Results 91 to 100 of about 81,041 (236)

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, Dylan Armfield, Željko Tuković, Ivan Batistić   +3 more
wiley   +1 more source

Re-Orthogonalized/Affine GMRES and Orthogonalized Maximal Projection Algorithm for Solving Linear Systems

Algorithms
GMRES is one of the most powerful and popular methods to solve linear systems in the Krylov subspace; we examine it from two viewpoints: to maximize the decreasing length of the residual vector, and to maintain the orthogonality of the consecutive ...
Chein-Shan Liu, Chih-Wen Chang , Chung-Lun Kuo    +2 more
doaj   +1 more source

Hyper‐Reduced Model Based on the Proper Orthogonal Decomposition and the LU Factorization Applied to the Neutron Diffusion Eigenvalue Problem

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, A. Carreño, E. Javaloyas, D. Ginestar, G. Verdú   +4 more
wiley   +1 more source

Two Preconditioners for Time-Harmonic Eddy-Current Optimal Control Problems

Mathematics
In this paper, we consider the numerical solution of a large complex linear system with a saddle-point form obtained by the discretization of the time-harmonic eddy-current optimal control problem.
Xin-Hui Shao, Jian-Rong Dong
doaj   +1 more source

An Extended Krylov Subspace Method for Decoding Edge‐Based Compressed Images by Homogeneous Diffusion

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
wiley   +1 more source

The Block Preconditioned SOR Method for Solving Indefinite Complex Linear Systems

Numerical Linear Algebra with Applications, Volume 33, Issue 1, February 2026.
ABSTRACT In this paper we extend the theory of a block preconditioned SOR method studied by Hezari, Edalaptour, and Salkuyeh (2015) for the solution of indefinite complex linear systems. In particular, we consider the case where the key matrix S$$ S $$ has real eigenvalues which lie in (−∞,+∞)$$ \left(-\infty, +\infty \right) $$ and not only in [0,+∞)$$
M. A. Louka, N. M. Missirlis
wiley   +1 more source

Numerically Stable Recurrence Relations for the Communication Hiding Pipelined Conjugate Gradient Method

, 2019
Pipelined Krylov subspace methods (also referred to as communication-hiding methods) have been proposed in the literature as a scalable alternative to classic Krylov subspace algorithms for iteratively computing the solution to a large linear system in ...
Cools, Siegfried, Cornelis, Jeffrey, Vanroose, Wim   +2 more
core  

Deliberate Ill-Conditioning of Krylov Matrices [PDF]

, 2001
This paper starts o with studying simple extrapolation methods for the classical iteration schemes such as Richardson, Jacobi and Gauss-Seidel iteration.
Brandts, J.H.
core  

70 years of Krylov subspace methods: The journey continues

arXiv.org, 2022
E. Carson, J. Liesen, Z. Strakoš
semanticscholar   +1 more source

Preconditioned iterative solution of the 2D Helmholtz equation [PDF]

, 2002
Using a finite element method to solve the Helmholtz equation leads to a sparse system of equations which in three dimensions is too large to solve directly.
Giles, M. B., Laird, Alistair L.
core