A Storage Optimization Scheme for PITD Method Using Sparse Matrix-Vector Multiplication

Abstract

An improved variant of the precise-integration time-domain (PITD) method is proposed to eliminate the inverse matrix calculation and optimize the storage burden with the help of sparse computation. First, the dimensional expanding (DE) scheme is incorporated into PITD to address the matrix inversion problem due to external sources. Then, the dense matrix exponential is absorbed in sparse matrix-vector multiplications (SpMVs) without explicit evaluation. This SpMV-based technique involves only one sparse matrix and can utilize sparse computation efficiently, so as to greatly reduce memory costs ascribed to the matrix exponential. Moreover, the theoretical analysis of the algorithm performance is presented. The numerical results verify the validity and efficiency of the proposed method.