MLFMA for combined SIE (PMCHWT) and VIE formulation in electromagnetic simulation

Although the Integral Equation method is effective in electromagnetic simulation, its high cost hinders the application of this method in the simulation of electrically large problems. By employing a fast solver and constructing the formulation properly, the cost of the Integral equation method could be reduced significantly.;The work in this dissertation is an implementation of Multi-Level Fast Multipole Algorithm (MLFMA) based on the hybrid Volume Surface Integral Equation (VSIE) formulation, which can be employed to solve the scattering problems involving material scatterers. By combining the Surface Integral Equation (SIE) and Volume Integral Equation (VIE) formulation, the VSIE formulation possesses the advantage of both formulations and is capable of modeling large problem efficiently. In order to choose the proper formulation, the performances are compared for two SIE formulations in this work, which are the PMCHWT and Muller's formulation. Based on the intuitive comparison and numerical simulation results, the PMCHWT formulation is chosen over the Muller's formulation for the SIE part in the hybrid VSIE formulation.;Based on the analysis of MLFMA for the scattering problem of Perfect Electric Conductor (PEC), the storage requirement and complexity are analyzed for the MLFMA that solves material scattering problem based on VSIE formulation. The analysis shows that MLFMA could be used to accelerate the matrix-vector multiply for the material scattering problem discretized by VSIE formulation, although its cost is higher than the MLFMA of PEC problem. This statement is also supported by numerical simulation results.