Trefftz, Collocation and Other Boundary Methods
Speaker:Prof. Tzon-Tzer Lu
Head, Department of Applied Mathematics
National Sun Yat-sen University , Kaohsiung, Taiwan
Date & Time:30 Oct 2008 (Thursday) 15:00 - 16:00


We will survey the algorithms of the collocation method (CM), the Trefftz method (TM) and the collocation Trefftz method (CTM), and summarize the coupling techniques for the exterior and interior boundary conditions, which include the CTM (i.e., the indirect Trefftz method), the very original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Moreover, the error analysis is briefly addressed, and new numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm, and provides the most accurate solution with the best numerical stability.

In this talk we also use the Trefftz method to solve Stokes flow problems. The Stokes flow in two dimensions can be modeled by the biharmonic boundary value problem. Due to the domain corner and sudden change of the boundary conditions, its solution usually has singularity. The Trefftz method is the best method to solve such problems because of its exponential convergence. For bihamonic equation on a general sector with different boundary conditions, we first obtain its particular solutions. Then we use these particular solutions as basis functions in the Trefftz method to compute different models of Stokes flows.