Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning
(2008) In Journal of Computational Physics 227(20). p.88208840 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 nonstandard 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 nonstandard 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 1012. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 1014. (Less)
Please use this url to cite or link to this publication:
http://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 Triplejunction 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
 00219991
 DOI
 10.1016/j.jcp.2008.06.022
 language
 English
 LU publication?
 yes
 id
 299477ff86b048e592bd3dd67cca0d37 (old id 1223893)
 alternative location
 http://www.maths.lth.se/na/staff/helsing/JCP08b.pdf
 date added to LUP
 20081006 16:29:59
 date last changed
 20171001 03:50:46
@article{299477ff86b048e592bd3dd67cca0d37, 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 nonstandard 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 1012. In another example, five times as large but with a conductivity ratio of only a hundred, we achieve an estimated relative error of 1014.}, author = {Helsing, Johan and Ojala, Rikard}, issn = {00219991}, keyword = {Corner singularity Multiphase material Triplejunction Integral equation Mesh grading Conductivity}, language = {eng}, number = {20}, pages = {88208840}, publisher = {Elsevier}, series = {Journal of Computational Physics}, title = {Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning}, url = {http://dx.doi.org/10.1016/j.jcp.2008.06.022}, volume = {227}, year = {2008}, }