Type of Document	Master's Thesis
Author	Yao, Aixiang I Song
Author's Email Address	ayao@csgrad.cs.vt.edu
URN	etd-12398-18633
Title	An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations
Degree	Master of Science
Department	Computer Science
Advisory Committee	Advisor Name Title Ribbens, Calvin J. Committee Chair Beattie, Christopher A. Committee Member Watson, Layne T. Committee Member
Keywords	domain decomposition preconditioner parallel computing PDE distributed systems
Date of Defense	1998-02-05
Availability	unrestricted
Abstract The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. Communication cost and redundancy are explored as well. After experiments and analysis, we find that the three-level preconditioner D1 is the most efficient and scalable parallel preconditioner, compared to BJ and D0. The D1 preconditioner reduces both the number of iterations and computational time substantially. A new hybrid preconditioner is suggested which may combine the best features of D0 and D1.
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