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The Multifrontal Method

Abstract : Definition : The multifrontal method is a direct method for solving systems of linear equations Ax = b, when A is a sparse matrix and x and b are vectors or matrices. The multifrontal method organizes the operations that take place during the factorization of sparse matrices in such a way that the entire factorization is performed through partial factorizations of a sequence of dense and small submatrices. It is guided by a tree that represents the dependencies between those partial factorizations. In the following, the multifrontal method is formulated first for finite-element analysis and later generalized to assembled sparse matrices.
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Patrick Amestoy, Alfredo Buttari, Iain S. Duff, Abdou Guermouche, Jean-Yves L'Excellent, et al.. The Multifrontal Method. David Padua. Encyclopedia of Parallel Computing, Springer, pp.1209-1216, 2011, 978-0-387-09765-7. ⟨10.1007/978-0-387-09766-4_86⟩. ⟨hal-00787015⟩



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