A new explicit time-domain finite-element method based on element-level decomposition

A new explicit time-domain finite-element method (TDFEM), which is fundamentally different from traditional explicit TDFEM formulations for solving Maxwell's equations, is introduced. This new explicit TDFEM is derived from a recently developed TDFEM domain-decomposition algorithm by extending domain decomposition to the element level. This method solves dual-field second-order wave equations and computes the electric and magnetic fields in a leapfrog fashion. With the element-level decomposition, no global system matrix has to be assembled and solved as required in the implicit TDFEM, and each element is related to its neighboring elements in an explicit manner. Hence, the computational complexity of the method is reduced to only O(N) for both computer memory and CPU time. A hybrid explicit/implicit scheme is also proposed to alleviate a major disadvantage of the proposed explicit TDFEM formulation. In addition, the convergence behavior of the corresponding higher order algorithms and the stability issues are discussed.