Block preconditioning methods for asymptotic preserving scheme arising in anisotropic elliptic problems

11/16/2021
by   Lingxiao Li, et al.
0

Efficient and robust iterative solvers for strong anisotropic elliptic equations are very challenging. In this paper a block preconditioning method is introduced to solve the linear algebraic systems of a class of micro-macro asymptotic-preserving (MMAP) scheme. MMAP method was developed by Degond et al. in 2012 where the discrete matrix has a 2×2 block structure. By the approximate Schur complement 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, preconditioned GMRES iterative method is developed to solve the discrete equations. Several numerical tests show that block preconditioning methods can be a robust strategy with respect to grid refinement and the anisotropic strengths.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/18/2021

Schur complement based preconditioners for twofold and block tridiagonal saddle point problems

In this paper, two types of Schur complement based preconditioners are s...
research
04/12/2021

Asymptotic preserving scheme for anisotropic elliptic equations with deep neural network

In this paper, a new asymptotic preserving (AP) scheme is proposed for t...
research
02/12/2020

Algebraic multigrid block preconditioning for multi-group radiation diffusion equations

The paper focuses on developing and studying efficient block preconditio...
research
01/22/2020

Robust block preconditioners for poroelasticity

In this paper we study the linear systems arising from discretized poroe...
research
06/07/2022

Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems

Discretization of flow in fractured porous media commonly lead to large ...
research
12/14/2020

A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD

We present a scalable block preconditioning strategy for the trace syste...
research
11/25/2019

The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

We develop a novel iterative solution method for the incompressible Navi...

Please sign up or login with your details

Forgot password? Click here to reset