Fast Algorithms And Their Applications For Electromagnetic Problems Based On The Fast Multipole And Domain Decomposition Methods

Fast algorithms in the moment methods (MM), finite element method （FEM）, hybridfinite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA)have been designed, implemented, and studied for some challenging electromagneticproblems such as scattering by extremely large and deep cavities, large dielectric objectsand coated problems by employing fast multipole and domain decomposition methods.Furthermore, these fast algorithms have been applied to amalyze a series of practicalproblems such as targets characteristics，optical trapping.Fast algorithms studied in this dissertation mainly include three parts: the momentmethod based on surface integral equation for homogeneous objects; the finite elementmethod based on domain decomposition algorithm (DDM); higher-order FE-BI-MLFMAbased on DDM. To be more specific, the electric and magnetic current combined-fieldintegral equation (JMCFIE) with MLFMA is studied and applied for solving scattering bylarge homogeneous objects. The finite element tearing and interconnecting method (FETI)is studied and applied for large inhomogeneous objects. A parallelization approach of thehigher-order FE-BI-MLFMA is presented and implemented for scattering by large and deepcoated cavities loaded with obstacles. An efficient preconditioning algorithm named as thehybrid h-and p-Type multiplicative Schwarz (h-p-MUS) is presented for higher-orderFE-BI-MLFMA for large inhomogeneous objects. At last, a DDA-based FE-BI-MLFMA(DDA-FE-BI-MLFMA) as well as a decomposition-based preconditioner (DDP) for theconventional FE-BI-MLFMA are presented and studied in detail.Despite of the study on numerical performance of these fast algorithms, these fastalgorithms have been applied to solve a series of real challengeable problems. The fastalgorithm based on JMCFIE and hybrid MPI-OpenMP parallel MLFMA is applied to solvescattering by dielectric sphere with diameter as large as240wavelengths, modeled withmore than hundreds of millions unknowns. Furthermore, it is employed for computingradiation pressure force and torque on arbitrary shaped homogeneous particles in a shapedbeam in optical trapping and optical stress on surface of a soft particle. The FEM withFETI is applied to compute scattering by large inhomogeneous particles discretized intohundreds of millions unknowns. The paralleled higher-order FE-BI-MLFMA is employedto solve scattering by electrically large and deep cavities with size of4040100. The DDA-FE-BI-MLFMA and DDP-FE-BI-MLFMA are employed to solve scattering bylarge coated objects and large antenna arrays and frequency select surface (FSS).