A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs
We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference...
| Authors: | ; ; ; ; |
|---|---|
| Format: | Article |
| Publication date: | 2022 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/72513 |
| Online Access: | https://hdl.handle.net/20.500.14352/72513 |
| Access Level: | Open access |
| Keyword: | generalized finite differences meshless method parabolic partial differential equations Matemáticas (Matemáticas) Funciones (Matemáticas) 12 Matemáticas 1202 Análisis y Análisis Funcional |
| _version_ | 1878739967910346752 |
|---|---|
| author | Benito, Juan José |
| author2 | García, Ángel Negreanu Pruna, Mihaela Ureña, Francisco Vargas, Antonio M. |
| author2_role | author author author author |
| author_browse | Benito, Juan José García, Ángel Negreanu Pruna, Mihaela Ureña, Francisco Vargas, Antonio M. |
| author_facet | Benito, Juan José García, Ángel Negreanu Pruna, Mihaela Ureña, Francisco Vargas, Antonio M. |
| author_role | author |
| collection | Docta Complutense |
| description | We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference method (GFDM), which allows us to select well-conditioned stars. Several 2D and 3D examples, including the time variable, are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_cb5589c8ad7f00a2aca2a20b0aac2b51 |
| institution | Universidad Complutense de Madrid (UCM) |
| instname_str | Universidad Complutense de Madrid (UCM) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:docta.ucm.es:20.500.14352/72513 |
| publishDate | 2022 |
| publishDateSort | 2022 |
| publisher | MPDI |
| publisherStr | MPDI |
| reponame_str | Docta Complutense |
| spelling | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs Benito, Juan José García, Ángel Negreanu Pruna, Mihaela Ureña, Francisco Vargas, Antonio M. generalized finite differences meshless method parabolic partial differential equations Matemáticas (Matemáticas) Funciones (Matemáticas) 12 Matemáticas 1202 Análisis y Análisis Funcional We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear parabolic PDEs. The method is based on a moving least squares method, more precisely, the generalized finite difference method (GFDM), which allows us to select well-conditioned stars. Several 2D and 3D examples, including the time variable, are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time. MPDI https://hdl.handle.net/20.500.14352/72513 |
| spellingShingle | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs Benito, Juan José generalized finite differences meshless method parabolic partial differential equations Matemáticas (Matemáticas) Funciones (Matemáticas) 12 Matemáticas 1202 Análisis y Análisis Funcional |
| title | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| title_full | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| title_fullStr | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| title_full_unstemmed | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| title_short | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| title_sort | A Novel Spatio-Temporal Fully Meshless Method for Parabolic PDEs |
| topic | generalized finite differences meshless method parabolic partial differential equations Matemáticas (Matemáticas) Funciones (Matemáticas) 12 Matemáticas 1202 Análisis y Análisis Funcional |
| topic_facet | generalized finite differences meshless method parabolic partial differential equations Matemáticas (Matemáticas) Funciones (Matemáticas) 12 Matemáticas 1202 Análisis y Análisis Funcional |
| url | https://hdl.handle.net/20.500.14352/72513 |