Parallel depth first search. Part II. analysis
International Journal of Parallel Programming
Analyzing scalability of parallel algorithms and architectures
Journal of Parallel and Distributed Computing - Special issue on scalability of parallel algorithms and architectures
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Towards a fast parallel sparse symmetric matrix-vector multiplication
Parallel Computing - Linear systems and associated problems
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Isoefficiency: Measuring the Scalability of Parallel Algorithms and Architectures
IEEE Parallel & Distributed Technology: Systems & Technology
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper I) emphasizes construction of the block Jacobi preconditioner matrices. This is achieved in a preprocessing step, performed prior to the subsequent iterative linear solve step, considered in a companion paper (paper II). Results indicate that the block Jacobi routines scale remarkably well on parallel computing platforms, and should remain effective over tens of thousands of nodes.