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

Tuncer, O.; Lu, Chuan; Nair, N. V.; Shanker, B.; Kempel, Leo C.

doi:10.1109/tap.2009.2039322

Cited by 16 publications

(20 citation statements)

References 24 publications

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“…First, overlapping PU domains i are defined around each node i such that D [ i i . The PU domain i is constructed as a union of polyhedrons sharing the node i (Tuncer et al, 2010a). The vector basis function is then defined on this tessellation using two scalar functions, namely the PU function i .r/ and the local approximation function v i .r/.…”

Section: Spatial Basis Functionsmentioning

confidence: 99%

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A Hybrid Vector Generalized Finite-Element Method for Transient Electromagnetic Simulations

2014

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In this article, a hybrid vector generalized finite-element method is developed for time-domain electromagnetic analysis. Average and jump operators of the discontinuous Galerkin method are used to establish a domain decomposition framework for the vector generalized finite-element method such that they enable application of vector generalized finite-element methods to inhomogeneous problems without using additional basis functions at material interfaces. Moreover, they enable hybridization of the classical finite-element method and vector generalized finiteelement method such that advantages of each method can be exploited for more accurate computation of electromagnetic fields. In this article, the interior penalty discontinuous Galerkin method is used to enable communication among partitioned domains. Convergence characteristics of these hybrid methods are studied, and their applications to wave scattering problems are presented.

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Section: Spatial Basis Functionsmentioning

confidence: 99%

“…The method has been adapted to polyhedral tessellations and integrated with the boundary integral technique (Tuncer et al, 2010a(Tuncer et al, , 2010b(Tuncer et al, , 2012a. It has been shown to provide accurate and higher-order convergent solutions to EM problems.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Vector Generalized Finite-Element Method for Transient Electromagnetic Simulations

2014

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“…This is the construction of overlapping partition of unity (PU) domains Ω i on polyhedral meshes. We construct PU domain Ω i as a union of polyhedrons sharing the node i such that Ω = i Ω i [2]. Once we have established the framework of VGFEM, we define the vector basis function using two scalar functions: a partition of unity function and a local approximation function as described in [1].…”

Section: Theorymentioning

confidence: 99%

“…Since the introduction of the method, we have systematically advanced the theory and capability of the method. To this end, we developed a technique to define the VGFEM framework on polyhedral mesh structures (specifically brick elements), and studied the convergence and dispersion characteristics of the method rigourously [2]. In the same paper and in [3], we developed a hybrid VGFEM-Boundary Integral (VGFEM-BI) technique for scattering from cavity backed apertures.…”

Section: Introductionmentioning

confidence: 99%

Vector generalized finite element method on tetrahedral meshes and applications of its features in electromagnetic simulations

Tuncer

Şahin

Shanker

et al. 2011

2011 IEEE International Symposium on Antennas and Propagation (APSURSI)

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The vector generalized finite element method (VGFEM) offers several appealing features for solving electromagnetic (EM) problems. These include flexibility on the choice of basis functions, use of different types of basis functions or mixed polynomial orders within a simulation, and inclusion of physics in solution space. These features can be exploited to yield more accurate and convergent solutions to EM problems. In this paper, we would like to demonstrate use of mixed polynomial orders and use of mixed basis functions in the same simulation domain. The VGFEM framework defined on tetrahedral meshes is used in this demonstration for the analysis of both open and closed domain electromagnetic problems.

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“…Incorporating such flexibility into classical solvers is very difficult as one has to take steps to ensure continuity of the physical quantity being represented. In the finite element community, the need/desire to enrich the approximation space, as well as ensure continuity gave rise to the generalized finite element method 23,24,36,37 , and its variations 38,39,40 . The basis functions developed within this framework are continuous across domains and, as a result, do not need additional constraints to ensure continuity.…”

Section: Introductionmentioning

confidence: 99%

Generalized Method of Moments

2007

Encyclopedia of Measurement and Statistics

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The analysis of scattering from complex objects using surface integral equations is a challenging problem. Its resolution has wide ranging applications-from crack propagation to diagnostic medicine. The two ingredients of any integral equation methodology is the representation of the domain and the design of approximation spaces to represent physical quantities on the domain. The order of convergence depends on both the surface and geometry representation. For instance, most surface models are restricted to piecewise flat or second order tessellations. Similarly, the most commonly known basis spaces for acoustics are piecewise constant functions. What is desirable is a framework that permits adaptivity (of size and order) in both geometry and function representations. Unlike volumetric, differential equation solvers, such as the finite element method, developing an hpadaptive framework for surface integral equations is very difficult. This papers proposes a resolution to this problem by developing a novel framework that relies on reconstruction of the surface using locally smooth parameterizations, and defining partition of unity functions and higher order basis spaces on overlapping domains. This permits easy refinement of both the geometry and function representation. This capabilities of the proposed framework are shown via a number of numerical examples.

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

Cited by 16 publications

References 24 publications

A Hybrid Vector Generalized Finite-Element Method for Transient Electromagnetic Simulations

A Hybrid Vector Generalized Finite-Element Method for Transient Electromagnetic Simulations

Vector generalized finite element method on tetrahedral meshes and applications of its features in electromagnetic simulations

Generalized Method of Moments

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