MUMPS (MUltifrontal Massively Parallel sparse direct Solver) is a software application for the solution of large sparse systems of

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

equation In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for ...

s on

distributed memory In computer science, distributed memory refers to a Multiprocessing, multiprocessor computer system in which each Central processing unit, processor has its own private Computer memory, memory. Computational tasks can only operate on local data ...

parallel computers. It was developed in European project PARASOL (1996–1999) by CERFACS, IRIT- ENSEEIHT and RAL. The software implements the multifrontal method, which is a version of

Gaussian elimination In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can a ...

for large sparse systems of equations, especially those arising from the

finite element method Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat tran ...

. It is written in Fortran 90 with parallelism by

MPI MPI or Mpi may refer to: Science and technology Biology and medicine * Magnetic particle imaging, a tomographic technique * Myocardial perfusion imaging, a medical procedure that illustrates heart function * Mannose phosphate isomerase, an enzyme ...

and it uses BLAS and

ScaLAPACK The ScaLAPACK (or Scalable LAPACK) 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 interpro ...

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

INRIA The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name French Institute for Research in Comp ...

. The importance of MUMPS lies in the fact that it is a supported free implementation of the multifrontal method.

References

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External links

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WinMUMPS, files for compiling MUMPS on Windows
Free software programmed in Fortran Numerical software Public-domain software with source code {{free-software-stub