新領域積分法に基づくポアソン問題の境界要素法解析

概要

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The application of the boundary element method for solving boundary value problems with nonhomogeneous term such as Poisson's equation leads to an integral equation which contains domain integrals. Although these integrals do not introduce any new unknowns, they affect the efficiency of the method since the additional integration over the whole domain is required. In the analysis of non-linear or time-dependent problems using the boundary element method, the domain integral occupies the major part of the total computing time of the analysis. In this paper a new approach for the domain integrals is presented. The procedures are follows : First of all, the non-homogeneous term is supposed to be interpolated by the boundary values using polynomial expression for the region. The domain integrals are carried out in each triangular cell which is made of the source point and a line segment of the boundary. No subdivision is necessary for the region in this method prior to the calculation. Secondly, an analytical recursive formula is proposed in order to calculate the domain integral for a higher order polynomial interpolation function with high accuracy and at high speed. The efficiency of the formula is finally confirmed for some sample problems whose the exact solutions are known.
日本シミュレーション学会の論文
1991-03-15