The SEIDD Project

Many evolutionary (or time dependent) systems studied in sciences and engineering are governed by parabolic equations. To understand these systems quantitatively requires solving the governing equations to an adequate accuracy. Numerical solution of parabolic equations needs sampling points in both spatial and temporal dimensions, which results in large amounts of data, thereby demanding high computing power in both computing speed and memory capacity. The Stable Explicit-Implicit Domain Decomposition (SEIDD) is a class of globally non-iterative, non-overlapping Domain Decomposition algorithms for solving parabolic equations on parallel computers. Since global iterations and overlapping incur both computation and communication overheads, global non-iterativeness and non-overlapping are highly desired properties for domain decomposition algorithms.

Publications

Y. Zhuang and X.-H. Sun, Stable, Globally Non-iterative, Non-overlapping Domain Decomposition Parallel Solvers for Parabolic Problems, Proc. of the IEEE/ACM Conference on High Performance Networking and Computing (SC2001), Denver, Nov. 2001.
Y. Zhuang and X.-H. Sun, Stabilized Explicit-implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations, SIAM J. Sci. Comput., Vol. 24 (July 2002), No. 1, 335-358.
Y. Zhuang and X.-H. Sun, A Domain Decomposition Based Algorithm for Solving Heat Transferring Problems on Massively Parallel Computers, Technical report, November 2003.
Y. Zhuang and X.-H. Sun, A Domain Decomposition Algorithm for Solving Parabolic Equations on Massively Parallel Computers, Technical report, June 2004.
Y. Zhuang and X.-H. Sun, A highly parallel algorithm for the numerical simulation of unsteady diffusion processes, Proc. 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS 2005), Denver, Colorado, April, 2005.
Rajesh Vuta, A Cache Efficient algorithm for the Alternating Explicit Implicit Domain Decomposition, Mater thesis, December 2005, Department of Computer Science, Texas Tech University, Lubbock, Texas.
Rajkumar Murthy, Parallel Alternating Explicit Implicit Domain Decomposition Algorithm, Mater thesis, May 2006, Department of Computer Science, Texas Tech University, Lubbock, Texas.

This material is based upon work supported by the National Science Foundation under Grant No. 0305393. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.