Research On Integral Equation Domain Decomposition Method For Engineering Applications

With the development of technology,the demands of system level electromagnetic simulation are strongly increasing,in electronic engineering.However,the scales and complexity of system level electromagnetic simulation are still way beyond the capabilities of commercial software and existing computational electromagnetic method(CEM)technique.Fortunately,the domain decomposition method(DDM)provides an effective way to solve these problems.This dissertation focuses on the integral equation domain decomposition method for engineering application,carries out a serious of researches,including non-conformal,non-overlapping integral equation domain decomposition method for non-penetrable objects(IE-DDM),hybrid solvers domain decomposition method with mixed basis functions in the framework of IE-DDM(HS-DDM/MBFs),integral equation domain decomposition method for cavity objects(CAV-DDM),nonconformal multiple-traces Poggio-Miller-Chang-Harrington-Wu-Tsai(MT-PMCHWT)method for penetrable objects,EFIE-PMCHWT based domain decomposition method for multilayer dielectric/metallic composite objects and CEIE-IBC based integral equation domain decomposition for multi-scale coated objects.This dissertation begins with the equivalence principle of electromagnetic,then the surface integral equation(SIE)and SIE based non-conformal,non-overlapping DDM is derived on the basis of equivalence principle.By taking the inverse of each sub-domain matrix as a preconditioner and solving the matrix system equation with an inner-outer iterative procedure,the DDM can solve the multi-scale electromagnetic problems effectively.In order to solve the matrix equation and sub-domain matrix equation more effectively,the Krylov subspace based method GMRES and recycling Krylov subspace based method GCRO-DR is introduced.Integral equation domain decomposition method(IE-DDM)decomposes the original multi-scale objects into many independent sub-domains,and discretizes each sub-domain independently.Therefore,the higher order hierarchical vector basis functions are used in the electrically large smooth sub-domains to significantly reduce the number of unknowns,while traditional Rao-Wilton-Glisson basis functions are used for sub-domains with tiny structures.At the same time,different fast solvers to be used in different subdomains based on the property of different sub-domains to reduce the time and memory consumption.Here,the multilevel fast multipole algorithm(MLFMA)and hierarchical(?-)matrices method are combined in the framework of IE-DDM to enhance the capability of IE-DDM and realize efficient solution of multi-scale electromagnetic problems.The MLFMA is used to capture propagating wave physics in large,smooth regions,while?-Matrices is used to capture evanescent wave physics in small regions which are discretized with dense meshes.For the cavity objects,by imposing equivalent electric and magnetic currents on the aperture,the original problem is transformed into interior and exterior problems.Different from traditional method based on interior-exterior equivalence principle,this work couples the exterior and interior problems only through the transmission condition on the aperture.Based on this DDM,a well-posed combined field integral equation(CFIE)is successfully developed to realize fast solution of electromagnetic scattering from openended cavity with extremely thin or zero thickness.Compared to the electric field integral equation,the proposed CFIE significantly improves the convergence rate of iterative solvers.For the electromagnetic modeling of dielectric objects,a non-conformal multipletraces PMCHWT(MT-PMCHWT)is proposed.This MT-PMCHWT is established by taking the interior region(dielectric space)and exterior region(free space)as independent sub-domains,enforcing the transmission conditions(TCs)on the EFIE and MFIE of interior and exterior sub-domains to ensure the continuities of fields.Compare to PMCHWT method,the non-conformal MT-PMCHWT allows the two sub-domains to be discretized with meshes of different sizes.This new method can not only get a betterconditioned matrix but also improve the efficiency of MLFMA to reduce the memory and time consumption.For the complex multilayer dielectric/metallic composite objects(open metallic surface printed on the interface of multilayer dielectric structures),an electric field integral equation(EFIE)-PMCHWT based domain decomposition method(DDM)is proposed.By taking the EFIE-PMCHWT as a sub-domain governing equation and enforcing the TCs on the touching-face,this method can not only improve the condition number,but also avoids the special junctions testing procedures.Additionally,a CFIE/EFIEPMCHWT based domain decomposition method(CFIE/EFIE-PMCHWT-DDM)is also developed to solving the EM scattering and radiation of microstrip mounted on large platform.For the multi-scale thin coated objects,a non-conformal non-overlapping integral equation domain decomposition method with impedance boundary condition(IE-DDMIBC)is proposed by taking the combined field integral equation with impedance boundary condition(CFIE-IBC)as sub-domain governing equations and enforcing the TCs on the touching-face to ensure the continuities of fields.