GMRES algorithms over 35 years
Q Zou - Applied Mathematics and Computation, 2023 - Elsevier
This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …
first consider basic algorithms and study their convergence. We then focus on acceleration …
Krylov methods for nonsymmetric linear systems
G Meurant, JD Tebbens - Cham: Springer, 2020 - Springer
Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations
with absorption, where the PDE is discretised using curl-conforming finite-element methods …
with absorption, where the PDE is discretised using curl-conforming finite-element methods …
Multi-resolution localized orthogonal decomposition for Helmholtz problems
M Hauck, D Peterseim - Multiscale Modeling & Simulation, 2022 - SIAM
We introduce a novel multi-resolution localized orthogonal decomposition (LOD) for time-
harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The …
harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The …
[图书][B] A Journey through the History of Numerical Linear Algebra
C Brezinski, G Meurant, M Redivo-Zaglia - 2022 - SIAM
A Journey through the History of Numerical Linear Algebra: Back Matter Page 1 Bibliography
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …
A unified theory of non-overlapping Robin–Schwarz methods: Continuous and discrete, including cross points
C Pechstein - Journal of Scientific Computing, 2023 - Springer
Non-overlapping Schwarz methods with generalized Robin transmission conditions were
originally introduced by B. Després for time-harmonic wave propagation problems and have …
originally introduced by B. Després for time-harmonic wave propagation problems and have …
A multilevel in space and energy solver for 3-D multigroup diffusion and coarse-mesh finite difference eigenvalue problems
BC Yee, B Kochunas, EW Larsen - Nuclear Science and …, 2019 - Taylor & Francis
Abstract The Multilevel in Space and Energy Diffusion (MSED) method accelerates the
iterative convergence of multigroup diffusion eigenvalue problems by performing work on …
iterative convergence of multigroup diffusion eigenvalue problems by performing work on …
Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem
We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-
version of the boundary element method (BEM) using the standard second-kind combined …
version of the boundary element method (BEM) using the standard second-kind combined …
Hermitian preconditioning for a class of non-Hermitian linear systems
N Spillane - SIAM Journal on Scientific Computing, 2024 - SIAM
This work considers the convergence of GMRES for nonsingular problems. GMRES is
interpreted as the generalized conjugate residual method which allows for simple proofs of …
interpreted as the generalized conjugate residual method which allows for simple proofs of …
Roots of matrices in the study of GMRES convergence and Crouzeix's conjecture
D Choi, A Greenbaum - SIAM Journal on Matrix Analysis and Applications, 2015 - SIAM
For any nonsingular matrix A and any positive integer m, the m th root, A^1/m, can be
defined using any branch cut of the m th root function that does not pass through an …
defined using any branch cut of the m th root function that does not pass through an …