Journal ArticleDOI
A New Low-Frequency Stable Potential Formulation for the Finite-Element Simulation of Electromagnetic Fields
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In this paper, the authors proposed a finite-element formulation for the frequency domain, which covers the entire range from static/stationary fields to wave propagation and does not involve any frequency-dependent thresholds, leading to complex symmetric system matrices and unique solutions.Abstract:
The finite-element formulation proposed in this paper is for the frequency domain and covers the entire range from static/stationary fields to wave propagation. It does not involve any frequency-dependent thresholds, leads to complex symmetric system matrices and unique solutions, and applies to the most general structures, comprising both lossy and lossless regions. Compared with non-stabilized methods, e.g., the electric field formulation, the price to be paid is one extra scalar potential in the lossy region. Numerical examples demonstrate that the proposed method is well-suited for direct and iterative solvers, and remains stable in the static case.read more
Citations
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Book ChapterDOI
Systems of Differential Algebraic Equations in Computational Electromagnetics
TL;DR: In this article, a survey of the most common approximations and formulations with a focus on their structural properties is presented, and the differential-algebraic character is discussed and quantified by the differential index concept.
Journal ArticleDOI
Subdomain Perturbation Finite-Element Method for Quasi-static Darwin Approximation
TL;DR: In this paper, the authors combine the Darwin finite element (FE) formulation with the subdomain perturbation (SDP) strategy to solve magneto and electroquasi-static problems.
Journal ArticleDOI
Finite Element Implementation of the Generalized-Lorenz Gauged A- $\Phi $ Formulation for Low-Frequency Circuit Modeling
TL;DR: In this paper, the generalized-Lorenz-gauged A-Phi$ (A-PHI$) formulation was proposed. But, the A-PHi$ formulation is not suitable for low-frequency circuit problems.
Journal ArticleDOI
Rigorous dc Solution of Partial Element Equivalent Circuit Models Including Conductive, Dielectric, and Magnetic Materials
Daniele Romano,Ivana Kovacevic-Badstubner,Mauro Parise,Ulrike Grossner,Jonas Ekman,Giulio Antonini +5 more
TL;DR: In this article, a rigorous derivation of the dc solution of three-dimensional partial element equivalent circuit (PEEC) formulation extended to include simultaneously conductive, dielectric, and magnetic materials is presented.
Journal ArticleDOI
Frequency-Stable Full Maxwell in Electro-quasistatic Gauge
Jörg Ostrowski,Ralf Hiptmair +1 more
TL;DR: The electro-quasistatic approximation of the Maxwell equations is commonly used to model coupled resistive/capacitive phenomena at low frequencies as discussed by the authors, but it neglects induction and becomes unstable in the sta...
References
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Journal ArticleDOI
Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements
TL;DR: Application of the new vector finite elements to the solution of a parallel-plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient, but further tests reveal that the optimum balance of the gradient and rotational components is problem-dependent.
Journal ArticleDOI
Solution of three dimensional eddy current problems by integral and differential methods
TL;DR: In this paper, a differential T, Omega formulation using nonconformal elements is presented, and the results obtained with this formulation for different treatments of the boundary conditions at infinity are shown and compared among themselves and with respect to a T integral formulation.
Journal ArticleDOI
A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes
TL;DR: A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes is presented, designed such that higher order basis functions vanish when they are projected onto a lower order finite-element space using the interpolation operator defined by Nedelec.
Journal ArticleDOI
p-Type multiplicative Schwarz (pMUS) method with vector finite elements for modeling three-dimensional waveguide discontinuities
Jin-Fa Lee,Din-Kow Sun +1 more
TL;DR: In this article, a p-type multiplicative Schwarz (pMUS) method was proposed for solving three-dimensional waveguide discontinuity problems, which used hierarchical curl-conforming basis functions that incorporated a discrete Hodge decomposition explicitly and treated each polynomial space as an abstract grid/domain in the Schwarz method.
Journal ArticleDOI
A Robust Maxwell Formulation for All Frequencies
TL;DR: In this article, a unified method for the stable numerical solution of the time-harmonic Maxwell's equations for any frequency is presented, based on an extended variational formulation of the full linear equations.