2010/10/07 by Alex Bespalov, Bespalov, Alexei, Norbert Heuer +1
Engineering · Physics and Astronomy · #41A10 #65N15 #65N38 #78M15 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1010.1459
openalex publication_date 2010/10/07 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We apply the hp-version of the boundary element method (BEM) for the\nnumerical solution of the electric field integral equation (EFIE) on a\nLipschitz polyhedral surface G. The underlying meshes are supposed to be\nquasi-uniform triangulations of G, and the approximations are based on either\nRaviart-Thomas or Brezzi-Douglas-Marini families of surface elements.\nNon-smoothness of G leads to singularities in the solution of the EFIE,\nseverely affecting convergence rates of the BEM. However, the singular\nbehaviour of the solution can be explicitly specified using a finite set of\npower functions (vertex-, edge-, and vertex-edge singularities). In this paper\nwe use this fact to perform an a priori error analysis of the hp-BEM on\nquasi-uniform meshes. We prove precise error estimates in terms of the\npolynomial degree p, the mesh size h, and the singularity exponents.\n