A frontal solver, conceived by
Bruce Irons, is an approach to solving
sparse linear systems which is used extensively in
finite element analysis
The 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 ...
. It is a variant of
Gauss elimination that automatically avoids a large number of operations involving zero terms.
A frontal solver builds a
LU or
Cholesky decomposition of a sparse matrix given as the assembly of element matrices by assembling the matrix and eliminating equations only on a subset of elements at a time. This subset is called the front and it is essentially the transition region between the part of the system already finished and the part not touched yet. The whole sparse matrix is never created explicitly. Only parts of the matrix are assembled as they enter the front. Processing the front involves
dense matrix operations, which use the CPU efficiently. In a typical implementation, only the front is in
memory, while the factors in the decomposition are written into
files
File or filing may refer to:
Mechanical tools and processes
* File (tool), a tool used to ''remove'' fine amounts of material from a workpiece
**Filing (metalworking), a material removal process in manufacturing
** Nail file, a tool used to gent ...
. The element matrices are read from files or created as needed and discarded.
A multifrontal solver of
Duff
Duff may refer to:
People
* Duff (surname)
* Duff (given name)
* Duff (nickname)
* Karen Duffy, an actress, model, and former MTV VJ once known as "Duff"
* Duff Roman, on-air name of Canadian radio personality and executive David Mostoway (bo ...
and
Reid is an improvement of the frontal solver that uses several independent fronts at the same time. The fronts can be worked on by different
processors, which enables
parallel computing
Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different fo ...
.
See
[Iain S Duff , Albert M Erisman , John K Reid, Direct methods for sparse matrices, Oxford University Press, Inc., New York, NY, 1986] for a monograph exposition.
See also
*
MUMPS
MUMPS ("Massachusetts General Hospital Utility Multi-Programming System"), or M, is an imperative, high-level programming language with an integrated transaction processing key–value database. It was originally developed at Massachusetts Gener ...
*
Skyline matrix In scientific computing, skyline matrix storage, or SKS, or a variable band matrix storage, or envelope storage scheme is a form of a sparse matrix storage format matrix that reduces the storage requirement of a matrix more than banded storage. In ...
*
Banded matrix
References
Numerical linear algebra
Numerical software
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