Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning
(2008) In Journal of Computational Physics 227(20). p.8820-8840- Abstract
- We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners... (More)
- We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of 10-12. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 10-14. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1223893
- author
- Helsing, Johan LU and Ojala, Rikard LU
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Corner singularity Multiphase material Triple-junction Integral equation Mesh grading Conductivity
- in
- Journal of Computational Physics
- volume
- 227
- issue
- 20
- pages
- 8820 - 8840
- publisher
- Elsevier
- external identifiers
-
- wos:000260267700005
- scopus:50249139169
- ISSN
- 0021-9991
- DOI
- 10.1016/j.jcp.2008.06.022
- 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
- 299477ff-86b0-48e5-92bd-3dd67cca0d37 (old id 1223893)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/JCP08b.pdf
- date added to LUP
- 2016-04-01 12:14:48
- date last changed
- 2022-01-27 00:55:18
@article{299477ff-86b0-48e5-92bd-3dd67cca0d37,
abstract = {{We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, mixed, and tested on some familiar problems in materials science. The recursive compressed inverse preconditioning, the major novelty of the paper, turns out to be particularly powerful and, when it applies, eliminates the need for mesh grading completely. In an electrostatic example for a multiphase granular material with about two thousand corners and triple junctions and a conductivity ratio between phases up to a million we compute a common functional of the solution with an estimated relative error of 10-12. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 10-14.}},
author = {{Helsing, Johan and Ojala, Rikard}},
issn = {{0021-9991}},
keywords = {{Corner singularity Multiphase material Triple-junction Integral equation Mesh grading Conductivity}},
language = {{eng}},
number = {{20}},
pages = {{8820--8840}},
publisher = {{Elsevier}},
series = {{Journal of Computational Physics}},
title = {{Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning}},
url = {{https://lup.lub.lu.se/search/files/2843793/3878574.pdf}},
doi = {{10.1016/j.jcp.2008.06.022}},
volume = {{227}},
year = {{2008}},
}