Parallel Communication Analysis for Sparse Cholesky Factorization Algorithms
نویسنده
چکیده
We focus on linear systems stemming from discretization of PDEs. The non-zero structure of matrices of such systems depends on the discretized domain and the stencil in use. Analyzing parallel communication for an arbitraty problem seems unfeasible. Thus, we are dealing with a model problem: a square k-by-k mesh and a 5-point stencil. Presumably, the results for other stencils using the same mesh will differ from the results for the 5-point stencil only by a lower-order term, which is acceptable, since we are primarily interested in an asymptotic behavior of parallel Cholesky.
منابع مشابه
Scalable Parallel Algorithms for Solving Sparse Systems of Linear Equations∗
We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...
متن کاملHighly Scalable Parallel Algorithms for Sparse Matrix Factorization
In this paper, we describe scalable parallel algorithms for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithms substantially improve the state of the art in parallel direct solution of sparse linear sys...
متن کاملA Highly Scalable Parallel Algorithm for Sparse Matrix Factorization
In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithm substantially improves the state of the art in parallel direct solution of sparse linear sy...
متن کاملMinimizing Communication in Numerical Linear Algebra
In 1981 Hong and Kung proved a lower bound on the amount of communication (amount of data moved between a small, fast memory and large, slow memory) needed to perform dense, n-by-n matrix-multiplication using the conventional O(n3) algorithm, where the input matrices were too large to fit in the small, fast memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and extended it...
متن کاملParallel Sparse Cholesky Factorization
Sparse matrix factorization plays an important role in many numerical algorithms. In this paper we describe a scalable parallel algorithm based on the Multifrontal Method. Computational experiments on a Parsytec CC system with 32 processors show that large sparse matrices can be factorized in only a few seconds.
متن کامل