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 Nystr\"om (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.

翻译：本文提出、测试并分析了采用高阶基于Chebyshev的边界积分方程（CBIE）方法的H-矩阵加速直接求解器，针对高对比度介电材料和电大尺寸理想电导体对象的性能进行了评估。与同类方法（例如局部校正Nyström（LCN）方法）相比，CBIE的矩阵填充性能对于中小规模问题被证明是快速的，这归因于其通过全局变量变换法处理奇点的方式。然而，对于电大尺寸散射问题，当采用直接求解方法时，矩阵填充和分解仍然主导求解时间。为解决此问题，本文采用了H-矩阵框架，有效解决了这一挑战，并确立了CBIE作为求解具有病态矩阵方程的散射问题的一种有竞争力的高阶方法。通过大量数值结果证明了该方法的有效性，展示了其对电大尺寸、接近物理谐振或具有大介电常数问题的鲁棒性。所提求解器处理任意几何形状的能力也通过考虑来自复杂CAD模型的各种散射示例得到了验证。