Speaker: Dr. Chang Yang (杨畅博士)

Time: 11:20-12:20, 10 April 2024 (Wednesday) (Beijing time)

Venue: A103,Lijiao Building, BNU

Tencent Meeting ID: 926-201-973

Abstract

Efficient and robust iterative solvers for strongly anisotropic elliptic equations are very challenging. Indeed, the discretization of this class of problems gives rise to a linear system with a condition number increasing with  anisotropic strength. This weakness is addressed clearly by adopting  the asymptotic-preserving (AP) discretizations. In this work a block preconditioning method is introduced to solve the linear algebraic systems of a class of micro-macro asymptotic-preserving (MMAP) scheme. The MMAP method was developed by Degond et al. in 2012 where its corresponding discrete matrix has a $2\times2$ block structure. Motivated by approximate Schur complements, a series of block preconditioners are constructed. We first analyze a natural approximate Schur complement that is the coefficient matrix of the original Non-AP discretization. However it tends to be singular for very small anisotropic parameters. We then improve it by using more suitable approximation for boundary rows of the exact Schur complement. With these block preconditioners, a preconditioned GMRES iterative method is developed to solve the discrete equations. Several numerical tests show that block preconditioning methods can be a practically useful strategy with respect to grid refinement and  anisotropic strengths.

About Dr. Yang

杨畅，博士毕业于法国里尔科技大学，现任哈尔滨工业大学副教授、博士生导师。主要研究方向为等离子体数学模拟及其相关算法研究，主要成果发表于SIAM Journal on Scientific Computing, SIAM Journal on Applied Mathematics, SIAM Multiscale Modeling & Simulation, Journal of Computational Phyiscs等。目前主持国家自然科学基金面上项目1项。