A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
Resumen:
In \cite{AcostaBorthagaray}, a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB finite element code for such a problem. The code is accompanied with a basic discussion of the theory relevant in the context. The main program is written in about 80 lines and can be easily modified to deal with other kernels as well as with time dependent problems. The present work fills a gap by providing an input for a large number of mathematicians and scientists interested in numerical approximations of solutions of a large variety of problems involving nonlocal phenomena in two-dimensional space.
| 2017 | |
| Este trabajo ha sido financiado parcialmente por CONICET, ANPCYT y UBA bajo las becas PIP 2014 1220130100034CO, PICT 2014-1771 y UBACYT 20020130100205BA | |
|
Finite elements Fractional Laplacian Nonlocal operators |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47832 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1875693216941998080 |
|---|---|
| author | Acosta, Gabriel |
| author2 | Bersetche, Francisco M. Borthagaray, Juan Pablo |
| author2_role | author author |
| author_facet | Acosta, Gabriel Bersetche, Francisco M. Borthagaray, Juan Pablo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Acosta Gabriel, Universidad de Buenos Aires, Argentina Bersetche Francisco M., Universidad de Buenos Aires, Argentina Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería. |
| dc.creator.none.fl_str_mv | Acosta, Gabriel Bersetche, Francisco M. Borthagaray, Juan Pablo |
| dc.date.accessioned.none.fl_str_mv | 2024-12-30T15:54:02Z |
| dc.date.available.none.fl_str_mv | 2024-12-30T15:54:02Z |
| dc.date.issued.none.fl_str_mv | 2017 |
| dc.description.abstract.none.fl_txt_mv | In \cite{AcostaBorthagaray}, a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB finite element code for such a problem. The code is accompanied with a basic discussion of the theory relevant in the context. The main program is written in about 80 lines and can be easily modified to deal with other kernels as well as with time dependent problems. The present work fills a gap by providing an input for a large number of mathematicians and scientists interested in numerical approximations of solutions of a large variety of problems involving nonlocal phenomena in two-dimensional space. |
| dc.description.es.fl_txt_mv | También publicado en Computers & Mathematics with Applications, vol. 74, no 4, 2017, pp 784-816. DOI: 10.1016/j.camwa.2017.05.026. |
| dc.description.sponsorship.none.fl_txt_mv | Este trabajo ha sido financiado parcialmente por CONICET, ANPCYT y UBA bajo las becas PIP 2014 1220130100034CO, PICT 2014-1771 y UBACYT 20020130100205BA |
| dc.format.extent.es.fl_str_mv | 46 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Acosta, G., Bersetche, F. y Borthagaray, J. A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2017, pp 1-46. arXiv:1610.05558v2. DOI: 10.48550/arXiv.1610.05558 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/47832 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.none.fl_str_mv | Mathematics. Numerical Analysis (math.NA), arXiv:1610.05558v2, may 2017, pp 1-46 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Finite elements Fractional Laplacian Nonlocal operators |
| dc.title.none.fl_str_mv | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | También publicado en Computers & Mathematics with Applications, vol. 74, no 4, 2017, pp 784-816. DOI: 10.1016/j.camwa.2017.05.026. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_ed6b0a4bac40767771d20f39bb82eaed |
| identifier_str_mv | Acosta, G., Bersetche, F. y Borthagaray, J. A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2017, pp 1-46. arXiv:1610.05558v2. DOI: 10.48550/arXiv.1610.05558 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/47832 |
| publishDate | 2017 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Acosta Gabriel, Universidad de Buenos Aires, ArgentinaBersetche Francisco M., Universidad de Buenos Aires, ArgentinaBorthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería.2024-12-30T15:54:02Z2024-12-30T15:54:02Z2017Acosta, G., Bersetche, F. y Borthagaray, J. A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2017, pp 1-46. arXiv:1610.05558v2. DOI: 10.48550/arXiv.1610.05558https://hdl.handle.net/20.500.12008/47832También publicado en Computers & Mathematics with Applications, vol. 74, no 4, 2017, pp 784-816. DOI: 10.1016/j.camwa.2017.05.026.In \cite{AcostaBorthagaray}, a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB finite element code for such a problem. The code is accompanied with a basic discussion of the theory relevant in the context. The main program is written in about 80 lines and can be easily modified to deal with other kernels as well as with time dependent problems. The present work fills a gap by providing an input for a large number of mathematicians and scientists interested in numerical approximations of solutions of a large variety of problems involving nonlocal phenomena in two-dimensional space.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2024-12-23T13:16:31Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) ABB17.pdf: 949394 bytes, checksum: 03fa9829ee3088d9022ba8ff9d71fdae (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2024-12-30T14:49:16Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) ABB17.pdf: 949394 bytes, checksum: 03fa9829ee3088d9022ba8ff9d71fdae (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-12-30T15:54:02Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) ABB17.pdf: 949394 bytes, checksum: 03fa9829ee3088d9022ba8ff9d71fdae (MD5) Previous issue date: 2017Este trabajo ha sido financiado parcialmente por CONICET, ANPCYT y UBA bajo las becas PIP 2014 1220130100034CO, PICT 2014-1771 y UBACYT 20020130100205BA46 p.application/pdfenengarXivMathematics. Numerical Analysis (math.NA), arXiv:1610.05558v2, may 2017, pp 1-46Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Finite elementsFractional LaplacianNonlocal operatorsA short FE implementation for a 2d homogeneous Dirichlet problem of a fractional LaplacianPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaAcosta, GabrielBersetche, Francisco M.Borthagaray, Juan PabloLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/47832/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/47832/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian Acosta, Gabriel Finite elements Fractional Laplacian Nonlocal operators |
| status_str | submittedVersion |
| title | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| title_full | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| title_fullStr | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| title_full_unstemmed | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| title_short | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| title_sort | A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian |
| topic | Finite elements Fractional Laplacian Nonlocal operators |
| url | https://hdl.handle.net/20.500.12008/47832 |
