/a>, SIAM J. Sci. Comput., 33 (2011), pp. 746-762.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">H. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/yc11.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems<\/span><\/a>, J. Sci. Comput., 47 (2011), pp. 258-280.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang, H.-L. Lin, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/hlc2010.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation<\/span><\/a>, ETNA, 37 (2010), pp. 239-251.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">H. Yang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/yc_dd19.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Domain decomposition methods for a complementarity problem<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Springer, (2010).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Liu and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/inverse_dd19.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Two-level multiplicative domain decomposition algorithm for recovering the Lame coefficient in biological tissues<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Springer, (2010).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">A. Barker and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/sisc2010.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction<\/span><\/a>, SIAM J. Sci. Comput., 32 (2010), pp. 2395-2417.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">A. Barker and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jcp09.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling<\/span><\/a>, J. Comput. Phys., 229 (2010), pp. 642-659.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Yang, J. Cao, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/water.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A fully implicit domain decomposition algorithm for shallow water equations on the cubed-sphere<\/span><\/a>, SIAM J. Sci. Comput., 32 (2010), pp. 418-438.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\"><span style=\"font-style: inherit;font-weight: inherit\">X.-C. Cai, S. Liu, and J. Zou,\u00a0<\/span><a style=\"font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;background-color: #ffffff;margin: 0px;padding: 0px;border: 0px;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/clz09.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel overlapping domain decomposition methods for coupled inverse elliptic problems<\/span><\/a><span style=\"font-style: inherit;font-weight: inherit\">, Comm. App. Math. Comp. Sci., 4 (2009), pp. 1-26.<\/span><\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd18_1.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Nonlinear overlapping domain decomposition methods<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Springer, 70 (2009), pp. 217-224.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">A. Barker and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd18_2.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">NKS for fully coupled fluid-structure interaction with application<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Springer, 70 (2009), pp.275-282.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, S. Liu, and J. Zou,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd17.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">An overlapping domain decomposition method for parameter identification problems<\/span><\/a>, Lecture Notes in Computational Science and Engineering, U. Langer, M. Discacciati, D.E. Keyes, O.B. Widlund, W. Zulehner (Eds.), Springer, Vol. 60, (2008), pp. 451-458.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Jin and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jin-cai-cicp.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A preconditioned recycling GMRES solver for stochastic Helmholtz problems<\/span><\/a>, Commun. Comput. Phys., 6 (2009), pp. 342-353.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Ovtchinnikov, F. Dobrian, X.-C. Cai, and D. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/odck.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems<\/span><\/a>, J. Comput. Phys., 225 (2007), pp. 1919-1936.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">C. Jin, X.-C. Cai, and C. Li,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jcl07.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel domain decomposition methods for stochastic elliptic equations<\/span><\/a>, SIAM J. Sci. Comput., 29 (2007), pp. 2096-2114.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/aspin2_06.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms<\/span><\/a>, Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp. 1603-1611.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Ovtchinnikov, F. Dobrian, X.-C. Cai, and D. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/odck_dd16.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Domain-decomposed fully coupled implicit methods for a magnetodydrodynamics problem<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Springer, (2006).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">E. Prudencio and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/inksz2.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization<\/span><\/a>, SIAM J. Sci. Comput., 29 (2007), pp. 964-985.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/etna06.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel fully coupled Schwarz preconditioners for saddle point problems<\/span><\/a>, ETNA, 22 (2006), pp. 146-162.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">E. Prudencio, R. Byrd, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/inksz.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems<\/span><\/a>, SIAM J. Sci. Comput., 27 (2006), pp. 1305-1328.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, L. Marcinkowski, and P. Vassilevski,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/asp.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems<\/span><\/a>, Applications of Mathematics, 50 (2005), pp. 247-275.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/jcp-aspin.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations<\/span><\/a>, J. Comput. Phys., 204 (2005), pp. 666-691.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">E. Prudencio, R. Byrd, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/pbc04.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Domain decomposition methods for PDE constrained optimization problems<\/span><\/a>, M. Dayde, J. Dongarra, V. Hernandez, and J. Palma, edt., Lecture Notes in Computer Science, Vol 3402, Springer, 2005.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Ovtchinnikov and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/oc-nlaa04.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">One-level Newton-Krylov-Schwarz algorithm for unsteady nonlinear radiation diffusion problem<\/span><\/a>, Numer. Lin. Alg. Applics., 11 (2004), pp. 867-881.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">F.-N. Hwang and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/hc-dd15.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Improving robustness and parallel scalability of Newton method through nonlinear preconditioning<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Vol. 40, R. Kornhuber, R. Hoppe, J. Periaux, O. Pironneau, O. Widlund, J. Xu, eds, Springer, 2004.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">M. Murillo and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/mc-nlaa04.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart<\/span><\/a>, Numer. Lin. Alg. Applics., 11 (2004), pp. 261-277.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">L. Marcinkowski and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/mc-dd15.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel performance of some two-level ASPIN algorithms<\/span><\/a>, Lecture Notes in Computational Science and Engineering, Vol. 40, R. Kornhuber, R. Hoppe, J. Periaux, O. Pironneau, O. Widlund, J. Xu, eds, Springer, 2004.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X. Yue, F.-N. Hwang, R. Shandas, and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/rmbs.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Simulation of branching blood flows on parallel computers<\/span><\/a>, Proceedings of Rocky Mountain Bioengineering Symposium, 2004.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, D. E. Keyes, and L. Marcinkowski,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/10page.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Nonlinear additive Schwarz preconditioners and applications in computational fluid dynamics<\/span><\/a>, International Journal for Numerical Methods in Fluids, 40 (2002), pp. 1463-1470.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, M. Dryja, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.colorado.edu\/faculty\/cai\/content\/restricted-additive-schwarz-preconditioners-harmonic-overlap-symmetric-positive-definite\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems<\/span><\/a>, SIAM J. Numer. Anal., 41 (2003), pp. 1209-1231.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, D. E. Keyes, and D. P. Young,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd13_1d.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flow<\/span><\/a>, Proceedings of the 13th International Conference on Domain Decomposition Methods, Oct. 9-12, 2000, France.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, M. Dryja, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd13.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">RASHO: A restricted additive Schwarz preconditioner with harmonic overlap<\/span><\/a>, Proceedings of the 13th International Conference on Domain Decomposition Methods, Oct. 9-12, 2000, France.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and D. E. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/aspin.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Nonlinearly preconditioned inexact Newton algorithms<\/span><\/a>, SIAM J. Sci. Comput., 24 (2002), pp. 183-200.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">R. Aitbayev, X.-C. Cai, and M. Paraschivoiu,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/acp.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel two-level methods for three-dimensional transonic compressible flow simulations on unstructured meshes<\/span><\/a>, Proceedings of Parallel CFD&#8217;99, 1999.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">M. Paraschivoiu, X.-C. Cai, M. Sarkis, D. P. Young, and D. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/aiaa99.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Multi-domain multi-model formulation for compressible flows: Conservative interface coupling and parallel implicit solvers for 3D unstructured meshes<\/span><\/a>, AIAA Paper 99-0784, 1999.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, M. Paraschivoiu, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd11.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">An explicit multi-model compressible flow formulation based on the full potential equation and the Euler equations on 3D unstructured meshes<\/span><\/a>, 11th International Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M. Cross, O. Widlund, eds., 1999.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">S. Goossens and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/goossens.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Lower dimensional interpolation in overlapping composite mesh difference methods<\/span><\/a>, 11th International Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M. Cross, O. Widlund, eds., 1999.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, T. Mathew, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/nmg.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations<\/span><\/a>, SIAM J. Numer. Anal., 37 (2000), pp. 1709-1728.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and J. Zou,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/l2.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Some observations on the $L^2$ convergence of the additive Schwarz preconditioned GMRES method<\/span><\/a>, Numer. Lin. Alg. Applics., 9 (2002), pp. 379-397.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, M. A. Casarin, Jr., F. W. Elliott, Jr., and, O. B. Widlund,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ccew_dd10.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Overlapping Schwarz algorithms for solving Helmholtz&#8217;s equation<\/span><\/a>, Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel, C. Farhat and X.-C. Cai, eds., AMS, pp. 437-445, 1998.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Y. Wu, X.-C. Cai, and D. E. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/wck_dd10.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Additive Schwarz methods for hyperbolic equations<\/span><\/a>, Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel, C. Farhat and X.-C. Cai, eds., AMS, pp. 513&#8211;521, 1998.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, C. Farhat, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd10.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations<\/span><\/a>, The Tenth International Conference on Domain Decomposition Methods for Partial Differential Equations, J. Mandel, C. Farhat and X.-C. Cai, eds, AMS, 1998.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ras.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A restricted additive Schwarz preconditioner for general sparse linear systems<\/span><\/a>, SIAM J. Sci. Comput., 21 (1999), pp. 792-797.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, M. Dryja, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/mortar.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Overlapping non-matching grid mortar element methods for elliptic problems<\/span><\/a>, SIAM J. Numer. Anal., 36 (1999), pp. 581-606.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, C. Farhat, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/flu.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Variable degree Schwarz methods for the implicit solution of unsteady compressible Navier-Stokes equations on two-dimensional unstructured meshes<\/span><\/a>, ICASE Report No. 96-48, NASA Langley Research Center, 1996.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, W. D. Gropp, D. E. Keyes, R. G. Melvin, and D. P. Young,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/nks96.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation<\/span><\/a>, SIAM J. Sci. Comput., 19 (1998), pp. 246-265.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, C. Farhat, and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/dd8.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Schwarz methods for the unsteady compressible Navier-Stokes equations on unstructured meshes<\/span><\/a>, Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., John Wiley &amp; Sons, Ltd., 1997.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, D. E. Keyes, and V. Venkatakrishnan,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ckv_dd8.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Newton-Krylov-Schwarz: An implicit solver for CFD<\/span><\/a>, Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., John Wiley &amp; Sons, Ltd., 1996.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and M. Sarkis,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/local.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Local multiplicative Schwarz algorithms for convection-diffusion equations<\/span><\/a>, East-West J. Numer. Math., 6 (1998).<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cgkt1.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Parallel implicit methods for aerodynamics<\/span><\/a>, Seventh International Conference on Domain Decomposition Methods for Partial Differential Equations, D. Keyes, J. Xu, eds., AMS, 1994.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and M. Dryja,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/caidryja.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Domain decomposition methods for monotone nonlinear elliptic problems<\/span><\/a>, Seventh International Conference on Domain Decomposition Methods for Partial Differential Equations, D. Keyes, J. Xu, eds., AMS, 1994.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/heid.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Newton-Krylov-Schwarz methods in CFD<\/span><\/a>, Proceedings of the International Workshop on the Navier-Stokes Equations, Notes in Numerical Fluid Mechanics, R. Rannacher, eds. Vieweg Verlag, Braunschweig, 1994.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/nnest.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">The use of pointwise interpolation in domain decomposition methods with non-nested meshes<\/span><\/a>, SIAM J. Sci. Comput., 16 (1995), pp. 250-256.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/chap1.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems<\/span><\/a>, in Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering, D. Keyes and Y. Saad and D. Truhlar, eds., SIAM, 1994.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai, W. D. Gropp, and D. E. Keyes,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cgk2.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems<\/span><\/a>, Numer. Lin. Alg. Applics., 1 (1994), pp. 477-504.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and Y. Saad,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/ogd.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Overlapping domain decomposition algorithms for general sparse matrices<\/span><\/a>, TR 93-027, Army High Performance Computing Research Center, University of Minnesota, 1993.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">B. Bialecki and X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/bc.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">$H^1$-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems<\/span><\/a>, SIAM J. Numer. Anal., 31 (1994), pp. 1128-1146.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/msm.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Multiplicative Schwarz methods for parabolic problems<\/span><\/a>, SIAM J. Sci. Comput., 15 (1994), pp. 587-603.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cai93.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">An optimal two-level overlapping domain decomposition method for elliptic problems in two and three dimensions<\/span><\/a>, SIAM J. Sci. Comput., 14 (1993), pp. 239-247.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and O. Widlund,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/cw2.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Multiplicative Schwarz algorithms for nonsymmetric and indefinite elliptic problems<\/span><\/a>, SIAM J. Numer. Anal., 30 (1993), pp. 936&#8211;952.<\/span><\/li><li style=\"margin: 0px 0px 10px;padding: 0px;border: 0px;font: inherit;vertical-align: baseline\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">X.-C. Cai and O. Widlund,\u00a0<a style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/caiwid1_www.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Domain decomposition algorithms for indefinite elliptic problems<\/span><\/a>, SIAM J. Sci. Stat. Comp., 13 (1992), pp. 243-258.<\/span><\/li><li><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">\u00a0X.-C. Cai,\u00a0<a style=\"font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;background-color: #ffffff;margin: 0px;padding: 0px;border: 0px;vertical-align: baseline;color: #0267a4\" href=\"https:\/\/www.fst.um.edu.mo\/personal\/wp-content\/uploads\/2022\/01\/asm.pdf\"><span style=\"margin: 0px;padding: 0px;border: 0px;font-style: inherit;font-variant: inherit;font-weight: inherit;line-height: inherit;vertical-align: baseline\">Additive Schwarz algorithms for parabolic convection-diffusion equations<\/span><\/a><span style=\"font-style: inherit;font-weight: inherit\">, Numer. Math., 60 (1990), pp. 41-62.<\/span><\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>L. Xu, R. Chen, and X.-C. Cai, A parallel fully implicit unstructured finite volume Lattice Boltzmann method for incompressible flows, Communications in Computational Physics, 37 (2025), p. 547-574. Z. Yan, R. Chen, F. Qi, and X.-C.Cai, A functional region-based approach for the numerical simulation of patient-specific cerebral blood flows with clinical validation, IEEE Transactions on &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.fst.um.edu.mo\/personal\/xccai\/publications\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Publications&#8221;<\/span><\/a><\/p>\n","protected":false},"author":186,"featured_media":0,"parent":917,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_canvas","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19099","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/19099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/users\/186"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/comments?post=19099"}],"version-history":[{"count":10,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/19099\/revisions"}],"predecessor-version":[{"id":54157,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/19099\/revisions\/54157"}],"up":[{"embeddable":true,"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/pages\/917"}],"wp:attachment":[{"href":"https:\/\/www.fst.um.edu.mo\/personal\/wp-json\/wp\/v2\/media?parent=19099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}