An iterative solution strategy for boundary element equations from mixed boundary value problems

Abstract

An iterative solution strategy is presented for mixed boundary value problems from the direct boundary element method, where both Dirichlet and Neumann constraints are prescribed on the boundary. In the mixed boundary value problem constraints are imposed upon the BEM system of equations Hu = Gq to Ax = b . The A matrix is fully-populated, unsymmetric, and made up of columns from H and G, corresponding to the Neumann and Dirichlet boundary conditions, respectively. In this work, the coefficient matrix A is rearranged to place the columns from H in the left-most columns of A and the columns from G in the right-most columns of A. The diagonal submatrix in A containing terms from G is then reduced by elimination while the diagonal submatrix containing terms from H is retained for iteration. Jacobi, Gauss-Seidel adn conjugate gradient normal iterative solvers are considered. Convergence of the proposed solution strategy is studied using four, two-dimensional potential and elasticity problems.