Paper Info
Title
Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations.
Abstract
In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver.As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100*MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.
Year
Venue
Field
2016
ICCS
Dynamic programming,Mathematical optimization,FLOPS,Floating point,Computer science,Extended finite element method,Finite element method,Solver,Partition (number theory),Sparse matrix
DocType
Citations 
PageRank 
Conference
2
0.40
References 
Authors
4
8
Name
Order
Citations
PageRank
Hassan AbouEisha1163.87
Konrad Jopek2254.44
Bartlomiej Medygral320.40
Szymon Nosek420.40
Mikhail Ju. Moshkov533560.44
Anna Paszyńska612517.77
Maciej Paszynski719336.89
Keshav Pingali83056256.64