An Investigation on FETD Solutions of Maxwell’s Equations in Irregular Grids using Topological Inverse Sparse Approximations

We investigate the construction of explicit time updates for the FETD (Finite Element Time Domain) method in irregular grids based on the second-order wave equation using topological inverse sparse approximation of the Hodge (mass) matrix. For the time domain solution of Maxwell’s equations, FETD has an advantage over FDTD because it naturally accommodates irregular unstructured grids. However, FETD has a major disadvantage of requiring a linear matrix solve at every time step. A topological sparse approximation of the inverse mass matrix has been proposed to overcome this problem. In this work, we examine the relationship between the approximation level (topological threshold parameter) and accuracy of the resulting FETD solutions. 1