| Abstract: | In boundary element methods, the evaluation of the weakly singular integrals can be performed either a) numerically, b) symbolically,
i.e., by explicit expressions, or c) in a combined manner. The explicit integration is of particular interest, when the integrals
contain the singularity or if the singularity is rather close to the integration domain. In this paper we describe the explicit
expressions for the sixfold volume integrals arising for the Newton potential, i.e., for a 1/r integrand. The volume elements are axi-parallel bricks. The sixfold integrals are typical for the Galerkin method. However,
the threefold integral arising from collocation methods can be derived in the same way.
Received April 18, 2001; revised September 17, 2001 Published online April 25, 2002 |
