An Improved Fast Finite Element Time-Domain Method Based on Compressive Sensing for Cavity Problems

To avoid directly solving linear equations for major time marching in the finite element time-domain (FETD) method, the compressive sensing (CS) theory is introduced to construct an explicit iterative scheme instead of an implicit form. In this method, Whitney elements and a leapfrog model are applied to time-dependent Maxwell curl equations for space and time discretization. After a small number of iterations, steps for linear equations in the initial time, the electric field intensity and magnetic flux density are updated just by the linear combination of results of previous time steps. Furthermore, a restart mechanism is built to control the computational complexity and accuracy over a long simulation time. The effectiveness of the new algorithm is verified by analyzing 3-D resonant cavities.