Accelerating numerics on PDEs using POD and Galerkin projection

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

Descripción

Título: Accelerating numerics on PDEs using POD and Galerkin projection
Autor/es:
  • Terragni, Filippo
  • Rapun Banzo, Maria Luisa
  • Vega de Prada, José Manuel
Tipo de Documento: Ponencia en Congreso o Jornada (Artículo)
Título del Evento: DSPDES 2010, Emerging Topics in Dynamical Systems and Partial Differential Equations
Fechas del Evento: 31/05/2010 - 04/06/2010
Lugar del Evento: Barcelona, España
Título del Libro: Proceedings of the DSPDES 2010, Emerging Topics in Dynamical Systems and Partial Differential Equations
Fecha: 2010
Materias:
Escuela: E.T.S.I. Aeronáuticos (UPM) [antigua denominación]
Departamento: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

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.

Más información

ID de Registro: 7527
Identificador DC: http://oa.upm.es/7527/
Identificador OAI: oai:oa.upm.es:7527
URL Oficial: http://www.dspdes2010.org/frontal/default.asp
Depositado por: Memoria Investigacion
Depositado el: 15 Jun 2011 09:45
Ultima Modificación: 20 Abr 2016 16:39
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