Telescopic hybrid fast solver for 3D elliptic problems with point singularities
This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by...
| Main Authors: | , , , , , , , , , |
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| Format: | Conference Paper |
| Published: |
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/51536 |
| _version_ | 1848758722945351680 |
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| author | Paszynska, A. Jopek, K. Banas, K. Paszynski, M. Gurgul, P. Lenerth, A. Nguyen, D. Pingali, K. Dalcin, L. Calo, Victor |
| author_facet | Paszynska, A. Jopek, K. Banas, K. Paszynski, M. Gurgul, P. Lenerth, A. Nguyen, D. Pingali, K. Dalcin, L. Calo, Victor |
| author_sort | Paszynska, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver. |
| first_indexed | 2025-11-14T09:48:31Z |
| format | Conference Paper |
| id | curtin-20.500.11937-51536 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:31Z |
| publishDate | 2015 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515362017-09-13T15:41:42Z Telescopic hybrid fast solver for 3D elliptic problems with point singularities Paszynska, A. Jopek, K. Banas, K. Paszynski, M. Gurgul, P. Lenerth, A. Nguyen, D. Pingali, K. Dalcin, L. Calo, Victor This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver. 2015 Conference Paper http://hdl.handle.net/20.500.11937/51536 10.1016/j.procs.2015.05.415 http://creativecommons.org/licenses/by-nc-nd/4.0/ fulltext |
| spellingShingle | Paszynska, A. Jopek, K. Banas, K. Paszynski, M. Gurgul, P. Lenerth, A. Nguyen, D. Pingali, K. Dalcin, L. Calo, Victor Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title | Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title_full | Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title_fullStr | Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title_full_unstemmed | Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title_short | Telescopic hybrid fast solver for 3D elliptic problems with point singularities |
| title_sort | telescopic hybrid fast solver for 3d elliptic problems with point singularities |
| url | http://hdl.handle.net/20.500.11937/51536 |