Domain Decomposition-Based Discontinuous Galerkin Time-Domain Method With Weighted Laguerre Polynomials

To further improve the computational efficiency of the existing wave equation-based discontinuous Galerkin time-domain (DGTD) method for modeling electrically small structures, the weighted Laguerre polynomials are incorporated to span the fields in the temporal domain, which finally results in a set of recursive linear equations related to the Laguerre polynomials to be solved. Compared with conventional time integration methods, the proposed approach requires much fewer iterations and thus shows considerable improvement in terms of computational efficiency. With respect to the first-order Maxwell’s curl equation-based DGTD method with weighted Laguerre polynomials, the proposed method reduces the unknowns by more than a half and gives a lighter linear system for solution. In addition, block iterative solvers and the block lower-diagonal-upper (LDU) direct solver can be applied to facilitating the solution at the subdomain level. Three numerical examples are included to demonstrate the accuracy and efficiency of the proposed method. With the weighted Laguerre polynomials, the wave equation-based DGTD method is expected to be more efficient for electrically small structure modeling.