Homogenization of Quasi-static Maxwell's Equations

  title={Homogenization of Quasi-static Maxwell's Equations},
  author={Xue Jiang and Weiying Zheng},
  journal={Multiscale Model. Simul.},
This paper studies the homogenization of quasi-static and nonlinear Maxwell's equations in grain-oriented (GO) silicon steel laminations. GO silicon steel laminations have multiple scales, and the ratio of the largest scale to the smallest scale can be up to $10^6$. Direct solution of three-dimensional nonlinear Maxwell's equations is very challenging and unrealistic for large electromagnetic devices. Based on the magnetic vector potential and the magnetic field, respectively, we propose two… 
Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type
Solvability of nonlinear partial differential systems involving the operator curl depends on the nature of nonlinearity of the equations and the type of the boundary conditions, and very often
Finite Element Methods For Wave Propagation With Debye Polarization In Nonlinear Dielectric Materials
In this paper, we consider the wave propagation with Debye polarization in nonlinear dielectric materials. For this model, the Rother's method is employed to derive the well-posedness of the
General Magneto-Static Model.
In this paper we study a nonlinear magneto-static model on a general domain which is multiply-connected and has $m$ holes, and under a nonlinear relation between magnetic induction $\bold B$ and
Eddy Current Model for Nondestructive Evaluation with Thin Cracks
The convergence of the approximate solution to the solution of the original eddy current problem is proved as the thickness of cracks tends to zero, and an error estimate is presented for homogeneous conducting materials.
On the Magneto-Heat Coupling Model for Large Power Transformers
This paper studies the magneto-heat coupling model which describes iron loss of conductors and energy exchange between magnetic field and Ohmic heat. The temperature influences Maxwell’s equations
The toolbox PHG and its applications
The main modules and some core algorithms of PHG are described, and some parallel applications based on PHG, including the computation of iron-loss for large power transformers, simulation of ionic transport in ion channels, parasitic extraction of interconnects in integrated circuits, ice sheet simulation, and spectral element simulation of elastic waves with PML, are introduced.


An Efficient Eddy Current Model for Nonlinear Maxwell Equations with Laminated Conductors
A new eddy current model for the nonlinear Maxwell equations with laminated conductors is proposed that avoids very fine or very anisotropic mesh in coating films and can reduce computations greatly in computing 3D eddy currents.
A Justification of Eddy Currents Model for the Maxwell Equations
It is shown that the eddy currents model approximates the full Maxwell system up to the second order with respect to the frequency if and only if an additional condition on the current source is fulfilled and otherwise it is a first-order approximation to the Maxwell equations.
A time-domain homogenization technique for laminated iron cores in 3-D finite-element models
The authors present a novel time-domain homogenization technique for laminated iron cores in three-dimensional (3-D) FE models of electromagnetic devices when using the magnetic vector potential
A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models
The authors present a novel nonlinear homogenization technique for laminated iron cores in three-dimensional (3-D) finite-element (FE) models of electromagnetic devices. The technique takes into
Multiscale Asymptotic Method for Maxwell's Equations in Composite Materials
The determination of higher-order correctors and the explicit convergence rate for the approximate solutions are determined and the multiscale finite element method is presented and the convergence result is derived.
Analysis of multilevel methods for eddy current problems
Analysis of those nodal multilevel decompositions of the spaces of edge finite elements that form the foundation of the multigrid methods provides a significant extension of the existing theory to the case of locally vanishing coefficients and nonconvex domains.
An Inner-Constrained Separation Technique for 3-D Finite-Element Modeling of Grain-Oriented Silicon Steel Laminations
Grain-oriented (GO) silicon steel laminations are widely used in iron cores and shielding structures of power equipments. When the leakage magnetic flux is very strong and enters the lamination plane
Nonlinear Homogenization Technique for Saturable Soft Magnetic Composites
This paper presents a mathematical homogenization technique able to handle fine periodic structures in presence of magnetic saturable/hysteretic media. The modeling approach, based on the multiple
Equivalent Permeability of Step-Lap Joints of Transformer Cores: Computational and Experimental Considerations
The paper develops an efficient computational method for establishing equivalent characteristics of magnetic joints of transformer cores, with special emphasis on step-lap design. By introducing an