Communications Project

Document Type:Master's Thesis
Name:Aixiang (I Song) Yao
Title:An Efficient Parallel Three-Level Preconditioner for Linear Partial Differential Equations
Degree:Master of Science
Department:Computer Science
Committee Chair: Calvin J. Ribbens
Committee Members:Layne T. Watson, Professor
Christopher Beattie, Associate Professor
Keywords:parallel computing, preconditioner, domain decomposition, PDE, distributed systems
Date of defense:February 5, 1998
Availability:Release the entire work immediately worldwide.


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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