Fast direct solution of method of moments applied to multiscale problems

Abstract

In a recent publication [1], we proposed a new convergence criterion for the Adapted Cross Approximation (ACA) algorithm, based on random sampling of the matrix that represents the residual error at each step of the algorithm. We presented some practical examples involving RCS computations of perfectly conducting benchmark targets exhibiting multiscale features, meaning that the mesh-size of the discrete model of the target is highly variable. These examples demonstrated a considerable improvement in the accuracy of the RCS result without appreciable loss of efficiency. In the presented examples, the solution was obtained by an iterative solver applied to an ACA-compressed Method of Moments impedance matrix. In this paper we apply the new method from [1] to the direct (non-iterative) solution of the MoM matrix. The results demonstrate that in this case, the advantage of the new method is far more important. Compared to ordinary ACA, the same accuracy is obtained in less than a quarter of the computation time