A numerical investigation of Schwarz domain decomposition techniques for elliptic problems on unstructured grids

Luca Formaggia, Alan Scheinine and Alfio Quarteroni

Mathematics and Computers in Simulation (MATCOM), 1997, vol. 44, issue 4, 313-330

Abstract: We consider a parallel implementation of the additive two-level Schwarz domain decomposition technique. The procedure is applied to elliptic problems on general unstructured grids of triangles and tetrahedra. A symmetric, positive-definite system of linear equations results from the discretization of the differential equations by a standard finite-element technique and it is solved with a parallel conjugate gradient (CG) algorithm preconditioned by Schwarz domain decomposition. The two-level scheme is obtained by augmenting the preconditioning system by a coarse grid operator constructed by employing an agglomeration-type algebraic procedure. The algorithm adopts an overlap of just a single layer of elements, in order to simplify the data-structure management involved in the domain decomposition and in the matrix-times-vector operation for the parallel conjugate gradient. Numerical experiments have been carried out to show the effectiveness of the procedure and they, in turn, show how even such a simple coarse grid operator is able to improve the scalability of the algorithm.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:44:y:1997:i:4:p:313-330

DOI: 10.1016/S0378-4754(97)00062-1

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