An iterative solution scheme for systems of weakly connected boundary element equations

In this paper an iterative scheme of first degree is developed for solving linear systems of equations. The systems investigated are those which are derived from boundary integral equations and are of the form ∑j=1N Hijxj = ci, i = 1, 2, . . . , N, where Hij are matrices, xj and ci are column vectors. In addition, N denotes the number of domains and for i ≠ j, Hij is considered to be small in some sense. These systems, denoted as weakly connected, are solved using first-order iterative techniques initially developed by the authors for solving single-domain problems. The techniques are extended to solve multi-domain problems. Novel solution strategies are investigated and procedures are developed which are computationally efficient. Computation times are determined for the iterative procedures and for elimination techniques indicating the benefits of iterative techniques over direct methods for problems of this nature.