IMF: An Incomplete Multifrontal $LU$-Factorization for Element-Structured Sparse Linear Systems
نویسندگان
چکیده
منابع مشابه
IMF: An Incomplete Multifrontal LU-Factorization for Element-Structured Sparse Linear Systems
We propose an incomplete multifrontal LU-factorization (IMF) preconditioner that extends supernodal multifrontal methods to incomplete factorizations. It can be used as a preconditioner in a Krylov-subspace method to solve large-scale sparse linear systems with an element structure; e.g., those arising from a finite element discretization of a partial differential equation. The fact that the el...
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Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily ...
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A well-known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A + A and use it as a computational graph to drive the numerical factorization. This approach, although very eÆcient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We in...
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Rank structures provide an opportunity to develop new efficient numerical methods for practical problems, when the off-diagonal blocks of certain dense intermediate matrices have small (numerical) ranks. In this work, we present a framework of structured direct factorizations for general sparse matrices, including discretized PDEs on general meshes, based on the multifrontal method and hierarch...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2013
ISSN: 1064-8275,1095-7197
DOI: 10.1137/100818996