Fast isogeometric solvers for explicit dynamics
In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that...
| Main Authors: | , |
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| Format: | Journal Article |
| Published: |
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/51554 |
| _version_ | 1848758726861783040 |
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| author | Gao, L. Calo, Victor |
| author_facet | Gao, L. Calo, Victor |
| author_sort | Gao, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V. |
| first_indexed | 2025-11-14T09:48:34Z |
| format | Journal Article |
| id | curtin-20.500.11937-51554 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:34Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515542017-09-13T15:35:58Z Fast isogeometric solvers for explicit dynamics Gao, L. Calo, Victor In finite element analysis, solving time-dependent partial differential equations with explicit time marching schemes requires repeatedly applying the inverse of the mass matrix. For mass matrices that can be expressed as tensor products of lower dimensional matrices, we present a direct method that has linear computational complexity, i.e., O(N), where N is the total number of degrees of freedom in the system. We refer to these matrices as separable matrices. For non-separable mass matrices, we present a preconditioned conjugate gradient method with carefully designed preconditioners as an alternative. We demonstrate that these preconditioners, which are easy to construct and cheap to apply (O(N)), can deliver significant convergence acceleration. The performances of these preconditioners are independent of the polynomial order (p independence) and mesh resolution (h independence) for maximum continuity B-splines, as verified by various numerical tests. © 2014 Elsevier B.V. 2014 Journal Article http://hdl.handle.net/20.500.11937/51554 10.1016/j.cma.2014.01.023 restricted |
| spellingShingle | Gao, L. Calo, Victor Fast isogeometric solvers for explicit dynamics |
| title | Fast isogeometric solvers for explicit dynamics |
| title_full | Fast isogeometric solvers for explicit dynamics |
| title_fullStr | Fast isogeometric solvers for explicit dynamics |
| title_full_unstemmed | Fast isogeometric solvers for explicit dynamics |
| title_short | Fast isogeometric solvers for explicit dynamics |
| title_sort | fast isogeometric solvers for explicit dynamics |
| url | http://hdl.handle.net/20.500.11937/51554 |