A QR Accelerated Volume-to-Surface Boundary Condition for the Finite-Element Solution of Eddy-Current Problems

Author

White, Daniel A. ; Fasenfest, Benjamin J. ; Rieben, Robert N. ; Stowell, Mark L.

Author_Institution

Defense Sci. Eng. Div., Lawrence Livermore Nat. Lab., CA

Volume

43

Issue

5

fYear

2007

fDate

5/1/2007 12:00:00 AM

Firstpage

1920

Lastpage

1933

Abstract

We are concerned with the solution of time-dependent electromagnetic eddy-current problems using a finite-element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. To meet this requirement, we propose a volume-to-surface boundary condition based on the Biot-Savart law. We found the Biot-Savart approach to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretized Biot-Savart law

Keywords

computational electromagnetics; eddy currents; finite element analysis; Biot-Savart law; air-vacuum regions; conductor boundaries; eddy current problems; finite element solutions; three-dimensional unstructured meshes; time-dependent electromagnetic eddy current problems; volume-to-surface boundary condition; Acceleration; Boundary conditions; Computational electromagnetics; Conductivity; Conductors; Finite element methods; Magnetic separation; Magnetostatics; Maxwell equations; Space charge; Biot–Savart law; Maxwell´s equations; computational electromagnetics; eddy currents; electromagnetic diffusion; low-rank approximation; parallel processing;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2006.889766

Filename

4156297