MUMPS (software)
Encyclopedia
MUMPS is a software application for the solution of large sparse
Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....

 systems of linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

 algebraic
Algebraic
Algebraic may refer to any subject within the algebra branch of mathematics and related branches like algebraic geometry and algebraic topology.Algebraic may also refer to:...

 equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...

s on distributed memory
Distributed memory
In computer science, distributed memory refers to a multiple-processor computer system in which each processor has its own private memory. Computational tasks can only operate on local data, and if remote data is required, the computational task must communicate with one or more remote processors...

 parallel computers. It was developed in European project PARASOL (1996–1999) by CERFACS, IRIT-ENSEEIHT and RAL
Rutherford Appleton Laboratory
The Rutherford Appleton Laboratory is one of the national scientific research laboratories in the UK operated by the Science and Technology Facilities Council . It is located on the Harwell Science and Innovation Campus at Chilton near Didcot in Oxfordshire, United Kingdom...

. The software implements the multifrontal method, which is a version of Gaussian elimination
Gaussian elimination
In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix...

 for large sparse systems of equations, especially those arising from the finite element method
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

. It is written in Fortran 90 with parallelism by MPI
Message Passing Interface
Message Passing Interface is a standardized and portable message-passing system designed by a group of researchers from academia and industry to function on a wide variety of parallel computers...

 and it uses BLAS
Blas
Blas is mainly a Spanish given name and surname, related to Blaise. It may refer to-Places:*Piz Blas, mountain in Switzerland*San Blas , many places - see separate article, also**Cape San Blas Light, lighthouse...

 and ScaLAPACK
ScaLAPACK
The ScaLAPACK library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently written in a Single-Program-Multiple-Data style using explicit message passing for interprocessor communication...

 kernels for dense matrix computations.
Since 1999, MUMPS has been supported by CERFACS, IRIT-ENSEEIHT, and INRIA.

The importance of MUMPS lies in the fact that it is a rare public domain
Public domain
Works are in the public domain if the intellectual property rights have expired, if the intellectual property rights are forfeited, or if they are not covered by intellectual property rights at all...

implementation of the multifrontal method, if not the only professional and supported one.

External links

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