Reduced Basis’ Acquisition by a Learning Process for Rapid On-line Approximation of Solution to PDE’s: Laminar Flow Past a Backstep

Reduced Basis’ Acquisition by a Learning Process for Rapid On-line Approximation of Solution to... Reduced basis methods for the approximation to parameter-dependent partial differential equations are now well-developed and start to be used for industrial applications. The classical implementation of the reduced basis method goes through two stages: in the first one, offline and time consuming, from standard approximation methods a reduced basis is constructed; then in a second stage, online and very cheap, a small problem, of the size of the reduced basis, is solved. The offline stage is a learning one from which the online stage can proceed efficiently. In this paper we propose to exploit machine learning procedures in both offline and online stages to either tackle different classes of problems or increase the speed-up during the online stage. The method is presented through a simple flow problem—a flow past a backward step governed by the Navier Stokes equations—which shows, however, interesting features. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Computational Methods in Engineering Springer Journals

Reduced Basis’ Acquisition by a Learning Process for Rapid On-line Approximation of Solution to PDE’s: Laminar Flow Past a Backstep

Loading next page...
 
/lp/springer_journal/reduced-basis-acquisition-by-a-learning-process-for-rapid-on-line-YCiGASf2Fb
Publisher
Springer Netherlands
Copyright
Copyright © 2017 by CIMNE, Barcelona, Spain
Subject
Engineering; Mathematical and Computational Engineering
ISSN
1134-3060
eISSN
1886-1784
D.O.I.
10.1007/s11831-017-9238-z
Publisher site
See Article on Publisher Site

Abstract

Reduced basis methods for the approximation to parameter-dependent partial differential equations are now well-developed and start to be used for industrial applications. The classical implementation of the reduced basis method goes through two stages: in the first one, offline and time consuming, from standard approximation methods a reduced basis is constructed; then in a second stage, online and very cheap, a small problem, of the size of the reduced basis, is solved. The offline stage is a learning one from which the online stage can proceed efficiently. In this paper we propose to exploit machine learning procedures in both offline and online stages to either tackle different classes of problems or increase the speed-up during the online stage. The method is presented through a simple flow problem—a flow past a backward step governed by the Navier Stokes equations—which shows, however, interesting features.

Journal

Archives of Computational Methods in EngineeringSpringer Journals

Published: Aug 5, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Access to DeepDyve database
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off