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

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  • Formaggia, Luca
  • Scheinine, Alan
  • Quarteroni, Alfio

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.

Suggested Citation

  • Formaggia, Luca & Scheinine, Alan & Quarteroni, Alfio, 1997. "A numerical investigation of Schwarz domain decomposition techniques for elliptic problems on unstructured grids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(4), pages 313-330.
    • Handle: RePEc:eee:matcom:v:44:y:1997:i:4:p:313-330
    DOI: 10.1016/S0378-4754(97)00062-1
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