Research Paper on A MULTI-FRONTAL, MULTI-THREAD, HYPERGRAPH GRAMMAR-BASED DIRECT SOLVER SCHEDULED IN A PARALLEL GALOIS ENVIRONMENT

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Title: A MULTI-FRONTAL, MULTI-THREAD, HYPERGRAPH GRAMMAR-BASED DIRECT SOLVER SCHEDULED IN A PARALLEL GALOIS ENVIRONMENT

Abstract: In this paper, a multifrontal direct solver algorithm based on an ancient parallel hypergraph grammar is developed by analyzing two-dimensional grids with point and edge singularities. These grids are represented by a hypergraph. In order to construct frontal matrices for these meshes, we define a series of hypergraph grammar productions that express the elimination of fully assembled nodes, the merging of the resulting Schur complements, and the repetition of the elimination and merging steps until only one frontal matrix is left. A dependency graph is plotted after the dependency relationship between hypergraph grammar productions is examined (which is equivalent to the elimination tree of a multifrontal solver algorithm). The hypergraph grammar productions enable us to create an efficient elimination tree based on the graph representation of the computational mesh when combined with the traditional multi-frontal solver algorithm that we use (not the global matrix itself). The creations of the hypergraph grammar are assigned to nodes on a dependency graph, implemented as tasks in the GALOIS parallel environment, and scheduled over the shared memory parallel machine in accordance with the developed dependency graph. The fact that

Keywords: graph grammar, direct solver, h adaptive nite element method, GALOIS

Paper Quality: SCOPUS / Web of Science Level Research Paper

Paper type: Analysis Based Research Paper

Subject: Computer Science

Writer Experience: 20+ Years

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