A parallel conjugate gradients algorithm for finite element analysis of electromagnetic fields

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Abstract
The exploitation of parallel and vector machine architectures provides new means of speeding up the finite element analysis of electromagnetic field problems. In this paper most operations in an iteration of the conjugate gradient algorithm are parallelized individually. New parallel algorithms appropriate to finite element data storage schemes are presented for Cholesky splitting of the coefficient matrix, sparse matrix multiplication, forward elimination, backward substitution, vector multiplication and vector addition. A Sequent Symmetry 81 parallel computer operating with four processors was employed for this purpose. Interestingly, it was found that parallelization profoundly improves the speed only when the matrix size is large. For relatively small matrices, the time required to allocate processors does away with the advantage of parallel computation.