Efficient Numerical Method For Physical Model Simplification And Algorithm Improvement Based On Integral Equation Method

In today's practical engineering,multi-scale targets with complex structure have a wide application in antenna design,circuit system design,and radar stealth and anti-stealth design.From the aspect of physical model,the multi-scale targets have electrical-large or even extremely electrical-large structures in macro,while have complex tiny detailed structure in local.As a result,for numerical simulation,it leads to the challenge of large number of unknowns,ill-conditioned system matrix,and slow convergence rate of iterative solutions.In order to address the above mentioned problems in the field of integral equation methods,a series of research works has been done and reported in this dissertation based on the simplification of physical model and improvement of existing algorithms.Firstly,the fundamental theories and concepts of integral equation methods have been briefly introduced,including the surface integral equation method based on the surface equivalence principle,the volume integral equation method based on the volume equivalence principle,discretization scheme and the related low-order or high-order basis functions over the target,the construction process and solving process of the system matrix,the fast algorithms for matrix vector multiplication process,and the inverse equivalent source based near field measurement of antenna.To address the problem of huge memory requirement for storing the basis pattern of basis functions defined on large patches in the multilevel fast multipole algorithm,a point-adaptive grouping scheme has been proposed to reduce the related memory cost for basis pattern optimally.The proposed scheme is based on a careful analysis of the physical model in the grouping process,and the related mathematical optimization problem solved by the clustering algorithm.It can reduce the total memory consumption of the simulation considerably,and is convenient to be implemented with the existing fast solvers.As a result,the proposed scheme is very suitable for the simulation of electrical-large or extremely electrical-large targets.To improve the condition number of the system matrix of multi-scale problem,an improved scheme of algebraic preconditioner has been proposed,where the matrix for preconditioning is constructed by filtering the near-field interactions on higher levels rather than the finest level of the related fast algorithms for multi-scale target.Considering the rank-deficient nature of the enlarged system matrix,the rank revealing adaptive cross approximation algorithm is applied to further increase the computational efficiency.The proposed scheme can speed up the iterative convergence rate considerably,and is easy to be implemented with the existing fast solvers.Besides,the multi-resolution basis function and the multi-resolution preconditioner are also developed in this dissertation,which have been reported to be efficient for multiscale problem.Numerical examples have been given to validate the performance of the related solver.Moreover,inspired by the multi-resolution basis functions,an improved set of roof-top basis functions has been proposed to efficiently analyze the conformal capacitive frequency selective surfaces.This scheme can improve the conditioning of the system matrix,thus save the total CPU time without increase the memory cost.To improve the conditioning of the high-contrast problem in multiscale target,an improved scheme of multilayer thin dielectric sheet model has been proposed,where a careful analysis of the related system matrix has been conducted.By using a limited number of scaling factors,the diagonal dominance of the system matrix can be recovered,almost without any memory increase.Consequently,the conditioning of the system matrix has been improved and the iterative convergence rate has been speeded up which results in an acceleration of the computational efficiency.The proposed scheme is very suitable to simulate the high-contrast thin dielectric sheet target.Finally,in order to improve the computational efficiency of the fast algorithm in near-field antenna measurement under space-limited,low frequency condition with small scale mesh discretization,a hierarchical fast solver for near-field antenna measurement has been proposed based on the adaptive cross approximation algorithm.Since the finest level box size of the fast algorithm can be set as small as possible,the proposed scheme can efficiently simulate the space-limited or low frequency near-field antenna measurement.To further improve the computational efficiency of the adaptive cross approximation algorithm,two geometrical adaptive grouping schemes for the planar and spherical measurement scenario have been proposed,respectively.