Theoretical modeling of large-scale electromagnetic problems using a hybrid MoM/FEM method, wavelets, and high-performance computing

The study presented here is aimed at the development of a fast and efficient full-wave technique for large and complex electromagnetic scattering and circuit problems by effectively combining three methods: a hybrid MoM/FEM technique, wavelet theory, and high-performance computing (HPC).; A hybrid MoM/FEM technique features the use of MoM in an open space radiating environment and FEM in a complex circuit environment. Therefore, in this technique, MoM uses the available Green's functions and avoids segmenting large, open spaces, while FEM allows for the treatment of the inhomogeneous materials and complex circuit geometries and eliminates the tedious analysis required to derive the appropriate Green's functions.; The incorporation of wavelet theory into the hybrid MoM/FEM technique can save a significant amount of memory. Because of the vanishing moment of wavelets, wavelet terms in the hybrid MoM/FEM linear system becomes much smaller than non-wavelet terms, and, therefore, many of them can be discarded without affecting the accuracy of the solution. Using a sparse matrix storage scheme, the resulting hybrid MoM/FEM linear system can be solved with very little memory.; HPC and efficient parallelization schemes can be used to satisfy the large memory requirements and to alleviate the high computation time for large scale electromagnetic problems. The task parallelization demonstrates scalable computational speed in FEM and MoM calculations, while the developed matrix decomposition method can solve large FEM and hybrid MoM/FEM linear systems with minimum cost of communication overhead.; A wavelet hybrid MoM/FEM method is verified in an aperture-coupled patch antenna case by comparing the computed results with measured data. We have demonstrated an accurate solution with the sparse hybrid MoM/FEM linear system obtained by the thresholding process. The effect of thresholding on the hybrid MoM/FEM linear system is closely examined by measuring the accuracy of the solution.; Finally, the developed technique is applied to a large antenna array system which has been very difficult to solve with conventional methods. The problem has been analyzed with three different multiresolution expansions, yielding numerous useful computational results. The effect of thresholding on the computed solution is rigorously studied for each level of multiresolution expansion, and the corresponding results are discussed in detail, including the achieved high sparsity of the hybrid MoM/FEM linear system. The technique developed in this study significantly reduces the computation time required to analyze large and complex microwave/millimeter-wave circuits, thus allowing for the rapid design and characterization of these systems.