Graph grammar-based multi-frontal parallel direct solver for two-dimensional isogeometric analysis
MetadataShow full item record
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 expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matrices at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU. © 2012 Published by Elsevier Ltd.
Paper presented at International Conference on Computational Science, ICCS 2012
Showing items related by title, author, creator and subject.
Grammar-based multi-frontal solver for one dimensional isogeometric analysis with multiple right-hand-sidesKuznik, K.; Paszynski, M.; Calo, Victor (2013)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 ...
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 ...