Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sides
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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.
Paper presented at International Conference on Computational Science, ICCS 2013
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Kuznik, K.; Paszynski, M.; Calo, Victor (2012)This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been ...
Kuznik, K.; Paszynski, M.; Calo, Victor (2013)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 ...
Paszynski, M.; Kuznik, K.; Calo, Victor (2012)In this paper we present a multi-frontal direct solver algorithm for one and two dimensional isogeometric finite element method. The solver algorithm is tested on heat transfer model problem. The algorithm is partitioned ...