Application of the multilevel adaptive cross-approximation on ground plane designs

In this paper, the multilevel adaptive cross approximation (MLACA) technique is presented. This method reduces the numerical complexity of both memory requirement and matrix-vector multiplication of integral equation with asymptotically smooth kernels. The method does not require explicitly the knowledge of the integral kernel and therefore can be integrated into existing boundary integral equation (BIE) and/or MoM codes easily. This paper extends the ACA to oscillatory integral kernel and applies it to the ground plane designs. We have demonstrated through numerical examples that for moderate-sized problems (less than few hundred thousand unknowns) the multilevel ACA algorithm is still very effective and reliable for computer modeling of electromagnetic radiation and scattering problems.