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Multidimensional numerical integration for meshless BEM. (English) Zbl 1033.65109
Summary: The conventional boundary element method (BEM) uses internal cells for the domain integrals, when nonlinear problems or problems with domain effects are solved. In the conventional BEM, however, the merit of the BEM, which is easy preparation of data, is lost. This paper presents numerical integration for a meshless BEM, which does not require internal cells. This method uses arbitrary internal points instead of internal cells. First, a multidimensional interpolation method for distribution in an arbitrary domain is shown using boundary integral equations. This method requires values on a boundary of a region and values at arbitrary internal points.
In this paper, multidimensional numerical integration is proposed using the above multidimensional interpolation method. This integration is useful for inelastic problems and thermal stress analysis with arbitrary internal heat generation. This method is based on an improved multiple-reciprocity BEM (triple-reciprocity BEM) for heat conduction analysis with heat generation. In order to investigate the efficiency of this method, several numerical examples are given.

##### MSC:
 65N38 Boundary element methods for boundary value problems involving PDEs 74A15 Thermodynamics in solid mechanics 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 74S15 Boundary element methods applied to problems in solid mechanics
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