Fast And Efficient Algorithms And Applications For Electromagnetic Analysis Of Electrically Large3-D Homogeneous Objects

The electromagnetic scattering of dielectric bodies is an important research topic in thefield of computational electromagnetics. It has a large volume of applications, includingradar system design, target identification (classification), and light pressure control ofdielectric body in space, screening and detection of biological cells, and studies on photoniccrystals. The method of moment (MoM) based on surface integral equations (SIE) is one ofthe most attractive methods to solve this type of problem due to its high accuracy andpowerful computing capability. Additionally, only surfaces of targets are required to bediscretized, the number of unknowns can be reduced significantly. However, theapplications with increasing complexity make the MoM system more challengeable to besolved accurately and efficiently. More efficient approaches are required to handle theMoM systems arising from these applicatioins. The goal of this dissertation is to satisfy thisrequirement by improving the efficiency and capability of the MoM associated with SIE forhomogeneous targets.There are several types of SIEs with different formulations. The widely employed onesinclude: the combined tangential formulation (CTF), the combined normal formulation(CNF) and the electric and magnetic current combined-field integral equation (JMCFIE).The accuracy, stability, and efficiency of these formuations are quite different although theSIEs are mathematically equivalent. With a comprehensive study on these different SIEformulations, CTF is selected in our study for its high accuracy and efficiency on memorycost. For large scale problems, iterative solvers are the common choice to solve the CTFmatrix system. However, the iterative solution suffers from problems in the followingseveral aspects. First, the matrix vector multiplication is as expensive asO(N2)becausethe impedance matrix is a full matrix. Second, the MoM impedance matrixes for dielectricobjects are oftern not well-conditioned and lead to a slow iterative convergence or even thefail in convergence. Third, different right hand sides (RHSs) are handled separately by theiterative solover. It makes the iterative solver perform awkwardly for systems with manyRHSs. Many efforts have been devoted to overcome the first difficulty. The multilevel fastmultipole algorithm (MLFMA) is the most efficient one among them, which can reduce thecost of matrix vector multiplication to O (N log N). We adopt it in our proposedalgorithms in combination with OpenMP parallelization to speed up the computation. In contrast, the other two difficulties are less perfectly solved. Based on this fact, our workfocuses majorly on the second and third difficulties.In order to efficiently solve the CTF matrix equation system, a lower triangularapproximate Schur preconditioner (LTASP) is proposed by making use of the Schurcomplement. The preconditioner is constructed from the near-field coupling part of theimpedance matrix. To approximate the inverse preconditioning matrix efficiently andaccurately, the incomplete LU factorization with dual thresholds (ILUT) is used.Acceletated by the LTASP computed by the dual-threshold ILUT, the convergence of thegeneralized minimal residual (GMRES) iterative solver is improved significantly.The excitation matrix consists of multiple RHSs is generally rank deficient.Conducting low-rank decomposition on the excitation matrix is an efficient approach toaccelerate the solution of multiple-RHS system. The decomposition can be realized by QRor SVD. However, QR and SVD are only suitable for problems with small number ofunknowns due to the high cost of the decompositions themselves. To overcome thisdifficulty, we investigate a high efficient matrix decomposition method, interpolativedecomposition (ID). By ultilizing randomness, the ID can be very efficient and accurate.Applying ID to the MoM impedance matrix, a fast algorithm is proposed and implemented.Numerical experiments validate the nice performance of ID on both accuracy andefficiency.A fast algorithm is propsed to accelerate the solution of the MoM systems with manyRHSs. The algorihm conducts ID on the excitation matrix to select a few RHSs which arerequired to be solved. In comparison with the original number of RHSs, the number ofRHSs required to be solved separately is quite small. The computation can then be speededup substantially. Taking the applications of evaluating radiation pressure force (RPF) as theexample, we employ the proposed algorithm to compute the RPF exerted on micro particlesby Gauss beams with multiple parameters and the force generated by the solar radiation ofthe so-called solar sails. Numerical experiments show that the proposed method is accuracycontrollable. The efficiency of the computation is substantially improved because thenumber of RHSs to be solved separatedly is reduced greatly.