Adaptive local multigrid methods for solving time-harmonic eddy-current problems

Oliver Sterz; Andreas Hauser; Gabriel Wittum

doi:10.1109/TMAG.2005.859064

Adaptive local multigrid methods for solving time-harmonic eddy-current problems

Oliver Sterz^*, Andreas Hauser, Gabriel Wittum

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive multi-grid scheme for time-harmonic eddy currents. Numerical experiments show that the standard multigrid scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.

Original language	English (US)
Pages (from-to)	309-318
Number of pages	10
Journal	IEEE Transactions on Magnetics
Volume	42
Issue number	2
DOIs	https://doi.org/10.1109/TMAG.2005.859064
State	Published - Feb 2006
Externally published	Yes

Keywords

Adaptive mesh-refinement
Eddy currents
Edge elements
Finite-element methods
Frequency domain
Local multigrid methods
Red-green refinement

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Electrical and Electronic Engineering

Access to Document

10.1109/TMAG.2005.859064

Cite this

@article{80637ba1e5144ee7929012bc95e7f38b,

title = "Adaptive local multigrid methods for solving time-harmonic eddy-current problems",

abstract = "The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive multi-grid scheme for time-harmonic eddy currents. Numerical experiments show that the standard multigrid scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.",

keywords = "Adaptive mesh-refinement, Eddy currents, Edge elements, Finite-element methods, Frequency domain, Local multigrid methods, Red-green refinement",

author = "Oliver Sterz and Andreas Hauser and Gabriel Wittum",

year = "2006",

month = feb,

doi = "10.1109/TMAG.2005.859064",

language = "English (US)",

volume = "42",

pages = "309--318",

journal = "IEEE Transactions on Magnetics",

issn = "0018-9464",

publisher = "Institute of Electrical and Electronics Engineers",

number = "2",

}

TY - JOUR

T1 - Adaptive local multigrid methods for solving time-harmonic eddy-current problems

AU - Sterz, Oliver

AU - Hauser, Andreas

AU - Wittum, Gabriel

PY - 2006/2

Y1 - 2006/2

N2 - The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive multi-grid scheme for time-harmonic eddy currents. Numerical experiments show that the standard multigrid scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.

AB - The efficient computation of large eddy-current problems with finite elements requires adaptive methods and fast optimal iterative solvers such as multigrid methods. This paper provides an overview of the most important implementation aspects of an adaptive multi-grid scheme for time-harmonic eddy currents. Numerical experiments show that the standard multigrid scheme can be modified to yield an O(N) complexity even for general adaptive refinement strategies, where the number of unknowns N can grow slowly from one to the next refinement level. Algorithmic details and numerical examples are given.

KW - Adaptive mesh-refinement

KW - Eddy currents

KW - Edge elements

KW - Finite-element methods

KW - Frequency domain

KW - Local multigrid methods

KW - Red-green refinement

UR - http://www.scopus.com/inward/record.url?scp=31344457278&partnerID=8YFLogxK

U2 - 10.1109/TMAG.2005.859064

DO - 10.1109/TMAG.2005.859064

M3 - Article

AN - SCOPUS:31344457278

SN - 0018-9464

VL - 42

SP - 309

EP - 318

JO - IEEE Transactions on Magnetics

JF - IEEE Transactions on Magnetics

IS - 2

ER -

Adaptive local multigrid methods for solving time-harmonic eddy-current problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this