Research On Nonconformal Volume Integral Equation-Based Characteristic Basis Function Method With Large-Size Block

In recent years,the numerical analysis of the electromagnetic scattering from the composite dielectric objects has always been a hot topic in the electromagnetic theory,its application ranges from target monitoring and recognition,design of antenna system,microwave biomedical imaging to stealth and anti-stealth technology and so on.This dissertation intensively studies the nonconformal electric volume integral equation-based characteristic basis function method(CBFM)with large-size block.Moreover,combined with several fast algorithms,the improved method is competent to analyze the scattering from the electrically large inhomogeneous dielectric objects with complex structure.According to the volume equivalence principle,the volume integral equation(VIE)for three-dimensional dielectric object is established.Then the numerical implementation of the method of moments(MoM)based on the Schaubert–Wilton–Glisson(SWG)basis functions is elaborated systematically.The MoM provides a precise analysis method for the electromagnetic scattering problems.However,it has been limited by the high computational consumption.In this dissertation,the more efficient CBFM is studied.The characteristic basis functions(CBFs)used in the CBFM can characterize the low-level basis functions representing the current density.And the number of CBFs is greatly less than that of low-level basis functions.We adopt the CBFM based on the singular value decomposition(SVD-CBFM),which is independent of the excitations and advantageous on analyzing the multi-excitation scattering problems.Furthermore,combined with the adaptive cross approximation(ACA)that is used to accelerate the construction of the reduced matrix,the ACA-SVD-CBFM remarkably reduces the computational complexity and memory requirement compared with the MoM,maintaining the comparable accuracy.As far as we know,there are rare researches which apply the SWG basis functions-based CBFM to analyze the scattering from composite dielectric objects.Hence,we have done a lot of simulation experiments to investigate the extension length and the block size of the CBFM in the context of dielectric object scattering.This dissertation concludes the minimum extension length without compromising the accuracy,and firstly proposes the large-size block strategy that is more suitable for dielectric objects.The utilization of large-size block,which usually contains several thousand low-level basis functions in each block,reduces the calculation of generating the CBFs.Moreover,it cuts down the number of the CBFs,saving the time of constructing and solving the reduced matrix equation.The large-size block strategy leads to the reduction of the efficiency on filling the mutual-impedance matrices and the increase of the self-impedance matrices dimensions.For addressing aforementioned problems,the multiscale adaptive cross approximation(MSACA)and Sherman-Morrison-Woodbury(SMW)formula-based algorithm(SMWA)are adopted.The MSACA subdivides the adjacent blocks into hierarchical structure to increase the proportion of nonadjacent mutual-impedance submatrices,effectively circumventing the limitation of ACA in calculating adjacent mutual-impedance matrices.The SMWA decomposes the self-impedance matrix that is hierarchical off-diagonal low-rank matrix into a product of block diagonal matrices,then uses the SMW formula or LU algorithm to calculate the inverse matrices of the sparse decomposition matrices.At the end,the product of the inverse matrices is used to approximate the inverse of the original self-impedance matrix.The SMWA remarkably reduces the computational complexity and memory requirement for generating the CBFs.Compared with the ACA-SVD-CBFM,the CBFM with large-size block that is combined with the MSACA and SMWA(SMWA-MSACA-CBFM)is considerably superior in analyzing scattering from electrically large dielectric objects without compromising the accuracy.To further improve the algorithm efficiency,the nonconformal mono-SWG basis functions are utilized to discrete the VIE.The nonconformal discretization permits to separately adopt various mesh sizes or basis function types depending on the local parameters,which provides a flexible and efficient scheme to model the inhomogeneous objects.In addition,taking advantage of that the conformal discretization produces less unknowns in homogeneous regions,the conformal SWG basis functions are used to model the inner of homogeneous parts.Meanwhile,the mono-SWG basis functions are applied to model the boundaries separating two mediums.The mixture discretization significantly cuts down the number of low-level basis functions required for modeling the inhomogeneous objects with complex structure,which greatly improves the efficiency of the SMWA-MSACA-CBFM and maintains excellent accuracy.