Publication
Reducing the ill conditioning in the method of fundamental solutions
| dc.contributor.author | Antunes, Pedro R. S. | |
| dc.date.accessioned | 2018-02-22T14:55:02Z | |
| dc.date.available | 2019-02-01T01:30:18Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | The method of fundamental solutions (MFS) is a meshless method for solving boundary value problems with some partial differential equations. It allows to obtain highly accurate approximations for the solutions assuming that they are smooth enough, even with small matrices. As a counterpart, the (dense) matrices involved are often ill-conditioned which is related to the well known uncertainty principle stating that it is impossible to have high accuracy and good conditioning at the same time. In this work, we propose a technique to reduce the ill conditioning in the MFS, assuming that the source points are placed on a circumference of radius R. The idea is to apply a suitable change of basis that provides new basis functions that span the same space as the MFS’s, but are much better conditioned. In the particular case of circular domains, the algorithm allows to obtain errors close to machine precision, with condition numbers of order O(1), independently of the number of points sources and R. | pt_PT |
| dc.description.sponsorship | The research was partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific project PTDC/MAT-CAL/4334/2014. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | 10.1007/s10444-017-9548-6 | pt_PT |
| dc.identifier.issn | 1019-7168 (Print) | |
| dc.identifier.issn | 1572-9044 (Online) | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/7172 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer Verlag | pt_PT |
| dc.subject | Laplace equation | pt_PT |
| dc.subject | Method of fundamental solutions | pt_PT |
| dc.subject | Ill Conditioning | pt_PT |
| dc.title | Reducing the ill conditioning in the method of fundamental solutions | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-CAL%2F4334%2F2014/PT | |
| oaire.citation.endPage | 365 | pt_PT |
| oaire.citation.startPage | 351 | pt_PT |
| oaire.citation.title | Advances in Computational Mathematics | pt_PT |
| oaire.citation.volume | Vol. 44, Nº1 | pt_PT |
| oaire.fundingStream | 3599-PPCDT | |
| person.familyName | Antunes | |
| person.givenName | Pedro | |
| person.identifier.ciencia-id | 6710-138C-A69D | |
| person.identifier.orcid | 0000-0003-1969-1860 | |
| person.identifier.rid | M-2406-2015 | |
| person.identifier.scopus-author-id | 55346859100 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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