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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
68/2001

Direct integration of the Newton potential over cubes including a program description

Wolfgang Hackbusch

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.

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.

Furthermore, this report contains a description of the program together with examples for its use. You can download the source as Pascal program or as C program (both GNU-zip compressed, approx. 27 kB).

Received:
Sep 25, 2001
Published:
Sep 25, 2001
MSC Codes:
65R20, 65N38, 68W30, 35Q99
Keywords:
newton potential, coulomb potential, direct integration, integral equations

Related publications

inJournal
2002 Repository Open Access
Wolfgang Hackbusch

Direct integration of the Newton potential over cubes

In: Computing, 68 (2002) 3, pp. 193-216