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Some Properties of the Optimal Preconditioner and the Generalized Superoptimal Preconditioner
Numerical Mathematics: Theory, Methods and Applications, 2010The optimal preconditioner and the superoptimal preconditioner were proposed in 1988 and 1992 respectively. They have been studied widely since then. Recently, Chen and Jin [6] extend the superoptimal preconditioner to a more general case by using the Moore-Penrose inverse.
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1995
Many structural analysis problems are concerned with friction contact phenomena. These problems are difficult to formulate and even more to solve because they are governed by multivalued tribological laws and some numerical resolutions can lead to unsymmetric operators.
Frédéric Lebon +2 more
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Many structural analysis problems are concerned with friction contact phenomena. These problems are difficult to formulate and even more to solve because they are governed by multivalued tribological laws and some numerical resolutions can lead to unsymmetric operators.
Frédéric Lebon +2 more
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Preconditioners in computational geomechanics: A survey
International Journal for Numerical and Analytical Methods in Geomechanics, 2011AbstractThe finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation.
GAMBOLATI, GIUSEPPE +2 more
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2004
Abstract A circulant matrix is a special form of Toeplitz matrix where each row of the matrix is a circular shift of its preceding row; see (1.6). Because of the periodicity, circulant systems can be solved efficiently via a deconvolution by discrete Fast Fourier Transforms (FFTs); see Section 3.2.1.
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Abstract A circulant matrix is a special form of Toeplitz matrix where each row of the matrix is a circular shift of its preceding row; see (1.6). Because of the periodicity, circulant systems can be solved efficiently via a deconvolution by discrete Fast Fourier Transforms (FFTs); see Section 3.2.1.
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Optimal and Superoptimal Circulant Preconditioners
SIAM Journal on Matrix Analysis and Applications, 1992The author investigates preconditioning methods for linear algebraic systems \(Ax=f\) with a dense positive definite matrix \(A\). He calls a conditioning matrix \(C\) optimal if it minimizes \(\| C-A\|\) and superoptimal if it minimizes \(\| I-C^{-1} A\|\), both in the Frobenius norm.
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On the Approximate Cyclic Reduction Preconditioner
SIAM Journal on Scientific Computing, 1999A preconditioning method for the iterative solution of large sparse systems of equations is introduced which is based on ideas both from ILU preconditioning and from multigrid. A multilevel structure is obtained by using maximal independent sets for graph coarsening.
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Multithreaded Direction Preserving Preconditioners
2014 IEEE 13th International Symposium on Parallel and Distributed Computing, 2014The scalability and robustness of a class of nonoverlapping domain decomposition preconditioners using 2-way nested dissection reordering is studied. We consider two different factorizations: nested and block versions. Both these variants have advantages and disadvantages.
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On a BPX-preconditioner for P1 elements
Computing, 1993An optimal multilevel preconditioner for nonconforming P1 elements discretizations of second order elliptic boundary value problems is derived. The resulting condition numbers are uniformly bounded with respect to the number of levels \(j\) which is known for the conforming case, and improve the previous results for nonconforming P1 elements.
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1994
We show by experimental results on some convection-diffusion type equations that the SOR iteration may be a promising preconditioner in conjunction with the GMRES method. Our results indicate that it is critical to take several Gauss-Seidel or SOR iterations, rather than just one, and that at least a factor of two improvement over Gauss-Seidel can be ...
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We show by experimental results on some convection-diffusion type equations that the SOR iteration may be a promising preconditioner in conjunction with the GMRES method. Our results indicate that it is critical to take several Gauss-Seidel or SOR iterations, rather than just one, and that at least a factor of two improvement over Gauss-Seidel can be ...
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