Natural hp -BEM for the electric field integral equation with singular solutions
Natural hp -BEM for the electric field integral equation with singular solutions
复制标题
具有奇异解的电场积分方程的自然 hp -BEM
DOI：
10.1002/num.20688
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发表时间：
2011
影响因子：
3.9
通讯作者：
Bespalov A
中科院分区：
文献类型：
--
作者：
Bespalov A
本文应用边界元法的hp-版本数值求解Lipschitz多面体表面上的电场积分方程。底层网格假定为Γ的准均匀三角剖分，近似基于Raviart-托马斯或Brezzi-道格拉斯-Marini曲面元素族。Γ的非光滑性导致EFIE解的奇异性，严重影响边界元法的收敛速度。然而，解的奇异行为可以使用有限的函数集（顶点、边和顶点边奇异性）显式指定，这些函数是幂函数和多对数项的乘积。在这篇文章中，我们利用这一事实来执行准均匀网格上的hp-BEM的先验误差分析。我们证明了精确的误差估计的多项式degreep，网格大小h，和奇异指数。© 2011 Wiley Periodicals，Inc.偏微分方程2012
We apply thehp‐version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface Γ. The underlying meshes are supposed to be quasi‐uniform triangulations of Γ, and the approximations are based on either Raviart‐Thomas or Brezzi‐Douglas‐Marini families of surface elements. Nonsmoothness of Γ leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behavior of the solution can be explicitly specified using a finite set of functions (vertex‐, edge‐, and vertex‐edge singularities), which are the products of power functions and poly‐logarithmic terms. In this article, we use this fact to perform an a priori error analysis of thehp‐BEM on quasi‐uniform meshes. We prove precise error estimates in terms of the polynomial degreep, the mesh sizeh, and the singularity exponents. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012