Results 11 to 20 of about 1,275 (248)
About analysis of large problems of structural mechanics on multi-core computers [PDF]
Инженерно-строительный журнал, 2013 The sparse direct solvers as well as iterative methods are considered for analysis of large-scale finite element problems of structural mechanics on multi-core computers.
S.Yu. Fialko
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Explicit conjugate gradient method with preconditioning [PDF]
Applications of Mathematics, 1994 The authors propose the matrix \(C = (I - \omega A)^{-1}\) as a preconditioner in the preconditioned conjugate gradient (PCCG) method for solving the system of algebraic equations \(Ax = b\). Convergence properties of this PCCG method are analyzed. Especially, a relation between the condition numbers of the matrices \(C^{-1} A\) and \(A\) is derived ...
Křížková, Jitka, Vaněk, Petr
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Corrigendum: Block Preconditioning for the Conjugate Gradient Method [PDF]
SIAM Journal on Scientific and Statistical Computing, 1985 Concerns the authors' paper [ibid. 6, 220-252 (1985; Zbl 0556.65022)].
Concus, P., Golub, G. H., Meurant, G.
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Preconditioned conjugate gradient methods for three‐dimensional linear elasticity [PDF]
International Journal for Numerical Methods in Engineering, 1994 AbstractFinite element modelling of three‐dimensional elasticity problems give rise to large sparse matrices. Various preconditioning methods are developed for use in preconditioned conjugate gradient iterative solution techniques. Incomplete factorizations based on levels of fill, drop tolerance, and a two‐level hierarchical basis are developed ...
Dickinson, J. K., Forsyth, P A.
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Mathematics, 2021 The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite ...
Jaroslav Haslinger +3 more
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GPU-Based N-1 Static Security Analysis Algorithm With Preconditioned Conjugate Gradient Method
IEEE Access, 2020 N-1 static security analysis (SSA) is an important method for power system stability analysis that requires solving N alternating-current power flows (ACPF) for a system with N elements to obtain strictly accurate results.
Meng Fu +5 more
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Condition number estimation of preconditioned matrices. [PDF]
PLoS ONE, 2015 The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results.
Noriyuki Kushida
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Mathematical Modelling and Analysis, 2013 A preconditioned iterative solution method is presented for nonlinear parabolic transport systems. The ingredients are implicit Euler discretization in time and finite element discretization in space, then an outer-inner (outer damped inexact Newton ...
Janos Karatson, Tamas Kurics
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m-Step Preconditioned Conjugate Gradient Methods [PDF]
SIAM Journal on Scientific and Statistical Computing, 1985 The paper deals with the solution of a sparse system of symmetric positive definite linear equations by preconditioned conjugate gradient methods. Necessary and sufficient conditions are found for the applicability of preconditioners that are based on taking m steps of an iterative method. The computer implementation of these methods is discussed.
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Shock and Vibration, 2021 The full-waveform inversion (FWI) of a Love wave has become a powerful tool for shallow-surface site characterization. In classic conjugate gradient algorithm- (CG) based FWI, the energy distribution of the gradient calculated with the adjoint state ...
Jianbo Guan, Yu Li, Guohua Liu
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