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Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method

Helsing, Johan LU orcid and Wadbro, E (2005) In Journal of Computational Physics 202(2). p.391-410
Abstract
Mikhlin's method for solving Laplace's equation in domains exterior to a number of closed contours is discussed with particular emphasis on the Dirichlet-Neutnann map. In the literature there already exit tyro computational modes for Mikhlin's method. Here a new mode is presented. The new mode is at least as stable as the previous modes. Furthermore, its computational complexity in the number of closed contours is better. As a result. highly. accurate solutions in domains exterior to tens of thousands of closed contours can be obtained on a simple workstation.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
fast solvers, integral equation, multiply connected domains, Laplace's equation, exterior problem, Dirichlet-Neumann map
in
Journal of Computational Physics
volume
202
issue
2
pages
391 - 410
publisher
Academic Press
external identifiers
  • wos:000225741800001
  • scopus:10244259131
ISSN
0021-9991
DOI
10.1016/j.jcp.2004.06.024
project
Harmonic Analysis and Applications
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
de2344fd-dc9a-47ff-9475-beca85b0c2be (old id 258453)
date added to LUP
2016-04-01 11:36:28
date last changed
2026-02-02 11:02:44
@article{de2344fd-dc9a-47ff-9475-beca85b0c2be,
  abstract     = {{Mikhlin's method for solving Laplace's equation in domains exterior to a number of closed contours is discussed with particular emphasis on the Dirichlet-Neutnann map. In the literature there already exit tyro computational modes for Mikhlin's method. Here a new mode is presented. The new mode is at least as stable as the previous modes. Furthermore, its computational complexity in the number of closed contours is better. As a result. highly. accurate solutions in domains exterior to tens of thousands of closed contours can be obtained on a simple workstation.}},
  author       = {{Helsing, Johan and Wadbro, E}},
  issn         = {{0021-9991}},
  keywords     = {{fast solvers; integral equation; multiply connected domains; Laplace's equation; exterior problem; Dirichlet-Neumann map}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{391--410}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Computational Physics}},
  title        = {{Laplace's equation and the Dirichlet-Neumann map: a new mode for Mikhlin's method}},
  url          = {{https://lup.lub.lu.se/search/files/2557987/3878577.pdf}},
  doi          = {{10.1016/j.jcp.2004.06.024}},
  volume       = {{202}},
  year         = {{2005}},
}