Development of a fundamental-solution-less boundary element method for exterior wave problems

Abstract

A fundamental-solution-less boundary element method, the scaled boundary finite-element method, has been developed recently for exterior wave problems. In this method, only the boundary is discretized yielding a reduction of the spatial dimension by one, but no fundamental solution is necessary. Seamless coupling with standard finite elements is straightforward. In this paper, the sparsity of the coefficient matrices of the scaled boundary finite-element equation is exploited in performing the partial Schur decomposition to reduce the required computer memory and time. The Gauss-Lobatto-Legendre shape functions with nodal quadrature are applied to the elements on boundary, which leads to lumped coefficient matrices and high-order elements. Numerical examples demonstrate that these advances, in combination with the Pade series solution for the dynamic stiffness matrix, increase significantly the computational efficiency of the scaled boundary finite-element method. Copyright © 2006 John Wiley and Sons, Ltd.