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

• Published in: IEEE transactions on antennas and propagation Vol. 58; no. 3; pp. 887 - 899
• Main Authors: Tuncer, O., Chuan Lu, Nair, N.V., Shanker, B., Kempel, L.C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Basis functions; Boundaries; Boundary integrals; Computational electromagnetics; Dispersions; Electromagnetic fields; Electromagnetic measurements; Exact sciences and technology; Finite element analysis; Finite element method; Finite element methods; generalized finite element methods (GFEM); High performance computing; Integral equations; Integrals; Mathematical analysis; Mathematical models; Moment methods; numerical dispersion; partition of unity methods; Polynomials; Radiolocalization and radionavigation; RCS; Shape; Studies; Telecommunications; Telecommunications and information theory; Vectors (mathematics); Radar cross section; RCS; Partition method; numerical dispersion; Helmholtz equation; Boundary integral method; Numerical method; Flexibility; Boundary integrals; generalized finite element methods (GFEM); Finite element method; partition of unity methods; Heterogeneity; Arbitrary shape body; Vector equation
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2009.2039322

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.