An Efficient and Error-Controllable Angular Sweep Algorithm for Electromagnetic Wave Scattering and its Analysis

Abstract

The angular sweep of electromagnetic wave scattering is formulated as a matrix equation with multiple right-hand sides (RHSs). Although the low-rank approximation of an RHS matrix is a popular choice for reducing the computational costs of multiple RHSs, only a small amount of research has been conducted to explore how this approximation impacts the solution quality. Furthermore, there has not been sufficient research on the quality of the solution as a function of the accuracy of the iterative solver. We present an error analysis of the approximated solution considering both the reduced number of RHSs and the tolerance of the iterative solver. Based on the error analysis, a new angular sweep algorithm is proposed with fine-tuned tolerances of the iterative solver for individual singular vectors. The different tolerances for each singular vector increase the efficiency of the proposed algorithm. Another benefit of the proposed algorithm is that the error can be bounded by a user-defined global tolerance. In addition, a variant of the generalized conjugate residual method for multiple RHSs is introduced to accelerate iterative solvers. Finally, numerical validation is conducted with three examples in which the discontinuous Galerkin surface integral equation method is applied. The experiments support two conclusions: tight upper and lower bounds of the solution error exist, and fine-tuning the tolerances reduces the computational costs.