Grammar based multi-frontal solver for isogeometric analysis in 1D
In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and e...
| Main Authors: | , , |
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| Format: | Conference Paper |
| Published: |
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/58596 |
| _version_ | 1848760300317179904 |
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| author | Kuznik, K. Paszynski, M. Calo, Victor |
| author_facet | Kuznik, K. Paszynski, M. Calo, Victor |
| author_sort | Kuznik, K. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability. |
| first_indexed | 2025-11-14T10:13:35Z |
| format | Conference Paper |
| id | curtin-20.500.11937-58596 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:13:35Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-585962017-11-24T05:46:21Z Grammar based multi-frontal solver for isogeometric analysis in 1D Kuznik, K. Paszynski, M. Calo, Victor In this paper, we present a multi-frontal direct solver for one-dimensional iso-geometric finite element method. The solver implementation is based on the graph grammar (GG) model. The GG model allows us to express the entire solver algorithm, including generation of frontal matrices, merging, and eliminations as a set of basic undividable tasks called graph grammar productions. Having the solver algorithm expressed as GG productions, we can find the partial order of execution and create a dependency graph, allowing for scheduling of tasks into shared memory parallel machine. We focus on the implementation of the solver with NVIDIA CUDA on the graphic processing unit (GPU). The solver has been tested for linear, quadratic, cubic, and higher-order B-splines, resulting in logarithmic scalability. 2013 Conference Paper http://hdl.handle.net/20.500.11937/58596 10.1016/j.procs.2013.05.325 unknown |
| spellingShingle | Kuznik, K. Paszynski, M. Calo, Victor Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title | Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title_full | Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title_fullStr | Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title_full_unstemmed | Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title_short | Grammar based multi-frontal solver for isogeometric analysis in 1D |
| title_sort | grammar based multi-frontal solver for isogeometric analysis in 1d |
| url | http://hdl.handle.net/20.500.11937/58596 |