Accelerating numerics on PDEs using POD and Galerkin projection

Terragni, Filippo and Rapun Banzo, Maria Luisa and Vega de Prada, José Manuel (2010). Accelerating numerics on PDEs using POD and Galerkin projection. In: "DSPDES 2010, Emerging Topics in Dynamical Systems and Partial Differential Equations", 31/05/2010 - 04/06/2010, Barcelona, España.

Description

Title: Accelerating numerics on PDEs using POD and Galerkin projection
Author/s:
  • Terragni, Filippo
  • Rapun Banzo, Maria Luisa
  • Vega de Prada, José Manuel
Item Type: Presentation at Congress or Conference (Article)
Event Title: DSPDES 2010, Emerging Topics in Dynamical Systems and Partial Differential Equations
Event Dates: 31/05/2010 - 04/06/2010
Event Location: Barcelona, España
Title of Book: Proceedings of the DSPDES 2010, Emerging Topics in Dynamical Systems and Partial Differential Equations
Date: 2010
Subjects:
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A method will be described to accelerate time-dependent numerical solvers of PDEs that is based on the combined use of proper orthogonal decomposition (POD) and Galerkin projection. POD is made on some sets of snapshots that are calculated using the numerical solver, and the governing equations are Galerkin-projected onto the POD-calculated modes. Snapshots calculation and Galerkin projection are made in interpersed time intervals. Switching between both is made using an a priori error estimate that provides quite good results. Several additional improvements make the method both robust and computationally e±cient. The method will be applied to two one-dimensional problems, a time-dependent Fisher equation and the complex the Ginzburg-Landau (GL) equation. In these two cases results are excellent, even in cases in which the GL equation exhibits transient chaos; compression factors (measuring the ratio of the total time span to the total length of the time intervals in which the full numerical solver is applied) are of the order of 10, and can be increased to 80 using a snapshots library to initiate the process. Application will also be made to a two-dimensional problem, namely the pulsating cavity problem, which describes the motion of liquid in a square box whose upper wall is moving back and forth in a quasi-periodic fashion. In this case, the numerical solver will be based on a rough (but quick) computational °uid dynamics (CFD) code that resembles those (industrial) codes that are usually used in Industry. Consequently, it is the numerical code and not the governing equations themselves that is projected into the POD modes. Results are again excellent; compression factors are again of the order of 10 and are increased using a snapshots library. Projection of the exact governing equations will also be considered. Several consequences of all these will be brie°y discussed.

More information

Item ID: 7527
DC Identifier: http://oa.upm.es/7527/
OAI Identifier: oai:oa.upm.es:7527
Official URL: http://www.dspdes2010.org/frontal/default.asp
Deposited by: Memoria Investigacion
Deposited on: 15 Jun 2011 09:45
Last Modified: 20 Apr 2016 16:39
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