Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary

Qiang Du; Xiaonan Wu

doi:10.1137/S0036142997330317

Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary

Qiang Du^*, Xiaonan Wu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

2 Downloads (Pure)

Abstract

For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg-Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain. Approximations of these boundary conditions with high accuracy are given, and their convergence properties are examined. Error estimates are derived for the finite element approximations with the approximate boundary conditions.

Original language	English
Pages (from-to)	1482-1506
Number of pages	25
Journal	SIAM Journal on Numerical Analysis
Volume	36
Issue number	5
DOIs	https://doi.org/10.1137/S0036142997330317
Publication status	Published - Sept 1999

Scopus Subject Areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Artificial boundary
Convergence
Finite element method
Ginzburg-Landau equations
H and l error estimates
Superconductivity
Unbounded domain

Access to Document

10.1137/S0036142997330317

Full TextFinal published version, 1.34 MB

Cite this

@article{7a8d3dcd9b354bbeb8bc6dd1d5b3e435,

title = "Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary",

abstract = "For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg-Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain. Approximations of these boundary conditions with high accuracy are given, and their convergence properties are examined. Error estimates are derived for the finite element approximations with the approximate boundary conditions.",

keywords = "Artificial boundary, Convergence, Finite element method, Ginzburg-Landau equations, H and l error estimates, Superconductivity, Unbounded domain",

author = "Qiang Du and Xiaonan Wu",

note = "Funding information: Department of Mathematics, Iowa State University, Ames, IA 50011, and Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (madu@uxmail.ust.hk). The research of this author was supported in part by NSF grant MS-9500718 and in part by a grant from HKRGC. * Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (xwu@hkbu.edu.hk). The work of this author was supported in part by the FRG grant of Hong Kong Baptist University. Publisher copyright: Copyright {\textcopyright} 1999 Society for Industrial and Applied Mathematics",

year = "1999",

month = sep,

doi = "10.1137/S0036142997330317",

language = "English",

volume = "36",

pages = "1482--1506",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "5",

}

TY - JOUR

T1 - Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary

AU - Du, Qiang

AU - Wu, Xiaonan

N1 - Funding information: Department of Mathematics, Iowa State University, Ames, IA 50011, and Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (madu@uxmail.ust.hk). The research of this author was supported in part by NSF grant MS-9500718 and in part by a grant from HKRGC. * Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong (xwu@hkbu.edu.hk). The work of this author was supported in part by the FRG grant of Hong Kong Baptist University. Publisher copyright: Copyright © 1999 Society for Industrial and Applied Mathematics

PY - 1999/9

Y1 - 1999/9

N2 - For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg-Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain. Approximations of these boundary conditions with high accuracy are given, and their convergence properties are examined. Error estimates are derived for the finite element approximations with the approximate boundary conditions.

AB - For three-dimensional simulations of the vortex phenomena in superconductors based on the Ginzburg-Landau (GL) theory, the physical variables must be solved in the whole space in general. Exact boundary conditions on an artificial boundary are discussed to reformulate the problem in a finite domain. Approximations of these boundary conditions with high accuracy are given, and their convergence properties are examined. Error estimates are derived for the finite element approximations with the approximate boundary conditions.

KW - Artificial boundary

KW - Convergence

KW - Finite element method

KW - Ginzburg-Landau equations

KW - H and l error estimates

KW - Superconductivity

KW - Unbounded domain

UR - http://www.scopus.com/inward/record.url?scp=0042230440&partnerID=8YFLogxK

U2 - 10.1137/S0036142997330317

DO - 10.1137/S0036142997330317

M3 - Journal article

AN - SCOPUS:0042230440

SN - 0036-1429

VL - 36

SP - 1482

EP - 1506

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 5

ER -

Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary

Abstract

Scopus Subject Areas

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this