This research demonstrates that parallelization improves cholesky factorization efficiency in finite element methods, suggesting significant gains for electromagnetic field analyses.
The simultaneous availability of several processors will soon be a common phenomenon. In the light of this, it is desirable to seek to parallelize existing algorithms so that they might be completed quickly. This paper presents parallel schemes for the solution of Cholesky's factorization and the associated forward elimination and backsubstitution. In the computation of electromagnetic field problems, we arrive at full, symmetric matrices by the boundary element method. Using the finite element method we get sparse symmetric matrices (stored using profile storage when using Cholesky's method). The application of the parallel methods presented in this paper to these special problems is examined. The study is then extended to the now popular conjugate gradients algorithm in finite element analysis of electromagnetic field problems, where an approximate Cholesky factorization is used together with forward elimination and backsubstitution in a repetitious setting with sparse storage. One of the algorithms proposed here is recommended for each of these situations.
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S. Ratnajeevan H. Hoole (1992) studied this question.
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