The variational indirect boundary element method: A strategy toward the solution of very large problems of site response

Boundary integral equation approaches and their discretization into boundar y element methods (BEM) have been useful to obtain solutions for numerous p roblems in dynamic elasticity. Well documented advantages over domain appro aches are dimension reduction, relatively easy fulfillment of radiation con ditions at infinity, and high accuracy of results. In spite of dimension re duction, the computational cost at high frequencies may easily exceed the c apacity of computing facilities. To overcome this problem, Galerkin's ideas may be used. The Indirect Boundary Element Method (IBEM) equations are the starting point of the proposed methodology. The boundary force density is expanded in terms of a complete set of functions. Weighting functions from the same complete set are used to minimize the error of this approximation. Once a significant subset is selected, the size of the resulting linear sy stem is much smaller than that of the IBEM method as currently applied. Mor eover, with appropriate trial functions, some matrix operations can be redu ced to Fourier transformations. In what follows, the formulation and some examples for scalar problems are presented. Simple 2-D topographies are studied, but the extension to 3-D re alistic configurations may well be treated on the same basis.