Boundary integral approximation of volume potentials in three-dimensional linear elasticity

A systematic treatment of volume potentials appearing in a boundary integral equation formulation of the three-dimensional Lamé equation is rigorously investigated and its usefulness demonstrated in the context of a collocation boundary element method. Developed to effectively deal with volume potentials without a volume-fitted mesh, the proposed approach initially converts elastic volume potentials, defined in the form of domain integrals featuring a non-trivial body force, into equivalent surface integrals. Then, the resulting boundary integrals are evaluated by means of well-established cubature methods. Details of these domain-to-boundary integral transformations are provided along with some examples to show the correctness of the calculation of the elastic Newton potential. Moreover, with the aid of an analytic integration technique developed to accurately compute singular surface integrals in linear elasticity, numerical examples dealing with mixed boundary-value problems for the three-dimensional Lamé equation are included to validate the proposed approach.