Error analysis in finite element models of electromagnetic fields

Biddlecombe, C.S.; Simkin, J.; Trowbridge, C.W.

doi:10.1109/tmag.1986.1064456

Cited by 29 publications

(7 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In presence of material discontinuities with corners, errors can arise in the solution derivatives, as stated in [18]. Anyway, this problem can be satisfactorily overcome by adopting a suitable fine mesh in the corner regions, which allows the achievement of the requested precision [19].…”

Section: Electromagnetic Field Problemmentioning

confidence: 99%

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

Bottauscio¹,

Chiampi²,

Manzin³

2008

Applied Mathematical Modelling

View full text Add to dashboard Cite

The electromagnetic diffusion and the electromechanical phenomena arising in a solid cylinder rotating inside a magnetic field are here analyzed. The study is developed through a time stepping Finite Element voltage-driven formulation, employing the sliding mesh technique for handling the cylinder motion. The influence on the dynamic behavior and energy dissipation of the material electric and magnetic properties, the geometrical parameters and the supply conditions is investigated considering a model problem.

show abstract

Section: Electromagnetic Field Problemmentioning

confidence: 99%

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

Bottauscio¹,

Chiampi²,

Manzin³

2008

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…In principle, the error could be estimated by a finite element approximation of problem (20). In order to ascertain whether this would be a good method, in practice, let us investigate about its computational cost.…”

Section: Error Estimationmentioning

confidence: 99%

“…In fact, if w is taken in the nth-order finite element space, uL exactly satisfies (6), so that (11) equals zero and no driving term survives in (20) except r " , which however, gives zero values for all the degrees of freedom of the nth-order finite element space concerning the boundary. Thus, the computational cost of the error estimation through (20) is comparable to that one of finding the finite element approximation uL . Notice that the estimated error so obtained would be equal to the difference between the finite element approximations by elements of order n#1 and n, respectively.…”

Section: Error Estimationmentioning

confidence: 99%

“…In order to reduce the computational cost of the error estimation, a problem roughly satisfied by the error separately in each element can be derived from (20). To this aim the integrals are again split and equation (20) is rewritten as…”

Section: Error Estimationmentioning

confidence: 99%

“…Another of the more heuristic methods we tried, estimates the error by computing the integral over the element of the difference between the nodally interpolated fields and the element constant fields [12,13,15,20,21]. Some of the estimators currently used are still based essentially on the same idea [18,22,23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adaptive finite element analysis of 2-D static and steady-state electromagnetic problems

Fernandes

Girdinio

1999

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

SUMMARYThe adaptive finite element methods developed by the authors for a class of 2-D problems in computational electromagnetics are presented. The cases covered are: magnetostatic, electrostatic, DC conduction and linear AC steady-state eddy currents, both plane and axialsymmetric. Theory is developed in the linear case only, but the resulting methods are applied on a heuristic basis also to non-linear cases and prove able to cope with them. These methods make use of an element-by-element error estimation and two different h-refinement techniques to adapt meshes made up of first or second-order triangular elements. Element-byelement error estimation has two main advantages: it is well suited to cope with the intricate geometries of electromagnetic devices and, at the same time, very cheap from a computational viewpoint. The local error is estimated by approximately solving a differential problem in each element. Theory on which this error estimation method is grounded is developed in full details and the underlying assumptions are pointed out. The presence in electromagnetic problems of surface currents and interfaces between different materials poses new problems in the error estimation with respect to other applications in which similar methods are used. The h-refinement technique can be selected between the bisection method and the centroid method followed by a Delaunay step. Accuracy and efficiency of the proposed method is discussed on the basis of previous work of the authors and further numerical experiments. Applications to realistic models showing good performances of the proposed methods are reported.

show abstract

Local error indicator in finite element analysis of Laplacian fields based on the green integration formula

Adamiak

1992

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe paper presents a simple and practical method for the local error assessment in the finite element solution of fields in linear media governed by the Laplace equation. The local error is estimated for each node or element of the mesh model by applying the Green integration formula, with the error distribution being used for the adaptive mesh refinement. Several alternatives of the local error estimation algorithm are compared and numerical examples are given for a typical %' -section potential problem. These confirm the efficiency of the proposed method.

show abstract

Error analysis in finite element models of electromagnetic fields

Cited by 29 publications

References 3 publications

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

Adaptive finite element analysis of 2-D static and steady-state electromagnetic problems

Local error indicator in finite element analysis of Laplacian fields based on the green integration formula

Contact Info

Product

Resources

About