Non-Overlapping Domain Decomposition Methods Interpreted as Multiplicative Subspace Correction Algorithms
نویسنده
چکیده
We interprete non-overlapping domain decomposition methods as multiplicative subspace correction algorithms in the framework of Xu [8]. This allows us to estimate the effects of the perturbation which is created by an inexact solution of the problems on the subdomains that must be solved in each iteration. The general results are applied to finite element discretizations of the Poisson and Stokes equations.
منابع مشابه
Convergence estimates for multigrid algorithms with SSC smoothers and applications to overlapping domain decomposition
In this paper we study convergence estimates for a multigrid algorithm with smoothers of successive subspace correction (SSC) type, applied to symmetric elliptic PDEs. First, we revisit a general convergence analysis on a class of multigrid algorithms in a fairly general setting, where no regularity assumptions are made on the solution. In this framework, we are able to explicitly highlight the...
متن کاملNon-Overlapping Domain Decom- position Methods
Non-overlapping domain decomposition methods are well-established and efficient algorithms for the solution of the large algebraic systems arising from finite element or finite difference discretizations of elliptic partial differential equations. They are well adapted to modern parallel computer architectures since they split the original problem into independent problems on the subdomains, wh...
متن کاملConvergence Rate of Overlapping Domain Decomposition Methods for the Rudin-Osher-Fatemi Model Based on a Dual Formulation
This paper is concerned with overlapping domain decomposition methods (DDMs), based on successive subspace correction (SSC) and parallel subspace correction (PSC), for the Rudin–Osher–Fatemi (ROF) model in image restoration. In contrast to recent attempts, we work with a dual formulation of the ROF model, where one significant difficulty resides in the decomposition of the global constraint of ...
متن کاملNon-overlapping Domain Decomposition Methods
Our intention in this paper is to give a uniied investigation on a class of non-overlapping domain decomposition methods for solving second order elliptic problems in two and three dimensions. The methods under scrutiny fall into two major categories: the substructuring type methods and the Neumann-Neumann type methods. The basic framework used for analysis is the parallel subspace correction m...
متن کاملA Parallel Line Search Subspace Correction Method for Composite Convex Optimization
In this paper, we investigate a parallel subspace correction framework for composite convex optimization. The variables are first divided into a few blocks based on certain rules. At each iteration, the algorithms solve a suitable subproblem on each block simultaneously, construct a search direction by combining their solutions on all blocks, then identify a new point along this direction using...
متن کامل