Accurate and Robust Surface MLFMA Solution for Scattering From a Large Plasma Object With Large Negative Permittivity

We present an accurate and robust surface integral equation (SIE) method for an electromagnetic (EM) analysis of large-scale plasma media with large negative permittivity. To accelerate the matrix-vector multiplication (MVM) in the iterative solution of the matrix equation, the multilevel fast multipole algorithm (MLFMA) is generally preferred. Traditional implementation of MLFMA will lead to inaccurate results or poor convergence due to the numerical instability arising from the large negative permittivity. To tackle this problem, we analyze the formula of MLFMA in detail and propose a simple and efficient truncation strategy to improve its robustness. A practical and elegant truncation bound is derived based on the ratios of matrix elements between an ordinary permittivity background medium and the negative permittivity plasma. Applying the proposed truncation strategy, the performance of several commonly used SIE formulations is investigated comprehensively. Numerical results demonstrate that the proposed method can avoid numerical instability while maintaining high efficiency for large-scale plasma media with large negative permittivity.