A kind of domain decomposition hierarchical time-domain finite-element method (TDFEM) discretized by discontinuous Galerkin method and solved by Crank-Nicolson algorithm

In this paper, a kind of domain decomposition time-domain finite-element method (TDFEM) discretized by discontinuous Galerkin method is presented. Hierarchical vector basis functions are used to improve the accuracy of the results obtained using sparse mesh with fewer unknowns. The Crank-Nicolson algorithm is also complemented for the time derivatives, which leads to an unconditional stable scheme for domain-decomposition hierarchical TDFEM. In each subdomain, matrices for both electric and magnetic fields are assembled together and the multifrontal sparse direct solver is used at the subdomain level. Compared to the original single-domain problem, the size of each subdomain is reduced, as well as the overall computational time.