A PARALLEL AMG FOR OVERLAPPING AND NON-OVERLAPPING DOMAIN DECOMPOSITION
Gundolf Haase · 2000
. There exist several approaches for the parallel solving of huge systems of linear equations resulting from the discretization of 2 nd order elliptic pdes. On the other hand, there exists a great demand on Algebraic Multigrid solvers (AMG) which have as input only matrix and right hand side or, as a substitute, the appropriate information per element. In this paper we propose a general parallel AMG algorithm using overlapping or non-overlapping data decompositions. Key words. Algebraic multigrid, parallel algorithms, domain decomposition, iterative solvers. AMS subject classifications. 65F10, 65N22, 65Y05. 1. Introduction. Without loss of generality we want to solve a second order pde with homogeneous Dirichlet boundary conditions in a domain\\Omega ae R d , d = 2; 3 such that the weak formulation is represented by Find u 2 X(\\Omega\\Gamma : a(u; v) = hF; vi 8v 2 X(\\Omega\\Gamma (1.1) with bilinear form a(u; v) : X \\Theta X 7! R and duality product hF; vi : X \\Theta X 7! R . A ...