Research On Integral Equation Domain Decomposition Method For Solving Electromagnetic Scattering From Electrically Extra Large Objects

The accurate analysis of electromagnetic scattering from complex objects is required in many fields,such as the stealth design of modern weapon platforms,the radar target recognition,and the research on anti-stealth radar technologies.However,at the operating frequency of airborne early warning radars and fire-control radars,the electrical size of these objects is usually very large,and the computational resources required for numerical simulations are also very huge.In addition,with the development of stealth technology,the precision of geometric modeling is constantly improved,and the detailed and heterotype structures,whose electrical size is very small,are also gradually taken into consideration.In numerical simulations,the co-existence of electrically large and small structures can easily lead to an ill-conditioned system matrix,making the iterative methods converge slowly or even difficult to converge,and thus reducing the accuracy and efficiency of numerical methods.Meanwhile,it is difficult to generate a conformal surface mesh with high quality for these multi-scale objects.In order to deal with these problems,this dissertation studies the integral equation baseddomain decomposition method(DDM),including an overlapping DDM(ODDM)suitable for solving electrically large problems and a non-overlapping DDM suitable for solving multi-scale problems.Firstly,this dissertation derives the surface integral equations based on the surface equivalence principle.The key steps to solve integral equations by the method of moments(MoM)are also introduced in detail,including the geometric modeling,the mesh generation,the principle for selecting testing and basis functions,the methods for solving matrix equations and so on.To accelerate the matrix-vector products,the multilevel fast multipole algorithm(MLFMA),the multilevel accelerated Cartesian expansions(MLACE)algorithm and their mixed-form MLFMA-MLACE are introduced.Secondly,this dissertation proposes a simply constructed ODDM(SODDM)which is used to reduce the peak memory requirement of electrically large problems and thus improve the ability of current platforms to handle large-scale problems.Different from the traditional ODDM,the buffer regions in SODDM are limited to only a single-layer of jagged triangular mesh cells.This not only simplifies the process for constructing buffer regions,but also reduces the number of extra unknowns introduced in sub-domain problems.Meanwhile,the SODDM introduces a current continuity condition to suppress the spurious edge effects caused by artificial boundaries,and thus ensure a stable convergence of stationary iterative methods.With this method,the electromagnetic scattering from a stealth bomber with length of about 900 wavelengths is successfully solved on a workstation with 96 GB RAM.Thirdly,a non-overlapping and non-conforming DDM based on integral equation discontinuous Galerkin(IEDG)formulations,named as the IEDG-DDM,is proposed in this dissertation.This method aims at generating non-conforming and high quality surface meshes for complex objects and improving the convergence of ill-conditioned matrix equations in large-scale and multi-scale problems.The IEDG-DDM decomposes the original object into several non-overlapping open surfaces,and imposes new interior penalty terms to guarantee the continuity of surface currents flowing across artificial boundaries.Compared with the existing DDMs without artificial surfaces,the IEDGDDM provides an effective domain decomposition preconditioner with no need to introduce an additional contour sub-domain,a buffer region,or a stabilization term.This improves the stability and usability of the IEDG-DDM in complex applications.The accuracy,eigenspectra,and convergence of this method is studied in detail.The ability of this method to handle real-world problems is verified by solving scattering from an electrically large and multi-scale aircraft carrier.Then,an improved impedance boundary condition(IBC)method is proposed to improve the convergence of the existing IBC method,especially in solving partially coated problems.This method treats the equivalent magnetic currents flowing across the partially coated boundaries separately from those flowing within the other regions.A hybrid form is used for modeling,and a better convergence is obtained without increasing the memory requirement or affecting the solution accuracy.On this basis,a non-overlapping and non-conforming IBC-IEDG-DDM is proposed for solving electromagnetic scattering from thin coated multi-scale objects.This method proposes an effective domain decomposition preconditioner for both fully coated and partially coated problems.Numerical examples show that the parameter of coated materials has no influence on the preconditioning performance of this method.The IBC-IEDG-DDM also provides an effective preconditioner for perfect electric conducting(PEC)problems and perfect magnetic conducting(PMC)problems.Finally,by applying the higher order hierarchical vector basis functions to the IEDG-DDM,a higher order IEDG-DDM(HO-IEDG-DDM)is proposed.In this method,the surface currents are expanded with mixed-order basis functions,and the number of unknowns as well as the memory requirement is maximally reduced.Meanwhile,this method provides an effective preconditioner which could significantly improve the convergence of higher order methods in complex multi-scale problems.