Low-Memory Implementation of PITD Method Using a Thresholding Scheme

A precise-integration time-domain (PITD) method with a thresholding scheme is proposed to reduce the computation cost of the matrix exponential for solving electromagnetic (EM) problems. The finiteness of EM wave speed is used to analyze the structure of the matrix exponential, revealing that the dense matrix exponential can become sparse. A thresholding scheme for eliminating tiny and thus unimportant elements is established to obtain the sparse matrix exponential, where the threshold value is selected by Von Neumann stability criterion and induced spurious solutions are avoided. Theoretical analyses and numerical results confirm that the proposed method can save a large amount of memory and the accuracy of the original method is inherited.