Two-level Solver Research Articles

Multilevel Optimized Schwarz Methods

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 May 2019Accepted: 22 July 2020Published online: 13 October 2020Keywordsmultilevel domain decomposition methods, optimized Schwarz methods, heterogeneous two-level solver, two-level Helmholtz solver, two-level Stokes--Darcy solverAMS Subject Headings65N55, 65N22, 65F10, 65F08Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3

A Class of Symmetric Factored Approximate Inverses and Hybrid Two-Level Solver

A new class of symmetric factored approximate inverses is proposed and used in conjunction with the Preconditioned Conjugate Gradient method for solving sparse symmetric linear systems. Additionally, a new hybrid two-level solver is proposed utilizing a block independent set reordering, in order to create the two level hierarchy. The Schur complement is formed explicitly by inverting the blocks created by reordering. Then, the preconditioned conjugate gradient method is used in conjunction with the symmetric factored approximate inverse to solve the reduced order linear system. Furthermore, numerical results on the performance and convergence behavior for solving various model problems are presented.

Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients

This paper proposes an adaptive strategy for reusing a previously constructed coarse space by algebraic multigrid to construct a two-level solver for a problem with nearby characteristics. A main target application is the solution of the linear problems that appear throughout a sequence of Markov chain Monte Carlo simulations of subsurface flow with uncertain permeability field. The efficacy of the method is demonstrated with extensive set of numerical experiments.

Global-basis two-level method for indefinite systems. Part 1: convergence studies

A robust two-level solver for high indefinite system of equations arising from the finite element discretization is developed. It is shown that the optimal coarse model is spanned by the spectrum of the highest eigenmodes of the smoothing iteration matrix. Convergence studies conducted on a model prolongation operator reveal pathological sensitivity to any deviation from the optimal coarse model. Copyright © 2000 John Wiley & Sons, Ltd.