Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides
This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm....
| Main Authors: | , , |
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| Format: | Conference Paper |
| Published: |
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/51366 |
| _version_ | 1848758680307105792 |
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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 | This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely the grammar productions, that can be executed squentially. The partial order of execution of the basic tasks is analyzed to provide the scheduling for the execution of the concurrent integration and multi-frontal solver algorithm. This graph grammar analysis allows for optimal concurrent execution of all tasks. The model has been implemented and tested on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple right hand sides related to the solution of non-stationary or inverse problems. © 2013 The Authors. Published by Elsevier B.V. |
| first_indexed | 2025-11-14T09:47:50Z |
| format | Conference Paper |
| id | curtin-20.500.11937-51366 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:47:50Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-513662017-09-13T15:41:42Z Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides Kuznik, K. Paszynski, M. Calo, Victor This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for onedimensional isogeometric finite element method. The model includes the integration of B-splines for construction of the element local matrices and the multi-frontal solver algorithm. The integration and the solver algorithm are partitioned into basic indivisible tasks, namely the grammar productions, that can be executed squentially. The partial order of execution of the basic tasks is analyzed to provide the scheduling for the execution of the concurrent integration and multi-frontal solver algorithm. This graph grammar analysis allows for optimal concurrent execution of all tasks. The model has been implemented and tested on NVIDIA CUDA GPU, delivering logarithmic execution time for linear, quadratic, cubic and higher order B-splines. Thus, the CUDA implementation delivers the optimal performance predicted by our graph grammar analysis. We utilize the solver for multiple right hand sides related to the solution of non-stationary or inverse problems. © 2013 The Authors. Published by Elsevier B.V. 2013 Conference Paper http://hdl.handle.net/20.500.11937/51366 10.1016/j.procs.2013.05.325 http://creativecommons.org/licenses/by-nc-nd/3.0/ fulltext |
| spellingShingle | Kuznik, K. Paszynski, M. Calo, Victor Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title | Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title_full | Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title_fullStr | Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title_full_unstemmed | Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title_short | Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| title_sort | grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides |
| url | http://hdl.handle.net/20.500.11937/51366 |