An Efficient Parallel Three-Level Preconditioner for Linear Elliptic Partial Differential Equations

(ABSTRACT) The primary motivation of this research is to develop and investigate parallel precondi-tioners 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 pre-conditioner 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. ACKNOWLEDGEMENTS I am greatly indebted to my advisor, Professor Calvin J. Ribbens for many stimulating discussions and his valuable advice throughout this work. Without his guidance, encouragement , and support, this paper would not have been possible. I would like to thank him and the other members of my committee, Dr. Watson and Dr. Beattie, for their guidance and assistance throughout my graduate studies. Finally, I would like to thank my friends and my family for being there when I needed them.