Results 61 to 70 of about 18,434 (156)
Accelerating Conjugate Gradient Solvers for Homogenization Problems With Unitary Neural Operators
International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.ABSTRACT Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous microstructures.
Julius Herb, Felix Fritzen
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All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems [PDF]
, 2010 Time-dependent partial differential equations (PDEs) play an important role in applied mathematics and many other areas of science. One-shot methods try to compute the solution to these problems in a single iteration that solves for all time-steps at the
Stoll, M., Wathen, A. J.
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Accelerated graph-based spectral polynomial filters
, 2015 Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces ...
Knyazev, Andrew, Malyshev, Alexander
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 3, March 2026.Abstract In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The energy response serves as an optimization criterion, whose computation involves solving Lyapunov equations.
J. Przybilla +3 more
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Performance of relaxed iterative methods for image deblurring problems
Journal of Algorithms & Computational Technology, 2019 In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms.
Jae H Yun
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A Jacobian‐Free Newton‐Krylov Method for Cell‐Centred Finite Volume Solid Mechanics
International Journal for Numerical Methods in Engineering, Volume 127, Issue 3, 15 February 2026.ABSTRACT This study proposes a Jacobian‐free Newton‐Krylov approach for finite‐volume solid mechanics. Traditional Newton‐based approaches require explicit Jacobian matrix formation and storage, which can be computationally expensive and memory‐intensive.
Philip Cardiff +3 more
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Computer Sciences & Mathematics ForumIn this work, we propose a nonlinear dynamic inverse solution to the diffusion problem based on Krylov Subspace Methods with spatiotemporal constraints. The proposed approach is applied by considering, as a forward problem, a 1D diffusion problem with a ...
Luis Fernando Alvarez-Velasquez +1 more
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Globally convergent techniques in nonlinear Newton-Krylov [PDF]
Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems.
Brown, Peter N., Saad, Youcef
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 3, 15 February 2026.ABSTRACT An efficient method for solving large eigenvalue problems efficiently can be developed using hyper‐reduced order models, such as those arising from the LU Proper Orthogonal Decomposition (LUPOD). The LUPOD employs dominant orthogonal modes along with a flexible number of collocation points to establish a reduced scalar product, thereby ...
A. Vidal‐Ferràndiz +4 more
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Numerical Linear Algebra with Applications, Volume 33, Issue 1, February 2026.ABSTRACT The heat equation is often used to inpaint dropped data in inpainting‐based lossy compression schemes. We propose an alternative way to numerically solve the heat equation by an extended Krylov subspace method. The method is very efficient with respect to the computation of the solution of the heat equation at large times.
Volker Grimm, Kevin Liang
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