Book ChapterDOI
Introduction to model order reduction
Wha Wil Schilders,Wha Wil Schilders +1 more
- Vol. 13, pp 3-32
TLDR
It is argued that much more complex problems can be addressed by making use of current computing technology and advanced algorithms, but that there is a need for model order reduction in order to cope with even morecomplex problems.Abstract:
In this first section we present a high level discussion on computational science, and the need for compact models of phenomena observed in nature and industry. We argue that much more complex problems can be addressed by making use of current computing technology and advanced algorithms, but that there is a need for model order reduction in order to cope with even more complex problems. We also go into somewhat more detail about the question as to what model order reduction is.read more
Citations
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Journal ArticleDOI
Prospective Interest of Deep Learning for Hydrological Inference
TL;DR: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad, or from public or private research centers.
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Damage detection in structural systems utilizing artificial neural networks and proper orthogonal decomposition
Journal ArticleDOI
Computational Reduction for Parametrized PDEs: Strategies and Applications
TL;DR: A compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.
Journal ArticleDOI
Gradient-enhanced surrogate modeling based on proper orthogonal decomposition
TL;DR: It is proved that the resulting predictor reproduces these inputs exactly up to the standard POD truncation error, so the enhanced predictor can be considered as (approximately) first-order accurate at the snapshot locations.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
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Methods of Conjugate Gradients for Solving Linear Systems
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BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems
TL;DR: Numerical experiments indicate that the new variant of Bi-CG, named Bi- CGSTAB, is often much more efficient than CG-S, so that in some cases rounding errors can even result in severe cancellation effects in the solution.
Journal ArticleDOI
Multi-level adaptive solutions to boundary-value problems
TL;DR: In this paper, the boundary value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes, and interactions between these levels enable us to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); and conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "°°-order" approximations and low n, even when singularities are present.