Interpolation and Multiple Numerical Integration Using Polyharmonic Function of Volume Distribution

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  • 体分布多重調和関数を用いた補間および多次元数値積分法
  • タイ ブンプ タジュウ チョウワ カンスウ オ モチイタ ホカン オヨビ タジゲン スウチ セキブンホウ

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Abstract

This paper presents an interpolation method and a numerical multiple integration using the boundary integral equations and a polyharmonic function of volume distribution. In the method using B-spline, points must be assigned in a gridiron layout. In the presented method using the polyharmonic function of volume distribution, arbitrary points can be assigned instead of using a gridiron layout, therefore it becomes easy to interpolate. This method requires a boundary geometry of the region and arbitrary internal points. The values at arbitrary point and the integral value are calculated after solving the discretized boundary integral equations. In order to investigate the efficiency of this method, several examples are given. Especially, a use of the polyharmonic function of volume distribution is effective for the three-dimensional case. The advantages of using the polyharmonic function of volume distribution are the decrease of CPU time and the stability of the interpolation.

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