Volume Integrals for Boundary Element Methods

We consider the numerical approximation of volume integrals over bounded domains D := {x ∈ R : H(x) ≤ 0}, where H : R → R is a suitable decidability function. The integrands may be smooth maps or singular maps such as those arising in the volume potentials for boundary element methods. An adaptive integration method is described. It utilizes an automatic simplicial subdivision of the domain. The integration step is based on ideas similar to those recently given by Georg [12] for surface integrals. Several examples illustrate the performance of the method.