Nonconformal Domain Decomposition Methods For FE-BI-MLFMA And Applications

The hybrid finite element-boundary integral-multilevel fast multipole algorithm(FE-BI-MLFMA)is one of full-wave numerical methods in computational electromagnetics,which has been widely applied for simulating open-region problem in electromagnetic(EM)engineering due to its accuracy and versatility.However,with progress of microwave technology,the EM engineering problems become extremely complex,FE-BI-MLFMA faces new challenge for the demands of practical engineering.The main problems are as follows:(1)The resulted matrix equation of FE-BI-MLFMA often has large dimention and has to be solved by iterative methods instead of direct methods.However,the FE-BI matrix equation often is not well-conditioned,and is hard to converge by iterative methods.(2)Although some advanced iterative solution algorithms are proposed for the FE-BI matrix equation,all of them require factorization of a large sparse matrix which is not easy to achieve for electrically large-scale engineering problem.Domain decomposition method(DDM)has been proved to be a powerful tool for large-scale computation.Over the past decade,DDM has been employed to the finite element method,finite difference method,and integral equation method in computational electromagnetics.The goal of this dissertation is applying DDM to FE-BI-MLFMA for simulating electrically large-scale complex objects.After several years of in-depth study,two domain partitioning schemes are proposed based on the charcateristics of FE-BI-MLFMA.The first domain partitioning scheme is separating the whole solution domain into exterior boundary integral surface and interior finite element region,and then further decomposing the interior finite element region into many subdomains.Under this scheme,we develop two nonconformal DDMs for FE-BI-MLFMA.The second domain partitioning scheme is decomposing both interior FE region and exterior BI surface into several subdomains.Namely,after decomposition,each subdomain consists of a FE volume-part and a BI surface-part.Under this scheme,we develop the third nonconformal DDM for FE-BI-MLFMA.The first type of DDM for FE-BI-MLFMA is nonconformal Schwarz DDM for FE-BI-MLFMA.In this method,the optimized Schwarz FE-DDM is used to formulate interior FE subdomains.The interior FE region are connected with the exterior BI suface by first-oder Robin-type transmission condition.Moreover,based on the form of DDM's final system equation,a ABC-SGS proconditioner is proposed to further impove the convergence.We also realize a robust union mesh based nonconformal integral technique for calculating the coupling matrices between different subdomains.The second type of DDM for FE-BI-MLFMA is nonconfomal FETI-DP DDMs for FE-BI-MLFMA.In these methods,the FETI-DP FE-DDM are used to formulate interior FE subdomains.The Dirichel-type transimission condition(DTC)and first-order Robin-type transimission condition(RTC)are both considered to connect the interior FE region and exterior boundary integral suface.In addition,the implement of RTC at interior FE subdomain interfaces is also by two methods which are Lagrange multiplier(LM)method and cement element(CE)method.Thus,there are four system equations.Various numerical experiments verify that the CE and DTC based method is the most effective FETI-DP DDM for FE-BI-MLFMA.The third type of DDM for FE-BI-MLFMA is nonconformal geometry-aware domain decomposition method of FE-BI-MLFMA.This method includes a volume-based optimized Schwarz FE-DDM and a surface-based interior penalty BI-DDM.The second-order RTC is employed on interfaces between FE subdomains and the first-order RTC is employed on interface between FE-part and BI-part in the same subdomain.Comparing to previous DDMs,the geometry-awave DDM for FE-BI-MLFMA has faster convergence,linear computational cost,and excellent scalability.Moreover,the geometry-aware property provides more flexible to create geometry and discretize the computational domain while allow to take full advantage of periodicity to save CPU time and memory.By using the developed DDMs of FE-BI-MLFMA,a series challenge problems have been analyzed in this dissertation,such as EM scattering from electrically large-scale composite objects,EM radiation from large-scale patched annenna arrays,EM scattering from large-scale frequency selective surface(FSS),challenging EM radiation from Vivaldi antenna array with FSS embedded radome.