2024/08/30 by Jin Hu, Hu, Jin, Emrah Sever +9
Computer Science · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2408.17116
openalex publication_date 2024/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g. the locally corrected Nyström (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models.