Explicit group over-relaxation methods for solving elliptic partial differential equations
Mathematics and Computers in Simulation
Parallel programming with MPI
Parallel programming: techniques and applications using networked workstations and parallel computers
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Scientific Parallel Computing
The performance of parallel iterative solvers
Computers & Mathematics with Applications
Modified explicit decoupled group method in the solution of 2-D elliptic PDES
MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
A multithreaded solver for the 2D Poisson equation
Proceedings of the 2012 Symposium on High Performance Computing
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Since their introduction, the four-point explicit group (EG) and explicit decoupled group (EDG) methods in solving elliptic PDE's have been implemented on various parallel computing architectures such as shared memory parallel computer and distributed computer systems. However, no detailed study on the performance analysis of these algorithms was done in any of these implementations. In this paper we developed performance models for these explicit group methods and present detailed study of their hypothetical implementation on two distributed memory multicomputers with different computation speed and communication bandwidth. Detailed performance analysis based on these models predicted different theoretical performance if the methods were implemented on the clusters. This was confirmed by the experimental results performed on the two distinct clusters. Theoretical analysis and experimental results indicated that both explicit group methods are scalable with respect to number of processors and the problem size.