基于第一类Whitney基函数的三维FEM/BEM混合方法中积分的计算

Evaluation of the Integrals Involved in 3-D FEM-BEM Hybrid Method Based on Whitney 1-Forms

给出了一种坐标变换方法,使基于第一类Whitney基函数的三维矢量有限元/边界元混合方法中积分的数值计算方便易行。利用三次坐标变换,将积分区域由任意的三角形区域变换成单位正方形区域,或由任意的四面体区域变换成单位正方体区域,从而混合方法中的积分可以方便地使用高斯-勒让德求积公式计算。通过数值实验对这种方法进行了检验。

A coordinate transformation method is presented, which facilitates the numerical evaluation of the integrals involved in the 3-D FEM-BEM hybrid method hased on Whitney 1-forms. The integral domain is mapped to a unit square region from any arbitrary triangular region, or to a unit cubic region from any arbitrary tetrahedral region by introducing three coordinate transformations. So the integrals involved in the hybrid method can be computed conveniently by Gauss-Legendre ibrmulation. And the method is verified by numerical experiments.