Time-dependent Eddy Current Problem Research Articles

A–[formula omitted] finite element method with composite grids for time-dependent eddy current problem

We investigate the A–ϕ finite element method with the global coarse grids and the local fine grids (composite grids) for solving a time-dependent eddy current problem, which can improve the accuracy of the coarse grid solutions in some subdomains of interest in the case when properly increasing computational costs. Meanwhile, to decrease calculation complexity and avoid dealing with a saddle-point problem from the traditional A–ϕ scheme, we design an iteration which combines the composite grid method with classic steepest descent such that the solutions of the unknowns A and ϕ for the global coarse grids domain are decoupled in two separate equations. We prove it converges with a bounded rate independent of the mesh sizes.

Analysis of a FEM–BEM model posed on the conducting domain for the time-dependent eddy current problem

The three-dimensional eddy current time-dependent problem is considered. We formulate it in terms of two variables, one lying only on the conducting domain and the other on its boundary. We combine finite elements (FEM) and boundary elements (BEM) to obtain a FEM–BEM coupled variational formulation. We establish the existence and uniqueness of the solution in the continuous and the fully discrete case. Finally, we investigate the convergence order of the fully discrete scheme.

A FE/BE coupling for the 3D time-dependent eddy current problem. Part II: a posteriori error estimates and adaptive computations

The discontinuous Galerkin method in time for the coupling of conforming finite element and boundary element methods was established in Part I of this paper, where quasi-optimal a priori error estimates are provided. In the second part, we establish a posteriori error estimates and so justify an adaptive space/time-mesh refinement algorithm for the efficient numerical treatment of the time-dependent eddy current problem.

An E-based mixed FEM and BEM coupling for a time-dependent eddy current problem

An E-based mixed FEM and BEM coupling for a time-dependent eddy current problem

An 𝐸-based mixed formulation for a time-dependent eddy current problem

In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric fieldE\boldsymbol {E}. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nédélec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and prove error estimates.

An H-based FEM-BEM formulation for a time dependent eddy current problem

In this paper, we study a time-dependent eddy current problem posed in the whole space. We prove that the problem has a well-posed weak formulation. We also show that the latter formulation admits a well-posed saddle point structure when the constraint satisfied by the magnetic field in the dielectric medium is handled by means of a Lagrange multiplier. Furthermore, we provide a BEM-FEM formulation of the problem that leads to a semi-discrete Galerkin scheme based on Nédélec's edge elements and Raviart–Thomas elements. Finally, we analyze the asymptotic behavior of the error in terms of the mesh size parameter.

An Adaptive Finite Element Method for the H- ψ Formulation of Time-dependent Eddy Current Problems

In this paper, we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the H ? ? formulation of eddy current problems with multiply connected conductors. Multiply connected domains are considered by making cuts. The competitive performance of the method is demonstrated by an engineering benchmark problem, Team Workshop Problem 7, and a singular problem with analytic solution.

Finite Element Differential–Algebraic Systems for Eddy Current Problems

Finite element discretization of some time-dependent eddy current problems yields ordinary differential–algebraic systems with large sparse matrices. Properties and stability of these systems are analyzed for two classes of eddy current problems: (i) two-dimensional coupled field-circuit problems with arbitrary external circuit connections between conductors; (ii) “2.5-dimensional” problems characterized by axisymmetric geometry and non-axisymmetric excitation. Extension of the analysis to many other formulations of eddy current problems in 2D and 3D is straightforward.

A stability paradox for time-stepping schemes in coupled field-circuit problems

The finite element model for the time dependent eddy current problem is coupled with mesh (loop) equations for arbitrary external circuits. Stability of the resultant system and the time-stepping scheme is analyzed. The backward difference scheme is shown to be stable, while the Crank-Nicholson method exhibits peculiar instability. Theoretical analysis is supported by numerical results for test and practical problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A method for circuit connections in time-dependent eddy current problems

The authors consider eddy current diffusion problems in which the electromagnetic field is computed in 2-D but external circuit connections, between the conductors with eddy currents are taken into account. The approach combines conventional circuit analysis techniques with the integro-differential finite element formulation of the transient eddy current problem. Conductors with eddy currents are treated as circuit elements with terminal voltages implicitly defined by the field equations. A numerical example is presented to illustrate the proposed formulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear Transient Finite Element Field Computation for Electrical Machines and Devices

This paper describes the procedure for analyzing nonlinear transient electromagnetic phenomena in electrical machines and devices with the finite element method. Two time integration methods are used which are based on (1) an implicit forward difference scheme and (2) the Crank-Nicholson method. The quasilinearization of the nonlinear matrix equation is handled by a simple chord iteration method in the former and the Newton-Raphson scheme in the latter. The associated variational expressions for the time-dependent diffusion equation are obtained in terms of energy-related functionals. The paper includes illustrative examples of application of the methods to one-and two-dimensional time-dependent eddy current problems in a conducting slab, a rotating machine under asynchronous operation, and a three- phase bus-bar enclosure.