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A robust and accurate solver of Laplace’s equation with general boundary conditions on general domains in the plane

Ojala, Rikard LU (2012) In Journal of Computational Mathematics 30(4). p.433-448
Abstract
A robust and general solver for Laplace’s equation on the interior of a simply connected

domain in the plane is described and tested. The solver handles general piecewise smooth

domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an

integral equation formulation of the problem. Difficulties due to changes in boundary

conditions and corners, cusps, or other examples of non-smoothness of the boundary are

handled using a recent technique called recursive compressed inverse preconditioning. The

result is a rapid and very accurate solver which is general in scope, its performance is

demonstrated via some challenging numerical tests.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Laplace's equation, Integral equations, mixed boundary conditions, Robin boundary conditions
in
Journal of Computational Mathematics
volume
30
issue
4
pages
433 - 448
publisher
Global Science Press
external identifiers
  • wos:000308511900007
  • scopus:84867069141
ISSN
0254-9409
DOI
10.4208/jcm.1201-m3644
language
English
LU publication?
yes
id
a79e8d43-9e26-48f5-91d8-19f629b80efb (old id 2971888)
alternative location
http://www.maths.lth.se/na/staff/helsing/LaplaceOjala.pdf
date added to LUP
2013-01-07 14:57:46
date last changed
2017-05-28 03:13:54
@article{a79e8d43-9e26-48f5-91d8-19f629b80efb,
  abstract     = {A robust and general solver for Laplace’s equation on the interior of a simply connected<br/><br>
domain in the plane is described and tested. The solver handles general piecewise smooth<br/><br>
domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an<br/><br>
integral equation formulation of the problem. Difficulties due to changes in boundary<br/><br>
conditions and corners, cusps, or other examples of non-smoothness of the boundary are<br/><br>
handled using a recent technique called recursive compressed inverse preconditioning. The<br/><br>
result is a rapid and very accurate solver which is general in scope, its performance is<br/><br>
demonstrated via some challenging numerical tests.},
  author       = {Ojala, Rikard},
  issn         = {0254-9409},
  keyword      = {Laplace's equation,Integral equations,mixed boundary conditions,Robin boundary conditions},
  language     = {eng},
  number       = {4},
  pages        = {433--448},
  publisher    = {Global Science Press},
  series       = {Journal of Computational Mathematics},
  title        = {A robust and accurate solver of Laplace’s equation with general boundary conditions on general domains in the plane},
  url          = {http://dx.doi.org/10.4208/jcm.1201-m3644},
  volume       = {30},
  year         = {2012},
}