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Cell‐based volume integration for boundary integral analysis
Author(s) -
Koehler Matthew,
Yang Ruoke,
Gray L.J.
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.3355
Subject(s) - volume integral , mathematics , mathematical analysis , boundary element method , boundary (topology) , singular integral , surface integral , galerkin method , integral equation , vertex (graph theory) , interpolation (computer graphics) , singular boundary method , multiple integral , green's function , nonlinear system , function (biology) , physics , finite element method , discrete mathematics , quantum mechanics , classical mechanics , evolutionary biology , biology , motion (physics) , graph , thermodynamics
SUMMARY The evaluation of volume integrals that arise in boundary integral formulations for non‐homogeneous problems was considered. Using the “Galerkin vector” to represent the Green's function, the volume integral was decomposed into a boundary integral, together with a volume integral wherein the source function was everywhere zero on the boundary. This new volume integral can be evaluated using a regular grid of cells covering the domain, with all cell integrals, including partial cells at the boundary, evaluated by simple linear interpolation of vertex values. For grid vertices that lie close to the boundary, the near‐singular integrals were handled by partial analytic integration. The method employed a Galerkin approximation and was presented in terms of the three‐dimensional Poisson problem. An axisymmetric formulation was also presented, and in this setting, the solution of a nonlinear problem was considered. Copyright © 2012 John Wiley & Sons, Ltd.