A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects

Tzoulis, A.; Eibert, Thomas F.

doi:10.1109/tap.2005.856348

Cited by 61 publications

(37 citation statements)

References 21 publications

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“…First, the numerical accuracy of our method is assessed by comparing the results of our method to the MoM-UTD scheme in [2] and to an alternative MLFMM-UTD formalism that is somewhat similar to the one presented in [14] as detailed below. Next, the efficiency of our method is demonstrated.…”

Section: Numerical Resultsmentioning

confidence: 99%

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A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

Karagounis

Zutter

Ginste

2016

IEEE Trans. Antennas Propagat.

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Section: Numerical Resultsmentioning

confidence: 99%

“…A hybrid MLFMM-UTD method has been presented in [14]. The method estimates the amplitude and phase of the UTD rays based on the MLFMM radiation pattern.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

Karagounis

Zutter

Ginste

2016

IEEE Trans. Antennas Propagat.

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“…Besides (14), other, unsymmetric resonance-free formulations exist, like the formulation used in [5].…”

Section: Analysis Of Hybrid Fe-bie Formulationsmentioning

confidence: 99%

The Poincaré–Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations

Demarcke

Rogier

2011

Antennas Wirel. Propag. Lett.

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Abstract-The Poincaré-Steklov operator provides a direct relation between the tangential electric and magnetic field at the boundary of a simply connected domain, and a discrete equivalent of the operator can be constructed from the sparse finite element (FE) matrix of that domain by forming the Schur complement to eliminate the interior unknowns. Identifying the FE system matrix as a discretized version of the Poincaré-Steklov operator allows us to describe and analyze FE and hybrid finite element-boundary integral equation (FE-BIE) formulations from an operator point of view. We show how this operator notation provides substantial theoretical insight into the analysis of spurious solutions in hybrid FE-BIE methods, and we apply the theory on a TM scattering example to predict the breakdown frequencies of different hybrid formulations. Index Terms-Hybrid methods, Electromagnetic scattering I. INTRODUCTIONThe hybrid FE-BIE method is a widely used approach to numerically solve electromagnetic scattering or radiation problems. It combines the versatility of the FE method to model complex inhomogeneous and anisotropic structures with the accuracy and efficiency of the BIE method to model large homogeneous and potentially unbounded domains. Traditionally, the FE formulation is set in a variational framework, which is extended with the BIE formalism to form a hybrid variational formulation. However, this approach relies on the internal field densities in the FE domain, and since the exact method used to couple both formulations seems to be very important to avoid spurious solutions, we expect that a hybrid formalism specifically focusing on the behavior of the formulations at the boundary will provide more theoretical insights.In this paper, we use the concept of a Poincaré-Steklov (PS) operator to describe the FE formulation in a domain by the relation it provides between the tangential electric and magnetic fields at the boundary of the domain. Hybrid formulations are easily formed by properly combining the PS and BIE operators. Unlike the classical variational framework, this operator notation retains the individual identities of the FE and BIE operators in FE-BIE formulations, and different properties regarding spurious solutions are easily derived. After outlining the general equations in Section II, we use the new operator notation in Section III to analyze the problem of spurious solutions in commonly used hybrid FE-BIE formulations. The theoretical results are then applied in Section IV to compare the analytical and the simulated breakdown frequencies of the different FE-BIE formulations for a TM scattering problem involving a single dielectric cylinder.

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“…Surface integral equation (SIE) methods [1][2][3][4][5][6][7] have shown to be effective in solving electromagnetic (EM) radiation and scattering problems. Applications range from advanced antenna design [8,9], stealth technologies [10,11], integrated circuits [12] to optics and photonics [13,14].…”

Section: Introductionmentioning

confidence: 99%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects

Cited by 61 publications

References 21 publications

A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

The Poincaré–Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

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A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects

Cited by 61 publications

References 21 publications

A Hybrid MLFMM&#x2013;UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

A Hybrid MLFMM&#x2013;UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

The Poincaré–Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

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A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems