| dc.contributor.author | Antunes, Pedro R. S. | |
| dc.date.accessioned | 2022-03-24T12:05:28Z | |
| dc.date.available | 2023-03-23T01:30:22Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and boundary conditions. The main drawback of the MFS is that the matrices involved typically are ill-conditioned and this may prevent to achieve high accuracy. In this work, we propose a new algorithm to remove the ill conditioning of the classical MFS in the context of Laplace equation defined in planar domains. The main idea is to expand the MFS basis functions in terms of harmonic polynomials. Then, using the singular value decomposition and Arnoldi orthogonalization we define well conditioned basis functions spanning the same functional space as the MFS's. Several numerical examples show that this approach is much superior to previous approaches, such as the classical MFS or the MFS-QR. | pt_PT |
| dc.description.sponsorship | The research was partially supported by FCT, Portugal, through the scientific project UIDB/00208/2020. | pt_PT |
| dc.description.version | info:eu-repo/semantics/acceptedVersion | pt_PT |
| dc.identifier.issn | 1017-1398 | |
| dc.identifier.issn | 1572-9265 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/11856 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer | pt_PT |
| dc.relation | Group of Mathematical Physics of the University of Lisbon | |
| dc.title | A well conditioned method of fundamental solutions for laplace equation | pt_PT |
| dc.type | preprint | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Group of Mathematical Physics of the University of Lisbon | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00208%2F2020/PT | |
| oaire.citation.title | Numerical Algorithms | pt_PT |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| 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 | openAccess | pt_PT |
| rcaap.type | preprint | pt_PT |
| relation.isAuthorOfPublication | bef314d2-4a78-4fba-aecd-9f4e8e19e70c | |
| relation.isAuthorOfPublication.latestForDiscovery | bef314d2-4a78-4fba-aecd-9f4e8e19e70c | |
| relation.isProjectOfPublication | a79ad082-93a2-48af-acd1-6c5f0fb42899 | |
| relation.isProjectOfPublication.latestForDiscovery | a79ad082-93a2-48af-acd1-6c5f0fb42899 |
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