s-step iterative methods for symmetric linear systems
Journal of Computational and Applied Mathematics
Microprocessing and Microprogramming
Predicting the behavior of finite precision Lanczos and conjugate gradient computations
SIAM Journal on Matrix Analysis and Applications
A parallel graph coloring heuristic
SIAM Journal on Scientific Computing
Data distributions for sparse matrix vector multiplication
Parallel Computing
Conjugate gradient and Lanczos methods for sparse matrices on distributed memory multiprocessors
Journal of Parallel and Distributed Computing
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
International Journal of Computer Mathematics
Parallel simulation of three–dimensional bursting with MPI and OpenMP
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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An implicit time-linearized finite difference discretization of partial differential equations on regular/structured meshes results in an n-diagonal block system of algebraic equations, which is usually solved by means of the Preconditioned Conjugate Gradient (PCG) method. In this paper, an analysis of the parallel implementation of this method on several computer architectures and for several programming paradigms is presented. For three-dimensional regular/structured meshes, a new implementation of the PCG method with Jacobi preconditioner is proposed. For the computer architectures and number of processors employed in this study, it has been found that this implementation is more efficient than the standard one, and can be applied to narrow-band matrices and other preconditioners, such as, for example, polynomial ones.