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Preconditioners for block Toeplitz systems based on circulant preconditioners
Numerical Algorithms, 2001The numerical solution of block Toeplitz systems by preconditioned conjugate gradient methods is considered. Two types of preconditioners based on circulant preconditioners are proposed by combining the ideas which are used in the construction of circulant preconditioners with Toeplitz-like preconditioners.
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An approximate BDDC preconditioner
Numerical Linear Algebra with Applications, 2007AbstractThe balancing domain decomposition by constraints (BDDC) preconditioner requires direct solutions of two linear systems for each substructure and one linear system for a global coarse problem. The computations and memory needed for these solutions can be prohibitive if any one system is too large.
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Multiresolution Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing, 2001Summary: We introduce a new preconditioner for elliptic partial differential equations (PDEs) on unstructured meshes. Using a wavelet-inspired basis we compress the inverse of the matrix, allowing an effective sparse approximate inverse by solving the sparsity vs. accuracy conflict. The key issue in this compression is to use second generation wavelets
Robert Bridson, Wei-Pai Tang
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Some Aspects of Circulant Preconditioners
SIAM Journal on Scientific Computing, 1993If \(T\) is a given \(n\times n\) Hermitian Toeplitz matrix, the circulant matrix \(C_ 0\) is determined which minimizes \(\| I-C^{-1/2}TC^{- 1/2}\|_ F\) among all circulant matrices \(C\). It is shown that \(C_ 0\) can be computed in \(O(n\log n)\) operations and that the eigenvalues of \(C_ 0^ 1T\) are asymptotically clustered around \(z=1\).
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M-preconditioner for M-matrices
Applied Mathematics and Computation, 2006The paper deals with the development and analysis of a preconditioner for the conjugate gradient approach to symmetric linear algebraic systems with a nonsingular \(M\)-matrix as coefficient matrix. Numerical results illustrate the convergence behavior of the new preconditioned conjugate gradient method.
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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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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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