In this paper we present a dynamic programming algorithm for finding optimal elimination trees for the multi-frontal direct solver algorithm executed over two dimensional meshes with point singularities. The elimination tree found by the optimization algorithm results in a linear computational cost of sequential direct solver. Based on the optimal elimination tree found by the optimization algorithm we construct heuristic sequential multi-frontal direct solver algorithm resulting in a linear computational cost as well as heuristic parallel multi-frontal direct solver algorithm resulting in a logarithmic computational cost. The resulting parallel algorithm is implemented on NVIDIA CUDA GPU architecture based on our graph-grammar approach. © 2014 Springer-Verlag.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)