A geometric frequency-domain wave propagation formulation for fast convergence of iterative solvers

The frequency-domain wave propagation problem is notoriously difficult to solve through iterative methods, because of the huge nullspace of the curl-curl operator. Direct methods are then usually employed, at the expense of great memory usage. Accelerated convergence of iterative methods can be obtained by a modification of the wave equation. In this paper, we introduce the modified wave equation in the Discrete Geometric Approach (DGA) framework. Moreover, the impedance boundary condition in the formulation is presented, together with a smart assembly technique that allows to greatly reduce the memory requirements.