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Iterative Solution Methods and Preconditioners for Block-Tridiagonal Systems of Equations
SIAM Journal on Matrix Analysis and Applications, 1992The authors study semicirculant preconditioners \(M\) used in CG-like iterative methods for solving linear systems \(Bu=b\) of \(n\) algebraic equations arising typically from the implicit time and finite difference spatial discretizations of initial-boundary value problems for linear systems of partial differential equations of the form \(\partial u ...
Holmgren, S., Otto, K.
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Advances in Iterative Methods and Preconditioners for the Helmholtz Equation
Archives of Computational Methods in Engineering, 2007The Helmholtz equation \(\nabla ^{2}u(\mathbf{x})+\kappa ^{2}u(\mathbf{x})=h( \mathbf{x}),\) where \(\nabla ^{2}\) is the Laplacian, \(\kappa \) is the wave number, \(h\) is a forcing function and \(u\) is the amplitude, finds applications in many important fields including aeroacoustics, under-water acoustics, seismic inversion and electromagnetics ...
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Iterative Substructuring Preconditioners for Mortar Element Methods in Two Dimensions
SIAM Journal on Numerical Analysis, 1999The paper is devoted to the construction of effective model grid operators (preconditioners) for classes of linear grid systems with positive operators. The suggested constructions lead to estimates of the spectral condition number like \(O(\log^2N)\); the model operators are almost spectrally equivalent to the original ones.
Achdou, Yves, Maday, Yvon, Widlund, Olof
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Computational and Applied Mathematics, 2021
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Lu-Bin Cui, Yu-Dong Fan, Yu-Tao Zheng
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Lu-Bin Cui, Yu-Dong Fan, Yu-Tao Zheng
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PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems
Numerical Algorithms, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cao, Shan-Mou, Wang, Zeng-Qi
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Efficient Preconditioner and Iterative Method for Large Complex Symmetric Linear Algebraic Systems
East Asian Journal on Applied Mathematics, 2017AbstractWe discuss an efficient preconditioner and iterative numerical method to solve large complex linear algebraic systems of the form (W + iT)u = c, where W and T are symmetric matrices, and at least one of them is nonsingular. When the real part W is dominantly stronger or weaker than the imaginary part T, we propose a block multiplicative (BM ...
Liao, Li Dan, Zhang, Guo Feng
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Advanced Studies: Euro-Tbilisi Mathematical Journal, 2021
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Bao, Wen-Bin, Miao, Shu-Xin
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Bao, Wen-Bin, Miao, Shu-Xin
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Japan Journal of Industrial and Applied Mathematics, 2021
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Cui, Lu-Bin +2 more
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Cui, Lu-Bin +2 more
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International Journal of Geomechanics, 2016
AbstractBecause most geotechnical analyses may involve elastoplastic geomaterials, a robust solution scheme is of critical importance to the efficiency of the entire finite-element (FE) computation. To accelerate the Krylov subspace iterative methods, some preconditioning techniques have been developed based on the factorization of elastic stiffness ...
Xi Chen +3 more
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AbstractBecause most geotechnical analyses may involve elastoplastic geomaterials, a robust solution scheme is of critical importance to the efficiency of the entire finite-element (FE) computation. To accelerate the Krylov subspace iterative methods, some preconditioning techniques have been developed based on the factorization of elastic stiffness ...
Xi Chen +3 more
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On Single Precision Preconditioners for Krylov Subspace Iterative Methods
2008Large sparse linear systems Ax= barise in many scientific applications. Krylov subspace iterative methods are often used for solving such linear systems. Preconditioning techniques are efficient to reduce the number of iterations of Krylov subspace methods.
Hiroto Tadano, Tetsuya Sakurai
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