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Numerical Treatment of Domain Integrals without Internal Cells in Three-Dimensional BIEM Formulations

Yoshihiro Ochiai1, Vladimir Sladek2
Dept. of Mech. Eng., Kinki University, Kowakae 3-4-1, Higashi Osaka, 577-8502 Japan, E-Mail:
Institute of Construction and Architecture, Slovak Academy of Science, 845 03 Bratislava, Slovakia

Computer Modeling in Engineering & Sciences 2004, 6(6), 525-536.


The conventional boundary element method (BEM) uses internal cells for the domain integralsCwhen solving nonlinear problems or problems with domain effects. This paper is concerned with conversion of the domain integral into boundary ones and some non-integral terms in a three-dimensional BIEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. The method is based on a three-dimensional interpolation method in this paper by using a polyharmonic function with volume distribution. In view of this interpolation method, the three-dimensional numerical integration is replaced by boundary ones and preceding calculation of some boundary densities and interior unknowns. The domain discretizetion procedure is completely eliminated. In order to investigate the efficiency of this method, several numerical examples are given.


Boundary Element Method, Domain integrals, Heat Conduction, Interpolation, Polyharmonic functions, Multiple-Reciprocity Method

Cite This Article

Ochiai, Y., Sladek, V. (2004). Numerical Treatment of Domain Integrals without Internal Cells in Three-Dimensional BIEM Formulations. CMES-Computer Modeling in Engineering & Sciences, 6(6), 525–536.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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