Computational linear algebra issues in the Galerkin boundary element method

This paper deals with the symmetric linear systems of equations arising in the Galerkin boundary element method. In particular, we consider the merits of direct and iterative solvers and present some numerical results which illustrate the way that solution costs vary with the number of boundary elements and indicate the possible advantages of iterative techniques (such as conjugate gradients) over direct (Gaussian elimination type) approaches. The first part of the paper is concerned with sequential implementations of the Galerkin boundary element method. We shall , also present results from a parallel implementation, running on an nCUBE machine. We shall consider the speed-ups obtained and for this purpose, it will be instructive to consider separately the three phases: 1. constructing the linear systeam, 2. solving the linear system, and 3. using the results to conpute interior solutions. Our results show clearly the benefits of parallel implementation, but they also demonstrate that these benefits may not be uniform across all aspects of the calculation.