The 3-D Unconditionally Stable Associated Hermite Finite-Difference Time-Domain Method

This article discussed the implementation of 3-D associated Hermite (AH) finite-difference time-domain (FDTD) method and its application in the analysis of lumped parameters modeling. Based on the paralleling-in-order scheme, the basic formula of the 3-D AH FDTD method, incorporated with complex frequency shifted (CFS) perfectly matched layer (PML) absorption boundary, was derived. Then, by using the Kronecker product scheme the coefficient matrix of the final matrix equation was fast generated and by using the permutation technology its bandwidth was compressed. Updating the coefficient matrix and source term of the matrix equation was implemented when dealing with the lumped parameters. To solve the final matrix to obtain the AH expanding coefficients, the direct or indirect methods, mainly by the iterative method, could be used. Finally, several numerical results were presented to validate the accuracy and efficiency of the proposed method.