Events for 06-2021

Instructors/Speakers Prof. Shu-Lin WU Professor School of Mathematics and Statistics Northeast Normal University Changchun, Jilin, China Abstract The mainstream parallel-in-time (PinT) algorithms, such as parareal and MGRiT, cannot efficiently handle the wave propagation problems, due to the poor convergence rate (or even divergence). New PinT algorithms are proposed in recent years and have shown promising advantages. These new PinT algorithms are called ParaDiag, which was permitted in 2020 by the PinT scientific committee to show and popularize on the homepage of this filed (http://parallel-in-time.org/codes/paradiag.html). In this talk we will discuss some variants and introduce some basic theoretical results. Biography Prof. Shulin WU obtained his Ph.D. degree in Huazhong University of Science and Technology in 2010. From 2010 to 2016, he ...

Instructors/Speakers Prof. Dongfang LI Professor School of Mathematics and Statistics Huazhong University of Science and Technology China Abstract An essential feature of the subdiffusion equations with the α-order time fractional derivative is the weak singularity at the initial time. The weak regularity of the solution is usually characterized by a regularity parameter δ∈(0,1)∪(1,2). Under this general regularity assumption, we present a rigorous analysis for the truncation errors and develop a new tool to obtain the stability results, i.e., a refined discrete fractional-type Gronwall inequality. After that, we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations. The present results fill the gap on some interesting convergence results of L1 scheme on δ∈(0,α)∪(α,1)∪(1,2]. Numerical experiments ...

Instructors/Speakers Prof. Fanhai ZENG Professor School of Mathematics Shandong University China Abstract We develop two fast memory saving methods for calculating the fractional integral and derivative operators. Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity for dealing with the fractional derivative operator. Our fast method simplifies the existing one . Biography Prof. Fanhai ZENG received his bachelor degree from Northwestern Polytechnical University in 2005. In ...

Instructors/Speakers Prof. Hao CHEN Associate Professor Chongqing Normal University Chongqing, China Abstract In this talk, we consider a modified Douglas splitting method for a class of differential matrix equations, including differential Lyapunov and differential Riccati equations. The method we consider is based on a natural three-term splitting of the equations. The implementation of the algorithm requires only the solution of a linear algebraic system with multiple right-hand sides in each time step. It is proved that the method is convergent of order two and it preserves the symmetry and positive semidefiniteness of solutions of differential Lyapunov equations. Moreover, we show how the method can be handled in a low-rank setting for large-scale computations. We also provide a theoretical a priori ...

Instructors/Speakers Prof. Qifeng ZHANG Associate Professor Zhejiang Sci-Tech University China Abstract In this talk, a novel fourth-order three-point compact operator for the nonlinear convection term is provided. The operator makes the numerical analysis of higher order nonlinear or linearly implicit difference schemes become possible for a wide class of nonlinear evolutionary equations under the unified framework. We take the classical viscous Burgers’equation as an example and establish a new conservative fourth-order implicit compact difference scheme based on the method of order reduction. A detailed theoretical analysis is carried out. Furthermore, we derive a three-level linearized compact difference scheme for viscous Burgers’equation based on the proposed operator. Applying the compact operator to other more complex and higher-order nonlinear evolutionary equations is ...