Parameter-robust Braess-Sarazin-type smoothers for linear elasticity problems

04/22/2022
by   Yunhui He, et al.
0

In this work, we propose three Braess-Sarazin-type multigrid relaxation schemes for solving linear elasticity problems, where the marker and cell scheme, a finite difference method, is used for the discretization. The three relaxation schemes are Jacobi-Braess-Sarazin, Mass-Braess-Sarazin, and Vanka-Braess-Sarazin. A local Fourier analysis (LFA) for the block-structured relaxation schemes is presented to study multigrid convergence behavior. From LFA, we derive optimal LFA smoothing factor for each case. We obtain highly efficient smoothing factors, which are independent of Lamé constants. Vanka-Braess-Sarazin relaxation scheme leads to the most efficient one. In each relaxation, a Schur complement system needs to be solved. Due to the fact that direct solve is often expensive, an inexact version is developed, where we simply use at most three weighted Jacobi iterations on the Schur complement system. Finally, two-grid and V-cycle multigrid performances are presented to validate our theoretical results. Our numerical results show that inexact versions can achieve the same performance as that of exact versions and our methods are robust to the Lamé constants.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/04/2022

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

We propose a block-structured multigrid relaxation scheme for solving th...
research
03/22/2022

Smoothing analysis of two robust multigrid methods for elliptic optimal control problems

In this paper we study and compare two multigrid relaxation schemes with...
research
11/30/2021

A novel multigrid method for elliptic distributed control problems

Large linear systems of saddle-point type have arisen in a wide variety ...
research
10/15/2021

Tweed and wireframe: accelerated relaxation algorithms for multigrid solution of elliptic PDEs on stretched structured grids

Two new relaxation schemes are proposed for the smoothing step in the ge...
research
11/12/2020

A data driven heuristic for rapid convergence of general Scheduled Relaxation Jacobi (SRJ) schemes

The Scheduled Relaxation Jacobi (SRJ) method is a viable candidate as a ...
research
07/05/2021

Weighted Relaxation for Multigrid Reduction in Time

Based on current trends in computer architectures, faster compute speeds...
research
03/06/2020

The linearization methods as a basis to derive the relaxation and the shooting methods

This chapter investigates numerical solution of nonlinear two-point boun...

Please sign up or login with your details

Forgot password? Click here to reset