Publication

A direct parallel sparse matrix solver

Kurt Appert, Ralf Gruber, Trach-Minh Tran
1996
Journal Articles

Abstract

The direct sparse matrix solver is based on a domain decomposition technique to achieve data and work parallelization. Geometries that have long and thin structures are specially efficiently tractable with this solver, provided that they can be decomposed mainly in one direction. Due to the separation of the algorithm into a factorization stage and a solution stage, time-dependent problems with a constant coefficient matrix are particularly well suited for this solver. The parallelization performances obtained on a Gray T3D show that the method scales up to at least 256 processors.

Official source

https://infoscience.epfl.ch/entities/publication/4039cf3b-595c-4918-9b58-2540ccbd5a6e

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Kurt Appert, Ralf Gruber, Trach-Minh Tran
1996
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/4039cf3b-595c-4918-9b58-2540ccbd5a6e

About this result

Related concepts (30)

Sparse matrix

In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.

Numerical linear algebra

Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.

Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.