Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method
In this paper we analyze the problem of implementing periodic boundary conditions in the isogeometric finite element method (ISO-FEM). The ISO-FEM method uses the B-spline-based basis functions, which facilitates usage of the same basis functions for approximation of the geometry as well as for the...
| Main Authors: | , , , |
|---|---|
| Format: | Journal Article |
| Published: |
2015
|
| Online Access: | http://hdl.handle.net/20.500.11937/55145 |
| _version_ | 1848759546328121344 |
|---|---|
| author | Los, M. Paszynski, M. Dalcin, L. Calo, Victor |
| author_facet | Los, M. Paszynski, M. Dalcin, L. Calo, Victor |
| author_sort | Los, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we analyze the problem of implementing periodic boundary conditions in the isogeometric finite element method (ISO-FEM). The ISO-FEM method uses the B-spline-based basis functions, which facilitates usage of the same basis functions for approximation of the geometry as well as for the numerical solution of the modeled physical phenomena. The usage of the B-spline based basis functions results in C^(p-1) global continuity of the solution. The drawback is a difficulty in implementing the periodic boundary conditions, and special dedicated methods are necessary. In this paper we present two algorithms implementing the periodic boundary conditions. The first one is an iterative algorithm that utilizes widely available block-diagonal LAPACK solver. The second one is a modification of the multi-frontal solver algorithm itself, and it requires a dedicated solver with its source code modified accordingly. The presented methods can be applied in one, two or three-dimensional isogeometric finite element method. |
| first_indexed | 2025-11-14T10:01:36Z |
| format | Journal Article |
| id | curtin-20.500.11937-55145 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:01:36Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-551452017-08-24T02:17:18Z Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method Los, M. Paszynski, M. Dalcin, L. Calo, Victor In this paper we analyze the problem of implementing periodic boundary conditions in the isogeometric finite element method (ISO-FEM). The ISO-FEM method uses the B-spline-based basis functions, which facilitates usage of the same basis functions for approximation of the geometry as well as for the numerical solution of the modeled physical phenomena. The usage of the B-spline based basis functions results in C^(p-1) global continuity of the solution. The drawback is a difficulty in implementing the periodic boundary conditions, and special dedicated methods are necessary. In this paper we present two algorithms implementing the periodic boundary conditions. The first one is an iterative algorithm that utilizes widely available block-diagonal LAPACK solver. The second one is a modification of the multi-frontal solver algorithm itself, and it requires a dedicated solver with its source code modified accordingly. The presented methods can be applied in one, two or three-dimensional isogeometric finite element method. 2015 Journal Article http://hdl.handle.net/20.500.11937/55145 restricted |
| spellingShingle | Los, M. Paszynski, M. Dalcin, L. Calo, Victor Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title | Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title_full | Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title_fullStr | Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title_full_unstemmed | Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title_short | Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method |
| title_sort | dealing with periodic boundary conditions for 1d, 2d and 3d isogeometric finite element method |
| url | http://hdl.handle.net/20.500.11937/55145 |