Paper Info
Title
Graph Grammar based Multi-thread Multi-frontal Direct Solver with Galois Scheduler.
Abstract
In this paper, we present a multi-frontal solver algorithm for the adaptive finite element method expressed by graph grammar productions. The graph grammar productions construct first the binary elimination tree, and then process frontal matrices stored in distributed manner in nodes of the elimination tree. The solver is specialized for a class of one, two and three dimensional h refined meshes whose elimination tree has a regular structure. In particular, this class contains all one dimensional grids, two and three dimensional grids refined towards point singularities, two dimensional grids refined in an anisotropic way towards edge singularity as well as three dimensional grids refined in an anisotropic way towards edge or face singularities. In all these cases, the structure of the elimination tree and the structure of the frontal matrices are similar. The solver is implemented within the Galois environment, which allows parallel execution of graph grammar productions. We also compare the performance of the Galois implementation of our graph grammar based solver with the MUMPS solver.
Year
DOI
Venue
2014
10.1016/j.procs.2014.05.086
Procedia Computer Science
Keywords
Field
DocType
h adaptive finite element method,multi-frontal direct solver,graph grammar,Galois environment
Mathematical optimization,Polygon mesh,Algebra,Matrix (mathematics),Computer science,Singularity,Thread (computing),Theoretical computer science,Grammar,Solver,Gravitational singularity,Binary number
Conference
Volume
ISSN
Citations 
29
1877-0509
7
PageRank 
References 
Authors
0.53
9
6
Name
Order
Citations
PageRank
Damian Goik1182.27
Konrad Jopek2254.44
Maciej Paszynski319336.89
Andrew Lenharth445619.94
Donald Nguyen541917.94
Keshav Pingali63056256.64