[Alumnos] Charla Dr. Victor Pereyra (fwd)

[Secretaria General de la FCAG]

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          Charla invitada del Dr. Victor Pereyra en la FCAGLP

           Viernes 14 de Diciembre, 12:00hs, Aula F (Óptica).

       Fast acoustic wave propagation simulation by model order reduction

                         Victor  Pereyra
            Weidlinger  Associates Mountain  View, CA,
                  3DGeo Inc, Santa Clara, CA and
       Computational Science Research Center, San Diego State Univ.

  We will  describe the ideas  behind a method for  reducing drastically
  the number  of degrees of  freedom in wave propagation  simulations by
  the method of Proper Orthogonal Decomposition.

  The basic tenants are:

  It is necessary to solve many related wave propagation problems, such
  as  in Oil  Exploration Earth  Imaging.  It  is feasible  to  use full
  fidelity  solvers to generate  snapshots of  the field  at appropriate
  times.  It  is feasible to calculate the  Singular Value Decomposition
  of the resulting matrix of snapshots.

  In  a pre-processing  stage, one  (or several,  but few)  full fidelity
  calculations  (expensive) are  performed.   A matrix  of snapshots  is
  created that may have many millions of rows (field variables), but
  only a few hundred columns (snapshots)  and a Singular Value 
Decomposition
  is calculated. By introducing an appropriate threshold, an orthogonal 
basis
  of the snapshots is chosen, containing the left singular vectors
  associated  with the  significant singular values.

  With this basis and a Ritz-Galerkin collocation approach, a set of time
  dependent coefficients is  derived by solving a small  set of Ordinary
  Differential Equations. This completes the calculation for the reduced
  system.

  We show some numerical results that give an idea of the quality of the
  approximate solutions obtained  by this method and the levels of data
  compression that arise.