New nonlinear algorithms for finite element analysis of 2D and 3D magnetic fields

Brauer, J.R.; Larkin, L.A.; MacNeal, B.E.; Ruehl, J.J.

doi:10.1063/1.348171

Cited by 3 publications

(6 citation statements)

References 3 publications

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“…The div A also decreases with increasing values for the penalty parameter. Figure 37 shows that the values of the electric ÿeld along a line parallel to theê 1 will over constrain the solution, and force it to be zero everywhere. Moreover, with the use of reduced integration, large penalty parameters lead to ill-conditioned matrices.…”

Section: Wave Propagation In a Cubementioning

confidence: 98%

“…where D 0 is related to E 0 = − grad˙ 0 , and hence˙ 0 , via the constitutive law (5) 1 . The boundary @ =: h˙ 0 ∪ g˙ 0 , where h˙ 0 is the part of the boundary on which the D 0 ·n ÿeld is speciÿed, and g˙ 0 is the remaining part of the boundary on which˙ 0 is speciÿed.…”

Section: The Electrostatic Problemsmentioning

confidence: 99%

“…Consider a device represented by the volume in Figure 8. If the applied voltage between surfaces (@ ) (1) and (@ ) (2) is represented by the complex quantity V , and the induced current is represented by I , the net power in the system is given by…”

Section: 23mentioning

confidence: 99%

“…Flow of current through a volume . A voltage is imposed at surfaces (@ ) (1) and (@ ) (2) . There is no current owing out of the other four sides, i.e.…”

Section: 23mentioning

confidence: 99%

“…where the solution vector { ˙ 0 } and the 'mass' matrix M are deÿned in Section 3.3. The capacitive energy in the circuit is equal to 1 2 CV 2 . The capacitance C is deÿned to be…”

Section: Static Problemmentioning

confidence: 99%

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Finite element analysis of advanced multilayer capacitors

Vu‐Quoc

Srinivas

Zhai

2003

Numerical Meth Engineering

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SUMMARYWe establish a systematic methodology to design and analyse electromagnetic components such as advanced multilayer ceramic capacitors (MLCCs) using the ÿnite element (FE) method. We employ a coupled formulation to compute the interaction between the electric and magnetic ÿelds. Unlike a linear distribution of current assumed in the circuit model, an accurate electrostatic solution to model the entire advanced MLCCs (4 × 4 × 27 = 432 cells) is presented. The FE solution is used to compute the lumped parameters for a range of frequencies. These lumped parameters are then used to compute the parasitic elements of the MLCCs. We introduce two algorithms to e ciently analyse the behaviour of a capacitor with changing frequency. The lower frequency (much below the selfresonant frequency of the capacitor) algorithm separates the e ect of the electric and magnetic ÿelds and reduces the computational e ort required to solve the FE problem, whereas, the high-frequency algorithm couples the e ect between the electric and the magnetic ÿelds. We use these algorithms in conjunction with a new multiple scale technique to e ectively determine the small values of R, L and C in MLCCs. The formulation, the implementation, and the numerical results demonstrate the e cacy of the present FE formulation and establish a systematic methodology to design and analyse advanced electromagnetic components.

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Section: Wave Propagation In a Cubementioning

confidence: 98%

Section: The Electrostatic Problemsmentioning

confidence: 99%

Section: 23mentioning

confidence: 99%

“…Flow of current through a volume . A voltage is imposed at surfaces (@ ) (1) and (@ ) (2) . There is no current owing out of the other four sides, i.e.…”

Section: 23mentioning

confidence: 99%

“…where the solution vector { ˙ 0 } and the 'mass' matrix M are deÿned in Section 3.3. The capacitive energy in the circuit is equal to 1 2 CV 2 . The capacitance C is deÿned to be…”

Section: Static Problemmentioning

confidence: 99%

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