A generalized tree-cotree gauge for magnetic field computation

Manges, John; Cendes, Z.J.

doi:10.1109/20.376275

Cited by 91 publications

(67 citation statements)

References 6 publications

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“…For homogeneous medium, (16) and (17) reduce to (12) and (13) when we choose α = 1 in (18), which reduces to the simple Lorenz gauge. Unlike the vector wave equations for inhomogeneous electromagnetic fields, the above do not have the apparent low-frequency breakdown difficulty when ∂ t = 0.…”

Section: Pertinent Equations-inhomogeneous Isotropic Casementioning

confidence: 99%

“…Therefore, the E-H formulation is not truly multi-scale, but exhibits catastrophic breakdown when the dimensions of objects become much smaller than the local wavelength. Different formulations using tree-cotree, or loop-tree decomposition [12][13][14][15][16], have to be sought when the frequency is low or the wavelength is long. Due to the low-frequency catastrophe encountered by E-H formulation, the vector potential formulation has become popular for solving low frequency problems [17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

122

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Abstract-The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic solutions that straddle both the quantum and classical physics regimes. The vector potential formulation using A and Φ (or A-Φ formulation) is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetics problems in inhomogenous media that can be extended to the anistropic case. An advantage of the resulting equations is their absence of catastrophic breakdown at low-frequencies. Hence, the usual differential equation solvers can be used to solve them over a wide range of scales and bandwidth. It is shown that the interface boundary conditions from the resulting equations reduce to those of classical Maxwell's equations. Also, the classical Green's theorem can be extended to such a formulation, resulting in an extinction theorem and a surface equivalence principle similar to the classical case. Moreover, surface integral equation formulations can be derived for piecewise homogeneous scatterers. Furthermore, the integral equations neither exhibit the low-frequency catastrophe nor the frequency imbalance observed in the classical formulation using E-H fields. The matrix representation of the integral equation for a PEC (perfect electric conductor) scatterer is given.

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Section: Pertinent Equations-inhomogeneous Isotropic Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Chew¹

2014

PIER

122

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“…The voltage across the admittance of the branch N p,q will create conduction and displacement currents in the branch N i,j . Following a similar derivation as when establishing (15), it is possible to find an expression for the magnetic flux …”

Section: Branch Equations For Edge Element Modelsmentioning

confidence: 99%

“…Following similar logic, the edge model of an element with an electric field, expressed by (15) and (16), will be known as the conductance-capacitance or edge electric (EE).…”

Section: Branch Equations For Edge Element Modelsmentioning

confidence: 99%

“…In early publications about the implementations of EEM the solution algorithms were preceded by procedures to form additional equations to arrive at a well posed system. Several methods were put forward, for example a method utilising the tree of the graph constructed from element edges [13,15]. In the FM-EE and EM-FE models a well posed system will be accomplished by adding the conditions V=0 and Ω=0.…”

Section: Modelmentioning

confidence: 99%

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Network models of three-dimensional electromagnetic fields

Demenko¹,

Sykulski²

2008

IET 7th International Conference on Computation in Electromagnetics (CEM 2008)

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Tree-Cotree Decompositions for First-Order Complete Tangential Vector Finite Elements

Manges¹,

Cendes²

1997

Int. J. Numer. Meth. Engng.

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SUMMARYEdge-based finite elements have important applications in modelling both quasi-static and high-frequency electromagnetic problems. Recent work has demonstrated that formulations that exploit the graph structure of the edge-based finite element mesh may be extended to higher-order elements. This paper presents the details of how such an extension to a first-order complete finite element is accomplished and illustrates its application in two-dimensional magnetostatics.1997 by John Wiley & Sons, Ltd.

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A generalized tree-cotree gauge for magnetic field computation

Cited by 91 publications

References 6 publications

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Network models of three-dimensional electromagnetic fields

Tree-Cotree Decompositions for First-Order Complete Tangential Vector Finite Elements

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