A Recursive Sparsification of the Inverse Hodge Matrix

When applying the theory of differential forms to solve wave propagation problems in time domain, we must solve at each time step a sparse linear system defined by the insertion of constitutive laws via the mass matrices. In this paper, we describe a recursive technique to efficiently calculate the approximated inverse of Hodge matrix. The fundamental idea is to recursively decompose the mass matrix in to a decreasing size sequence of matrices using block matrix inversion. During the recomposition process, the matrix is sparsified. Numerical results are presented to validate our approach.