Application of the tree-cotree splitting technique to the transient full-wave analysis based on the time-domain finite element method

In this paper, the authors apply the tree-cotree splitting (TCS) algorithm to the TDFEM to alleviate the constraint on the time-step size and to improve the convergence of iterative solutions at each time step. Compared with the conventional TDFEM, application of the TCS algorithm maintains the accuracy of the TDFEM solution but significantly reduces the number of iterations per time step for a preconditioned iterative solver to converge when the time-step size becomes relatively large. This desirable feature allows us to adopt a larger time-step size within the requirement of the temporal sampling rate to achieve a faster time-marching with a marginal additional cost. In addition, the proposed formulation effectively suppresses the late-time linear drift or instability, a problem associated with the conventional TDFEM.