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A comparison of domain integral evaluation techniques for boundary element methods
Author(s) -
Ingber Marc S.,
Mammoli Andrea A.,
Brown Mary J.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.217
Subject(s) - boundary element method , reciprocity (cultural anthropology) , discretization , fast multipole method , multipole expansion , mathematics , integral equation , domain (mathematical analysis) , computation , mathematical analysis , boundary (topology) , singular boundary method , acceleration , finite element method , algorithm , physics , classical mechanics , psychology , social psychology , quantum mechanics , thermodynamics
In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. Copyright © 2001 John Wiley & Sons, Ltd.