三次元ボアソン方程式の境界要素法解析における解析的領域積分公式の有効性

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  • Effectiveness of the Analytical Volume Integration Formula in Analyzing 3D-Poisson Equation by the Boundary Element Method
  • 3次元ポアソン方程式の境界要素法解析における解析的領域積分公式の有効性
  • 3ジゲン ポアソン ホウテイシキ ノ キョウカイ ヨウソホウ カイセキ ニ オ

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説明

This paper proposes an analytical volume integration formula which calculates the inhomogeneous term of Poisson equation in its boundary integral equation form. The formula evaluates the integral on the basis of one of the tetrahedral sub-regions of the concerned region, where the inhomogeneous term can be approximated by a polynomial with respect to the coordinates.<br>It is well known that the Boundary Element Method (B. E. M.) has a great advantage in analyzing engineering problems governed by the homogeneous partial differential equation. Namely, only the surface of the region under consideration needs to be separated into surface elements, where the number of unknowns is reduced, in comparison with that of the domain methods, such as Finite Element Method and Finite Difference Method. The region also has to be subdivided into volume elements, even in B. E. M., when the governing equation has an inhomogeneous term.<br>It must be stressed that the unknowns don't increase in this situation if the inhomogeneous term can be prescribed. However, the volume integration of the inhomogeneous term has to be carried out with high speed and high accuracy because the computing time of the analysis is almost expended in these integrations and also the weighing function of the integrand can have singularity. The proposed integration formula constitutes the recursive system, where the integral of a higher order term of the polynomial can be evaluated from the result of the lower order one. Moreover, the accuracy and speed of the computation is much higher than that of the ordinary numerical integration, such as the Gauss-Legendre method.

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