TY - GEN
T1 - Grammar-Based Multi-Frontal Solver for One Dimensional Isogeometric Analysis with Multiple Right-Hand-Sides
AU - Kuźnik, Krzysztof
AU - Paszyński, Maciej
AU - Calo, Victor M.
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2013/6/1
Y1 - 2013/6/1
N2 - This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for one- dimensional 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 algo- rithm. 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.
AB - This paper introduces a grammar-based model for developing a multi-thread multi-frontal parallel direct solver for one- dimensional 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 algo- rithm. 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.
UR - http://hdl.handle.net/10754/552434
UR - http://linkinghub.elsevier.com/retrieve/pii/S1877050913004687
UR - http://www.scopus.com/inward/record.url?scp=84897008851&partnerID=8YFLogxK
U2 - 10.1016/j.procs.2013.05.325
DO - 10.1016/j.procs.2013.05.325
M3 - Conference contribution
SP - 1574
EP - 1583
BT - Procedia Computer Science
PB - Elsevier BV
ER -