Nonoverlapping domain decomposition: A linear algebra viewpoint
In this work we consider the Helmholtz equation in a hyperparallelepiped Omega subset of R-d, d = 1, 2, 3, ..., under Dirichlet boundary conditions and for its solution we apply the averaging technique of the nonoverlapping Domain Decomposition, where Omega is decomposed in two, in general not equal, subdomains. Unlike what many researchers do that is first to determine regions of convergence and optimal values of the relaxation parameters involved at the PDE level, next discretize and then solve the linear system yielded using the values of the parameters determined, we determine regions of convergence and optimal values of the parameters involved after the discretization takes place, that is at the linear algebra level, and then use them for the solution of the Linear system. In the general case the parameters obtained in this work are not the same with the ones which are known and which have been obtained at the PDE level. (C) 2000 IMACS/Elsevier Science B.V. All rights reserved. Primary 65F10; 65N05; 65N35.
elliptic partial differential equations domain decomposition methods iterative methods