A High-Order Accurate Combined Field Integral Equation Solver for Scattering Problems in Domains with Corners

High-order integral equation solvers for electromagnetic scattering offer superior accuracy and efficiency compared to low-order methods. However, their performance degrades significantly when dealing with geometries that contain sharp edges and corners due to the singular behavior of the electromagnetic field components and the “density” (the solution of the Boundary Integral Equation (BIE) considered) near the corners. This paper presents a Regularized Combined Field Integral Equation (CFIE-R) formulation that maintains high accuracy near geometric singularities. The proposed approach introduces an operator regularization strategy to mitigate the impact of hypersingular operators, a corner regularization technique and precision-preserving techniques to enable stable, high-order convergence even in the presence of unbounded integral densities at corners. Numerical results demonstrate that the CFIE-R formulation achieves near 9th-order convergence for challenging geometries and outperforms traditional Nyström-based methods. This work provides a foundation for extending high-order integral equation solvers to complex three-dimensional scattering problems involving singular geometries.