Mathematics – Numerical Analysis
Scientific paper
2011-08-21
Mathematics
Numerical Analysis
14 pages
Scientific paper
In this paper we offer a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method under study is a generalization of the parallel Dichotomy Algorithm for solving systems of linear equations with tridiagonal matrices . Based on the approach developed, we propose a parallel realization of the domain decomposition method (the Schur complement method). The calculation of acoustic wave fields by the spectral-difference technique has proved the efficiency of the developed parallel algorithms. A near-linear dependence of a speedup value on the number of processors is attained both using several and several thousands of processors. The innovation of this study is in that the developed parallel algorithm for solving block-tridiagonal systems of equations allows and effective and, which is no less important, simple realization of efficient numerical procedures for solving engineering tasks on a supercomputer.
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