A priori error analysis of the BEM with graded meshes for the electric field integral equation on polyhedral surfaces

作者：Bespalov A^*; Nicaise S

来源：Computers & Mathematics with Applications, 2016, 71(8): 1636-1644.

DOI：10.1016/j.camwa.2016.03.013

• Electromagnetic scattering
• Electric field integral equation
• Boundary element method
• Anisotropic elements
• Graded mesh
• A priori error analysis

The Galerkin boundary element discretisations of the electric field integral equation (EFIE) on Lipschitz polyhedral surfaces suffer slow convergence rates when the underlying surface meshes are quasi-uniform and shape-regular. This is due to singular behaviour of the solution to this problem in neighbourhoods of vertices and edges of the surface. Aiming to improve convergence rates of the Galerkin boundary element method (BEM) for the EFIE on a Lipschitz polyhedral closed surface Gamma, we employ anisotropic meshes algebraically graded towards the edges of Gamma. We prove that on sufficiently graded meshes the h-version of the BEM with the lowest-order Raviart-Thomas elements regains (up to a small order of epsilon > 0) an optimal convergence rate (i.e., the rate of the h-BEM on quasi-uniform meshes for smooth solutions).

• 出版日期2016-4