Recursive update-discrete singular convolution method for modeling highly resonant structures

This paper presents a new frequency-domain technique for modeling highly resonant structures. A recursive update (RU) scheme is adopted to solve Maxwell's equations. The discrete singular convolution (DSC) method is applied to discretize the curl operators in Maxwell's equations, and a regularization technique is utilized to treat arbitrarily oriented current sources in structured grids. Different from conventional frequency-domain methods, the proposed method doesn't need to solve a matrix equation, and its memory usage is very low. Furthermore, the RU scheme is always convergent as long as the marching step size is small enough. This renders the proposed method very useful in modeling highly resonant structures, where iterative solvers encounter convergence problem. Employing the high efficiency and accuracy of the DSC method, the RU-DSC method is more efficient than the RU-finite difference method. With the flexibility of the regularization technique, the proposed method can easily handle tilted current sources in structured grids. Numerical examples are presented to demonstrate the aforementioned advantages of our proposed method.