A Generalized Point-Matching Method for Solving Electromagnetic Problems

The Nyström method has been a robust numerical method for solving electromagnetic (EM) problems by integral equation approach. However, the method relies on quadrature rules to select the discrete points in the point-matching process and this has greatly reduced the flexibility of the method because there are not many appropriate choices on quadrature rules in practice. In this work, a generalized point-matching method (GPMM) is proposed to remedy the problem. The GPMM removes the restriction of quadrature rules and can freely select the number and location of discrete points where the matching is enforced. Although the method loses the simplicity of generating far-interaction matrix elements by directly sampling the integrands in the Nyström method, it brings the freedom of choosing matched points which may be desirable in some applications. A numerical example is provided to demonstrate the method and its good performance has been seen.