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Simple multidimensional integration of discontinuous functions with application to level set methods
Author(s) -
Müller B.,
Kummer F.,
Oberlack M.,
Wang Y.
Publication year - 2012
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.4353
Subject(s) - hexahedron , discretization , discontinuous galerkin method , simple (philosophy) , tetrahedron , polygon mesh , quadrilateral , grid , mathematics , level set (data structures) , polynomial , basis function , set (abstract data type) , numerical integration , algorithm , function (biology) , level set method , numerical analysis , geometry , computer science , mathematical analysis , finite element method , artificial intelligence , engineering , philosophy , epistemology , evolutionary biology , biology , programming language , structural engineering , segmentation , image segmentation
SUMMARY We present a simple, tree‐based approach for the numerical integration over volumes and surfaces defined by the zero iso‐contour of a level set function. The work is motivated by a variant of the discontinuous Galerkin method that is characterized by discontinuous enrichments of the polynomial basis. Although numerical results suggest that the presently achieved accuracy is comparable with methods based on discretized delta functions and on the geometric reconstruction of the interface, the presented approach is conceptually simpler and applicable to almost arbitrary grid types, which we demonstrate by means of numerical experiments on triangular, quadrilateral, tetrahedral and hexahedral meshes. Copyright © 2012 John Wiley & Sons, Ltd.