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Cubature techniques for 3-D Galerkin BEM


Sauter, S (1996). Cubature techniques for 3-D Galerkin BEM. In: Hackbusch, W; Wittum, G. Boundary elements: implementation and analysis of advanced algorithms (Kiel, 1996). Braunschweig: Vieweg, 29-44.

Abstract

We present cubature methods for the approximation of surface integrals arising from Galerkin discretizations of 3-D boundary integral equations. This numerical integrator is fully implicit in the sense that the form of the kernel function, the surface parametrization, the trial and test space, and the order of the singularity of the kernel functions are not used explicitly. Different kernels can be treated by just replacing the subroutine which evaluates the kernel function in certain surface points.
Furthermore, the implementation of the integrator is relatively easy since it can be checked on simple test kernels as, e.g., polynomials where the exact integrals are available. We discuss the convergence of the cubature methods together with a stability and consistency analysis in order to determine the minimal cubature orders a priori.

We present cubature methods for the approximation of surface integrals arising from Galerkin discretizations of 3-D boundary integral equations. This numerical integrator is fully implicit in the sense that the form of the kernel function, the surface parametrization, the trial and test space, and the order of the singularity of the kernel functions are not used explicitly. Different kernels can be treated by just replacing the subroutine which evaluates the kernel function in certain surface points.
Furthermore, the implementation of the integrator is relatively easy since it can be checked on simple test kernels as, e.g., polynomials where the exact integrals are available. We discuss the convergence of the cubature methods together with a stability and consistency analysis in order to determine the minimal cubature orders a priori.

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Additional indexing

Other titles:Proceedings of the 12th GAMM-Seminar, Kiel, Germany, January 19-21, 1996
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1996
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:27
Publisher:Vieweg
Series Name:Notes on Numerical Fluid Mechanics
Number:54
ISSN:0179-9614
ISBN:3-528-07654-2
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0881.65107
http://opac.nebis.ch/F/?local_base=EBI01&con_lng=GER&func=find-b&find_code=090&request=000602727
Permanent URL: https://doi.org/10.5167/uzh-22561

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