Frequency Domain Hybrid Finite Element Methods for Electromagnetics

Volakis, John L.; Sertel, Kubilay; Usner, B.C.

doi:10.2200/s00038ed1v01y200606cem010

Cited by 19 publications

(14 citation statements)

References 132 publications

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“…In the second step of the SGM, the expansions (2) are substituted into (1) and the result is subjected to a Galerkin testing procedure [20], meaning that the equations are weighted with the same set of polynomials using the inner product (3). This leads to the following set of equations:…”

Section: B Stochastic Galerkin Methods (Sgm)mentioning

confidence: 99%

Variability Analysis of Interconnects Terminated by General Nonlinear Loads

Biondi

Ginste

Zutter

et al. 2013

IEEE Trans. Compon., Packag. Manufact. Technol.

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Section: B Stochastic Galerkin Methods (Sgm)mentioning

confidence: 99%

Variability Analysis of Interconnects Terminated by General Nonlinear Loads

Biondi

Ginste

Zutter

et al. 2013

IEEE Trans. Compon., Packag. Manufact. Technol.

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“…The numerical simulation of the scattering problem (1)-(4) at a heterogeneous domain typically combines a boundary element method (BEM) [38,41,51], with unknown current densities in a finite-dimensional subspace of H − 1 2 (div Γ , Γ), with a finite element method [44,45], with an unknown electric field in a finitedimensional subspace of H(curl, Ω − ), resulting in a hybrid FEM-BEM method, sometimes called FE-BI (finite element, boundary integral) method [39,52,53]. In this way, the advantages of both methods, i.e., the natural incorporation of heterogeneous material parameters in FEM and the inherent validity of the radiation condition of the scattered fields in BEM, are combined.…”

Section: Preconditioned Reduced Hybrid Fem-bem Formulationmentioning

confidence: 99%

A Calderón multiplicative preconditioner for the electromagnetic Poincaré–Steklov operator of a heterogeneous domain with scattering applications

Dobbelaere

Zutter

Hese

et al. 2015

Journal of Computational Physics

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In the context of hybrid formulations, the Poincaré-Steklov operator acting on traces of solutions to the vector Helmholtz equation in a heterogeneous interior domain with a smooth boundary is regularized by a well-known boundary integral operator related to the homogeneous exterior domain. For the first time, this property allows us to simultaneously construct a Calderón multiplicative preconditioner for the discretized operator and for a 3-D hybrid finite/boundary element method formulation, applicable to electromagnetic scattering problems. Numerical examples demonstrate the effectiveness of this novel preconditioning scheme, even for heterogeneous domains with non-smooth boundaries.

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“…The classic approach to construct a hybrid FE-BIE formulation is to combine the EFF and the EFIE [3], [8]. Making use of (4) and the first equation of (8b), the following system is obtained:…”

Section: A Eff and Efiementioning

confidence: 99%

“…Previous contributions demonstrated that formulations applying the electric field integral equation (EFIE) or the magnetic field integral equation (MFIE) as BIE method in combination with an FE method contain certain 'forbidden frequencies' if the background medium is lossless [3], [5]- [12]. At these frequencies, the EFIE and MFIE are not uniquely defined and the sourceless hybrid system contains non-trivial solutions that introduce errors on the result.…”

Section: Introductionmentioning

confidence: 99%

Rigorous Analysis of Internal Resonances in 3-D Hybrid FE-BIE Formulations by Means of the Poincaré–Steklov Operator

Boeykens

Rogier

Hese

et al. 2013

IEEE Trans. Microwave Theory Techn.

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Abstract-3D hybrid finite element (FE) -boundary integral equation (BIE) formulations are widely used because of their ability to simulate large inhomogeneous structures in both open and bounded simulation domains by applying each method where it is the most efficient. However, some formulations suffer from breakdown frequencies at which the solution is not uniquely defined and errors are introduced due to internal resonances. In this paper, we investigate the occurrence of spurious solutions resulting from these resonances by using the concept of the Poincaré-Steklov or Dirichlet-to-Neumann operator, which provides a relation between the tangential electric field and the electric current on the boundary of a domain. By identifying this operator in both the FE and the BIE method, several new properties of internal resonances in 3D hybrid FE-BIE formulations are easily derived. Several conformal and nonconformal formulations are studied and the theory is then applied to a scattering problem.

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Frequency Domain Hybrid Finite Element Methods for Electromagnetics

Cited by 19 publications

References 132 publications

Variability Analysis of Interconnects Terminated by General Nonlinear Loads

Variability Analysis of Interconnects Terminated by General Nonlinear Loads

A Calderón multiplicative preconditioner for the electromagnetic Poincaré–Steklov operator of a heterogeneous domain with scattering applications

Rigorous Analysis of Internal Resonances in 3-D Hybrid FE-BIE Formulations by Means of the Poincaré–Steklov Operator

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