Paper Info
Title
Graph Grammar-Based Multi-Frontal Parallel Direct Solver For Two-Dimensional Isogeometric Analysis
Abstract
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.
Year
DOI
Venue
2012
10.1016/j.procs.2012.04.160
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE, ICCS 2012
Keywords
Field
DocType
parallel computing, isogeometric analysis, models of concurrency, graph grammar
Isogeometric analysis,Computer science,Grammar-based code,Algorithm,Graph bandwidth,Artificial intelligence,Clique-width,Solver,Graph (abstract data type),Moral graph,Machine learning,Voltage graph
Journal
Volume
ISSN
Citations 
9
1877-0509
3
PageRank 
References 
Authors
0.50
6
3
Name
Order
Citations
PageRank
krzysztof kuźnik1142.22
Maciej Paszynski219336.89
Victor M. Calo319138.14