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Integral equation methods for elliptic problems with boundary conditions of mixed type

Helsing, Johan LU (2009) In Journal of Computational Physics 228(23). p.8892-8907
Abstract
Laplace’s equation with mixed boundary conditions, that is, Dirichlet conditions on parts of the boundary and Neumann conditions on the remaining contiguous parts, is solved on an interior planar domain using an integral equation method. Rapid execution and high accuracy is obtained by combining equations which are of Fredholm’s second kind with compact operators on almost the entire boundary with a recursive compressed inverse preconditioning technique. Then an elastic problem with mixed boundary conditions is formulated and solved in an analogous manner and with similar results. This opens up for the rapid and accurate solution of several elliptic problems of mixed type.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Second kind integral equation, Elasticity, Mixed boundary value problem, Potential theory
in
Journal of Computational Physics
volume
228
issue
23
pages
8892 - 8907
publisher
Elsevier
external identifiers
  • wos:000271671100021
  • scopus:70349745702
ISSN
0021-9991
DOI
10.1016/j.jcp.2009.09.004
language
English
LU publication?
yes
id
17f5a795-89bd-4983-8158-5f2b134a2c39 (old id 1487788)
alternative location
http://www.maths.lth.se/na/staff/helsing/JCP09b.pdf
date added to LUP
2009-10-14 09:48:14
date last changed
2017-11-19 03:37:41
@article{17f5a795-89bd-4983-8158-5f2b134a2c39,
  abstract     = {Laplace’s equation with mixed boundary conditions, that is, Dirichlet conditions on parts of the boundary and Neumann conditions on the remaining contiguous parts, is solved on an interior planar domain using an integral equation method. Rapid execution and high accuracy is obtained by combining equations which are of Fredholm’s second kind with compact operators on almost the entire boundary with a recursive compressed inverse preconditioning technique. Then an elastic problem with mixed boundary conditions is formulated and solved in an analogous manner and with similar results. This opens up for the rapid and accurate solution of several elliptic problems of mixed type.},
  author       = {Helsing, Johan},
  issn         = {0021-9991},
  keyword      = {Second kind integral equation,Elasticity,Mixed boundary value problem,Potential theory},
  language     = {eng},
  number       = {23},
  pages        = {8892--8907},
  publisher    = {Elsevier},
  series       = {Journal of Computational Physics},
  title        = {Integral equation methods for elliptic problems with boundary conditions of mixed type},
  url          = {http://dx.doi.org/10.1016/j.jcp.2009.09.004},
  volume       = {228},
  year         = {2009},
}