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Further Development of Vector Generalized Finite Element Method and Its Hybridization With Boundary Integrals

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5 Author(s)
O. Tuncer ; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI, USA ; Chuan Lu ; N. V. Nair ; B. Shanker
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Recently, vector generalized finite element method (VGFEM) was introduced for the solution of the vector Helmholtz equation, and its applicability was validated for canonical problems. VGFEM uses a local Helmholtz decomposition to construct basis functions in overlapping local domains of some canonical shape. While using a canonical shape for local domains adds flexibility to the method, one needs to provide information regarding boundaries of domains/inhomogeneities. The need for surface information proves to be a bottleneck in using the method for a larger class of problems. This paper is targeted towards overcoming these deficiencies; here, we will introduce the modifications to this method that permit interfacing with arbitrarily shaped local domains (to facilitate interfacing with existing meshing software), integrate this method with boundary integrals and provide a framework for studying dispersion. As will be apparent, the hybridization of the method with boundary integrals is not a simple adaptation of existing methods onto the VGFEM framework. Likewise, dispersion analysis is nontrivial due to the overlapping nature of VGFEM basis functions. A range of practical problems has been analyzed within the presented framework and results are compared either against measurements or existing FEM data to validate the presented methodology.

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IEEE Transactions on Antennas and Propagation  (Volume:58 ,  Issue: 3 )