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Combinatorial Optimization of Matrix-Vector Multiplication for Finite Element Assembly

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Title: Combinatorial Optimization of Matrix-Vector Multiplication for Finite Element Assembly
Author(s): Wolf, Michael M.; Heath, Michael T.
Subject(s): numerical analysis computer science
Abstract: It has been shown that combinatorial optimization of matrix-vector multiplication can lead to faster evaluation of finite element stiffness matrices. Based on a graph model characterizing relationships between rows, an efficient set of operations can be generated to perform matrix-vector multiplication for this problem. We improve the graph model by extending the set of binary row relationships and solve this combinatorial optimization problem optimally for the binary row relationships implemented, yielding significantly improved results over previous published graph models. We also extend the representation by using hypergraphs to model more complicated row relationships, expressing a three-row relationship with a three-vertex hyperedge, for example. Our initial greedy algorithm for this hypergraph model has yielded significantly better results than the graph model for many matrices.
Issue Date: 2009-02
Genre: Technical Report
Type: Text
URI: http://hdl.handle.net/2142/11520
Other Identifier(s): UIUCDCS-R-2009-3033
Rights Information: You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).
Date Available in IDEALS: 2009-04-23
 

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