BEM for variable coefficient second-order problems

Abstract

A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a computable approximation of the boundary operator from a Galerkin discretisation of the underlying elliptic differential operator in a one-time preprocessing step, for instance by conforming finite elements. The resulting algebraic formulation retains the dimension reduction intrinsic to boundary integral methods and is compatible with standard data-sparse matrix compression techniques.