Sparse and explicit FETD via approximate inverse Hodge (mass) matrix

Finite-element time-domain (FETD) simulations of Maxwell equations in irregular simplicial grids require the solution of a sparse linear system involving the Hodge (mass) matrix at each time step. This can be avoided by mass lumping techniques that approximate the mass matrix by a diagonal matrix, but not without shortcomings. In this communication, we propose an alternative approach to yield a conditionally stable, fully explicit, and sparse FETD by using a sparse approximate inverse of the mass matrix.