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A frontal solver, due to Bruce Irons〔Irons, B. M., 1970. A frontal solution scheme for finite element analysis. Int. J. Numer. Methods Eng. 2, 5--32〕 is an approach to solving sparse linear systems which is used extensively in finite element analysis.〔Renaud Sizaire, keyFE2 User Manual, 2005, Sec. I.4.2 Solving_linear_system (online ) 〕 It is a variant of Gauss elimination that automatically avoids a large number of operations involving zero terms.〔Hayrettin Kardestuncer, Ed. ''Finite Element Handbook''.〕 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. However, elements can be stored in-core in a clique sequence as recently proposed by Areias.〔P. Areias, T. Rabczuk, J.I. Barbosa, The extended unsymmetric frontal solution for multiple-point constraints, Engineering Computations, v.31 n.7, pp. 1582 - 1607, Nov. 2014 ()〕 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. The element matrices are read from files or created as needed and discarded. A multifrontal solver of Duff and Reid〔I. S. Duff , J. K. Reid, The Multifrontal Solution of Indefinite Sparse Symmetric Linear, ACM Transactions on Mathematical Software (TOMS), v.9 n.3, p.302-325, Sept. 1983 (DOI 10.1145/356044.356047 )〕 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. 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 *Skyline matrix *Banded matrix 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Frontal solver」の詳細全文を読む スポンサード リンク
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