Multi-solver schemes for electromagnetic modeling of large and complex objects

Boundary integral equation;Buffa-Christiansen function;Combined field integral equation (CFIE);Compute unified device architecture (CUDA);Electromagnetic scattering;Finite element method;Finite element-boundary integral (FE-BI);Hybrid parallel programming model;Multi-graphics processing unit (GPU);Message passing interface (MPI);Multilevel fast multipole algorithm;Multi-solver scheme;Open Multi-Processing (OpenMP);Radar cross section;Robin transmission condition;Method of moments (MoM)

Guan, Jian

关键词: Boundary integral equation;    Buffa-Christiansen function;    Combined field integral equation (CFIE);    Compute unified device architecture (CUDA);    Electromagnetic scattering;    Finite element method;    Finite element-boundary integral (FE-BI);    Hybrid parallel programming model;    Multi-graphics processing unit (GPU);    Message passing interface (MPI);    Multilevel fast multipole algorithm;    Multi-solver scheme;    Open Multi-Processing (OpenMP);    Radar cross section;    Robin transmission condition;    Method of moments (MoM);   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/98097/GUAN-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The work in this dissertation primarily focuses on the development of numerical algorithms for electromagnetic modeling of large and complex objects.First, a GPU-accelerated multilevel fast multipole algorithm (MLFMA) is presented to improve the efficiency of the traditional MLFMA by taking advantage of GPU hardware advancement. The proposed hierarchical parallelization strategy ensures a high computational throughput for the GPU calculation. The resulting OpenMP-based multi-GPU implementation is capable of solving real-life problems with over one million unknowns with a remarkable speedup. The radar cross sections (RCS) of a few benchmark objects are calculated to demonstrate the accuracy of the solution. The results are compared with those from the CPU-based MLFMA and measurements. The capability and efficiency of the presented method are analyzed through the examples of a sphere, an aircraft, and a missile-like object. Compared with the 8-threaded CPU-based MLFMA, the OpenMP-CUDA-MLFMA method can achieve from 5 to 20 times total speedup.Second, an efficient and accurate finite element--boundary integral (FE-BI) method is proposed for solving electromagnetic scattering and radiation problems. A mixed testing scheme, in which the Rao-Wilton-Glisson and the Buffa-Christiansen functions are both employed as the testing functions, is first presented to improve the accuracy of the FE-BI method. An efficient absorbing boundary condition (ABC)-based preconditioner is then proposed to accelerate the convergence of the iterative solution. To further improve the efficiency of the total computation, a GPU-accelerated MLFMA is applied to the iterative solution. The RCSs of several benchmark objects are calculated to demonstrate the numerical accuracy of the solution and also to show that the proposed method not only is free of interior resonance corruption, but also has a better convergence than the conventional FE-BI methods. The capability and efficiency of the proposed method are analyzed through several numerical examples, including a large dielectric coated sphere, a partial human body, and a coated missile-like object. Compared with the 8-threaded CPU-based algorithm, the GPU-accelerated FE-BI-MLFMA algorithm can achieve a total speedup up to 25.5 times.Third, a multi-solver (MS) scheme based on combined field integral equation (CFIE) is proposed. In this scheme, an object is decomposed into multiple bodies based on its material property and geometry. To model bodies with complicated materials, the FE-BI method is applied. To model bodies with homogeneous or conducting materials, the method of moments is employed. Specifically, three solvers are integrated in this multi-solver scheme: the FE-BI(CFIE) for inhomogeneous objects, the CFIE for dielectric objects, and the CFIE for conducting objects. A mixed testing scheme that utilizes both the Rao-Wilton-Glisson and the Buffa-Christiansen functions is adopted to obtain a good accuracy of the proposed multi-solver algorithm. In the iterative solution of the combined system, the MLFMA is applied to accelerate computation and reduce memory costs, and an ABC-based preconditioner is employed to speed up the convergence. In the numerical examples, the individual solvers are first demonstrated to be well conditioned and highly accurate. Then the validity of the proposed multi-solver scheme is demonstrated and its capability is shown by solving scattering problems of electrically large missile-like objects.Fourth, a MS scheme based on Robin transmission condition (RTC) is proposed. Different from the FE-BI method that applies BI equations to truncate the FE domain, this proposed multi-solver scheme employs both FE and BI equations to model an object along with its background. To be specific, the entire computational domain consisting of the object and its background is first decomposed into multiple non-overlapping subdomains with each modeled by either an FE or BI equation. The equations in the subdomains are then coupled into a multi-solver system by enforcing the RTC at the subdomain interfaces. Finally, the combined system is solved iteratively with the application of an extended ABC-based preconditioner and the MLFMA. To obtain an accurate solution, both the Rao-Wilton-Glisson and the Buffa-Christiansen functions are employed as the testing functions to discretize the BI equations. This scheme is applied to a variety of benchmark problems and the scattering from an aircraft with a launched missile to demonstrate its accuracy, versatility, and capability. The proposed scheme is compared with the MS-CFIE to illustrate the differences between the two schemes.Fifth, to further improve the modeling capability, an accelerated MS method is developed on distributed computing systems to simulate the scattering from very large and complex objects. The parallelization strategy is to parallelize different subdomains individually, which is different from the parallelized domain decomposition methods, where the subdomains are handled in parallel. The multilevel fast multipole algorithm is parallelized to enable computation on many processors. The modeling strategy using the MS-RTC method is also discussed so that one can easily follow the guideline to model large and complex objects. Numerical examples are given to show the parallel efficiency of the proposed strategy and the modeling capability of the proposed method.Finally, the specific absorption rate (SAR) in a human head at 5G frequencies is simulated by taking advantage of the MS-RTC method. Based on the strong skin effect, the human head model is first simplified to reduce the computation cost. Then the MS-RTC method is applied to model the human head. Numerical examples show that the MS method is very efficient in solving electromagnetic fields in the human head and the simplified human head model can be used in the SAR simulation with an acceptable accuracy.