A two-grid finite-element/reduced basis scheme for the approximation of the solution of parameter dependent PDE

Abstract : In the frame of optimization process in industrial framework, where numerical simulation is used at some stage, the same problem, modeled with partial differential equations depending on a parameter has to be solved many times for different sets of parameters. The reduced basis method may be successful in this frame and recent progress have permitted to make the computations reliable thanks to a posteriori estimators and to extend the method to non linear problems thanks to the "magic points" interpolation. However, it may not always be possible to use the code (for example of finite element type that allows for evaluating the elements of the reduced basis) to perform all the "off-line" computations required for an efficient performance of the reduced basis method. We propose here an alternating approach based on a coarse grid finite element the convergence of which is accelerated through the reduced basis and an improved post processing.
Document type :
Conference papers
Complete list of metadatas

Cited literature [6 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01420726
Contributor : Mathias Legrand <>
Submitted on : Tuesday, December 20, 2016 - 11:17:32 PM
Last modification on : Tuesday, February 18, 2020 - 4:28:10 PM
Long-term archiving on: Tuesday, March 21, 2017 - 2:45:38 AM

File

r_G5O17BA7.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-01420726, version 1

Citation

Rachida Chakir, Yvon Maday. A two-grid finite-element/reduced basis scheme for the approximation of the solution of parameter dependent PDE. 9e Colloque national en calcul des structures, CSMA, May 2009, Giens, France. ⟨hal-01420726⟩

Share

Metrics

Record views

279

Files downloads

70