Higher-order finite element-boundary integral methods for electromagnetic scattering and radiation analysis.

摘要

Higher-order finite element-boundary integral (FE-BI) methods are studied for fast and accurate numerical analysis of electromagnetic scattering and radiation problems. First, a higher-order FE-BI method is presented for the scattering analysis of large, deep, and arbitrarily shaped open cavities. A special frontal solver is first designed for the discretized FE-BI system. The special frontal solver is implemented with higher-order tetrahedral elements and mixed-order prism elements. It is then parallelized on Origin 2000 clusters in NCSA to exploit the power of supercomputers, and a high efficiency using up to 64 processors is achieved. Furthermore, a general frontal algorithm is proposed for the analysis of cavities with arbitrary geometries and complex internal configurations, which is hard to handle using the previous special frontal algorithm. Second, the previous special and general frontal algorithm are employed for efficient and accurate analysis of microwave waveguide devices. Two solution algorithms are used. The first one uses mixed-order triangular prism elements in conjunction with the special frontal solver. The second solution algorithm employs higher-order tetrahedral elements, which are particularly suitable for modeling complex devices, in conjunction with the multifrontal solver, which is an extension of the general frontal solver. Third, a general higher-order finite element-adaptive absorbing boundary method (FE-AABC) is developed for the scattering and radiation analysis of general inhomogenious objects. The proposed method derives an adaptive numerical absorbing boundary condition (ABC) for the finite element solution based on boundary integral equations. Fourth, a highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid FE-BI method to electromagnetic scattering and radiation problems. A solution algorithm consisting of two iteration loops is proposed, in which the outer iteration accelerates the convergence of the inner iteration. It is shown that the previously proposed FE-AABC method is only a special case of this approach. Finally, a numerical scheme, which integrates the techniques developed above, is presented to simulate electromagnetic scattering and radiation from a large and arbitrarily shaped body, possibly coated with inhomogeneous composite materials, with large and deep cavities. Numerical examples are presented to demonstrate the accuracy, efficiency, and versatility of this scheme.