Preconditioners for Krylov subspace methods: An overview
JW Pearson, J Pestana - GAMM‐Mitteilungen, 2020 - Wiley Online Library
When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …
frequently required to construct a mathematical model, and then resolve this model …
[图书][B] Krylov subspace methods: principles and analysis
J Liesen, Z Strakos - 2013 - books.google.com
The mathematical theory of Krylov subspace methods with a focus on solving systems of
linear algebraic equations is given a detailed treatment in this principles-based book …
linear algebraic equations is given a detailed treatment in this principles-based book …
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 …
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert
spaces. Our key observation is that the general approach from [P. Heid and TP Wihler …
spaces. Our key observation is that the general approach from [P. Heid and TP Wihler …
Rate optimality of adaptive finite element methods with respect to overall computational costs
We consider adaptive finite element methods for second-order elliptic PDEs, where the
arising discrete systems are not solved exactly. For contractive iterative solvers, we …
arising discrete systems are not solved exactly. For contractive iterative solvers, we …
Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
R Becker, M Brunner, M Innerberger… - ESAIM: Mathematical …, 2023 - esaim-m2an.org
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but
only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element …
only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element …
Rate optimal adaptive FEM with inexact solver for nonlinear operators
We prove convergence with optimal algebraic rates for an adaptive finite element method for
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …
nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also …
Estimating and localizing the algebraic and total numerical errors using flux reconstructions
This paper presents a methodology for computing upper and lower bounds for both the
algebraic and total errors in the context of the conforming finite element discretization of the …
algebraic and total errors in the context of the conforming finite element discretization of the …
Interplay between discretization and algebraic computation in adaptive numerical solutionof elliptic pde problems
Abstract The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE
boundary value and eigenvalue problems is a numerical scheme that automatically and …
boundary value and eigenvalue problems is a numerical scheme that automatically and …
Sharp algebraic and total a posteriori error bounds for h and p finite elements via a multilevel approach. Recovering mass balance in any situation
We present novel H (div) and H 1 liftings of given piecewise polynomials over a hierarchy of
simplicial meshes, based on a global solve on the coarsest mesh and on local solves on …
simplicial meshes, based on a global solve on the coarsest mesh and on local solves on …