Convergence analysis of multigrid methods with residual scaling techniques

Residual Scaling Techniques in Multigrid , I : Equivalence Proof

This paper addresses the residual scaling techniques (coarse-grid-correction optimization techniques) in multigrid methods. We survey recent developments in this area and prove the equivalence of the over-weighted residual technique and the over-correction technique. This leads to the proof of mathematical equivalence of the pre-scaling and post-scaling acceleration techniques. Two theorems hav...

Residual Scaling Techniques in Multigrid, I: Equivalence Proof

Convergence Analysis of Perturbed Two-Grid and Multigrid Methods

We consider multigrid methods for symmetric positive definite linear systems. We present a new algebraic convergence analysis of two-grid schemes with inexact solution of the coarse grid system. This analysis allows us to bound the convergence factor of such perturbed two-grid schemes, assuming only a certain bound on the convergence factor for the unperturbed scheme (with exact solution of the...

Convergence Analysis of Geometric Multigrid Methods for Solving Data- Sparse Boundary Element Equations Convergence Analysis of Geometric Multigrid Methods for Solving Data-sparse Boundary Element Equations

The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometric multigrid methods for solving large-scale, data-sparse boundary element equations arising from t...

Analysis of Minimal Residual Smoothing in Multigrid