SUMMARYThe unsymmetric matrix equations generated from the boundary element method (BEM) can be solved iteratively, with convergence to the correct solution guaranteed, if the boundary element system of equations can be first transformed into an equivalent, diagonally dominant system. A transformation is presented which selectively annihilates terms in the coefficient matrix of the system Ax = b until an equivalent, row diagonally dominant system, if available, is obtained. The new, row diagonally dominant system is well suited for use with Jacobi and Gauss-Seidel point iterative equation solvers. The diagonal dominizing transformation presented in this work is not suitable for large systems of equations but is useful as a research tool for studying the importance of diagonal dominance in the iterative solution of equations generated from the BEM. A simple Laplacian problem is used to examine the structure of the BEM equations and to introduce the diagonal dominizing transformation. The importance of diagonal dominance is shown by comparing iterative convergence of positive-definite, symmetric positive-definite and diagonally dominant systems of BEM equations obtained from a plane strain elasticity problem.

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