Results 71 to 80 of about 81,041 (236)

Krylov Subspace Methods in the Electronic Industry [PDF]

, 2006
In most practical cases, the convergence of the GMRES method applied to a linear algebraic system Ax -- b is determined by the distribution of eigenvalues of A. In theory, however, the information about the eigenvalues alone is not sufficient for determining the convergence. In this paper the previous work of Greenbaum et al.
Heres, P.J., Schilders, W.H.A.
openaire   +2 more sources

Application of High‐Order Direct Flux Reconstruction and Stiffness‐Resilient Time Integration to Simulations of Idealized Atmospheric Flows

International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 448-468, April 2026.
The proposed work implements a direct flux reconstruction method for spatial discretization and a stiffness‐resilient exponential time integration method for temporal discretization on the cube‐sphere grid. A space‐time tensor formalism is employed to provide a general representation in any curvilinear coordinate system. This combination enables highly
Stéphane Gaudreault, Christopher Subich, Shoyon Panday, Martin Charron, Vincent Magnoux, Valentin Dallerit, Mayya Tokman   +6 more
wiley   +1 more source

EVSS‐Based Simulation Techniques for the Viscoelastic Fluids With Pure Polymer Melts Using Three‐Field Approach

International Journal for Numerical Methods in Fluids, Volume 98, Issue 4, Page 492-509, April 2026.
This paper presents a finite element method for simulating highly viscoelastic flows of pure polymer melts using the Elastic Viscous Stress Splitting formulation. The method avoids higher‐order derivatives in the weak formulation by reformulating the convective term in the constitutive equation.
R. Ahmad, P. Zajac, S. Turek
wiley   +1 more source

Developing Hessian–Free Second–Order Adversarial Examples for Adversarial Training

International Journal of Applied Mathematics and Computer Science
Recent studies show that deep neural networks (DNNs) are extremely vulnerable to elaborately designed adversarial examples. Adversarial training, which uses adversarial examples as training data, has been proven to be one of the most effective methods of
Qian Yaguan, Zhang Liangjian, Wang Yuqi, Ji Boyuan, Yao Tengteng, Wang Bin   +5 more
doaj   +1 more source

An Alternative HSS Preconditioner for the Unsteady Incompressible Navier-Stokes Equations in Rotation Form

Journal of Applied Mathematics, 2012
We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the ...
Jia Liu
doaj   +1 more source

Chebyshev semi-iteration in Preconditioning [PDF]

, 2008
It is widely believed that Krylov subspace iterative methods are better than Chebyshev semi-iterative methods. When the solution of a linear system with a symmetric and positive definite coefficient matrix is required then the Conjugate Gradient method ...
Rees, Tyrone, Wathen, A. J.
core  

Approximation of the Pseudospectral Abscissa via Eigenvalue Perturbation Theory

Numerical Linear Algebra with Applications, Volume 33, Issue 2, April 2026.
ABSTRACT Reliable and efficient computation of the pseudospectral abscissa in the large‐scale setting is still not settled. Unlike the small‐scale setting where there are globally convergent criss‐cross algorithms, all algorithms in the large‐scale setting proposed to date are at best locally convergent.
Waqar Ahmed, Emre Mengi
wiley   +1 more source

Local Fourier Analysis of the Complex Shifted Laplacian preconditioner for Helmholtz problems

, 2013
In this paper we solve the Helmholtz equation with multigrid preconditioned Krylov subspace methods. The class of Shifted Laplacian preconditioners are known to significantly speed-up Krylov convergence.
Bayliss, Berenger, Bollhöfer, Brandt, Brandt, Briggs, Elman, Erlangga, Erlangga, Erlangga, Ernst, Gijzen, Haber, Osei-Kuffuor, Reps, Reps, Rodrigo, Saad, Simoncini, Stüben, Trottenberg, Van der Vorst, Wienands, Wienands   +23 more
core   +1 more source

Toward Genuine Efficiency and Cluster Robustness of Preconditioned CG‐Like Eigensolvers

Numerical Linear Algebra with Applications, Volume 33, Issue 2, April 2026.
ABSTRACT The locally optimal block preconditioned conjugate gradient (LOBPCG) method is a popular solver for large and sparse Hermitian eigenvalue problems. However, recently proposed alternatives for its single‐vector version LOPCG indicate certain problematic cases with less accurate preconditioners and clustered target eigenvalues.
Ming Zhou, Klaus Neymeyr
wiley   +1 more source

Krylov Implicit Integration Factor Methods for Semilinear Fourth-Order Equations

Mathematics, 2017
Implicit integration factor (IIF) methods were developed for solving time-dependent stiff partial differential equations (PDEs) in literature. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368–388], IIF methods are designed to ...
Michael Machen, Yong-Tao Zhang
doaj   +1 more source