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 …
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs
A Ern, M Vohralík - SIAM Journal on Scientific Computing, 2013 - SIAM
We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …
nonlinear partial differential equations of diffusion type. To solve these systems, some …
Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics
S Chaillat, M Bonnet - Wave Motion, 2013 - Elsevier
This article is mainly devoted to a review on fast BEMs for elastodynamics, with particular
attention on time-harmonic fast multipole methods (FMMs). It also includes original results …
attention on time-harmonic fast multipole methods (FMMs). It also includes original results …
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 …
[图书][B] Preconditioning and the conjugate gradient method in the context of solving PDEs
Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …
speed of everything. Within science, it has led to the publication explosion, which reflects the …
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems
L El Alaoui, A Ern, M Vohralík - Computer Methods in Applied Mechanics …, 2011 - Elsevier
We derive a posteriori error estimates for a class of second-order monotone quasi-linear
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …
diffusion-type problems approximated by piecewise affine, continuous finite elements. Our …
[图书][B] Accuracy verification methods: Theory and algorithms
The importance of accuracy verification methods was understood at the very beginning of
the development of numerical analysis. Recent decades have seen a rapid growth of results …
the development of numerical analysis. Recent decades have seen a rapid growth of results …
A residual a posteriori error estimate for the Virtual Element Method
S Berrone, A Borio - Mathematical Models and Methods in Applied …, 2017 - World Scientific
A residual-based a posteriori error estimate for the Poisson problem with discontinuous
diffusivity coefficient is derived in the case of a virtual element discretization. The error is …
diffusivity coefficient is derived in the case of a virtual element discretization. The error is …
[HTML][HTML] Parallel algorithm for solving overdetermined systems of linear equations, taking into account round-off errors
D Lukyanenko - Algorithms, 2023 - mdpi.com
The paper proposes a parallel algorithm for solving large overdetermined systems of linear
algebraic equations with a dense matrix. This algorithm is based on the use of a modification …
algebraic equations with a dense matrix. This algorithm is based on the use of a modification …
[HTML][HTML] Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics …
In this paper we develop adaptive iterative coupling schemes for the Biot system modeling
coupled poromechanics problems. We particularly consider the space–time formulation of …
coupled poromechanics problems. We particularly consider the space–time formulation of …