Survey of multifidelity methods in uncertainty propagation, inference, and optimization

B Peherstorfer, K Willcox, M Gunzburger - Siam Review, 2018 - SIAM
In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

Multiphysics simulations: Challenges and opportunities

DE Keyes, LC McInnes, C Woodward… - … Journal of High …, 2013 - journals.sagepub.com
We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

[图书][B] Finite elements II

A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

[图书][B] The mathematical theory of finite element methods

SC Brenner - 2008 - Springer
Untitled Page 1 Page 2 15 Texts in Applied Mathematics Editors JE Marsden L. Sirovich SS
Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton Page 3 Texts in Applied …

Algebraic multigrid methods

J Xu, L Zikatanov - Acta Numerica, 2017 - cambridge.org
This paper provides an overview of AMG methods for solving large-scale systems of
equations, such as those from discretizations of partial differential equations. AMG is often …

[图书][B] Finite elements: Theory, fast solvers, and applications in solid mechanics

D Braess - 2001 - books.google.com
" This definitive introduction to finite element methods has been updated thoroughly for this
third edition, which features important new material for both research and application of the …

[图书][B] Domain decomposition methods for partial differential equations

A Quarteroni, A Valli - 1999 - academic.oup.com
Abstract Domain decomposition methods are designed to allow the effective numerical
solution of partial differential equations on parallel computer architectures. They comprise a …

A convergent adaptive algorithm for Poisson's equation

W Dörfler - SIAM Journal on Numerical Analysis, 1996 - SIAM
We construct a converging adaptive algorithm for linear elements applied to Poisson's
equation in two space dimensions. Starting from a macro triangulation, we describe how to …

[图书][B] Newton methods for nonlinear problems: affine invariance and adaptive algorithms

P Deuflhard - 2011 - books.google.com
This book deals with the efficient numerical solution of challenging nonlinear problems in
science and engineering, both in finite dimension (algebraic systems) and in infinite …

[图书][B] Iterative solution of large sparse systems of equations

W Hackbusch - 1994 - Springer
The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …