Paper Info
Title
Hypergraph Grammar-Based, Multi-Thread, Multi-Frontal Direct Solver Scheduled In Parallel Galois Environment
Abstract
In this paper, we analyze two-dimensional grids with point and edge singularities in order to develop an efficient parallel hypergraph grammar-based multifrontal direct solver algorithm. We express these grids by a hypergraph. For these meshes, we define a sequence of hypergraph grammar productions expressing the construction of frontal matrices, eliminating fully assembled nodes, merging the resulting Schur complements, and repeating the process of elimination and merging until a single frontal matrix remains. The dependency relationship between hypergraph grammar productions is analyzed, and a dependency graph is plotted (which is equivalent to the elimination tree of a multifrontal solver algorithm). We utilize a classical multi-frontal solver algorithm; the hypergraph grammar productions allow us to construct an efficient elimination tree based on the graph representation of the computational mesh (not the global matrix itself). The hypergraph grammar productions are assigned to nodes on a dependency graph, and they are implemented as tasks in the GALOIS parallel environment and scheduled according to the developed dependency graph over the shared memory parallel machine. We show that our hypergraph grammar-based solver outperforms the parallel MUMPS solver.
Year
DOI
Venue
2019
10.7494/csci.2019.20.1.3010
COMPUTER SCIENCE-AGH
Keywords
DocType
Volume
graph grammar, direct solver, h adaptive finite element method, GALOIS
Journal
20
Issue
ISSN
Citations 
1
1508-2806
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Maciej Paszynski119336.89
Konrad Jopek2254.44
Anna Paszyńska312517.77
Muhammad Amber Hasaan400.34
Keshav Pingali53056256.64