Abstract
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.
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Acknowledgments
The work of MP and AP was supported by Polish National Science Center grant UMO-2012/07/B/ST6/01229. The work of PG was partly supported by The European Union by means of European Social Fund, PO KL Priority IV: Higher Education and Research, “Activity 4.1: Improvement and Development of Didactic Potential of the University and Increasing Number of Students of the Faculties Crucial for the National Economy Based on Knowledge, Subactivity 4.1.1: Improvement of the Didactic Potential of the AGH University of Science and Technology Human Assets”, UDA POKL.04.01.01-00-367/08-00.
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AbouEisha, H., Gurgul, P., Paszyńska, A., Paszyński, M., Kuźnik, K., Moshkov, M. (2014). An Automatic Way of Finding Robust Elimination Trees for a Multi-frontal Sparse Solver for Radical 2D Hierarchical Meshes. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55195-6_50
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DOI: https://doi.org/10.1007/978-3-642-55195-6_50
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