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H. B. Keller and V. Pereyra, “Symbolic Generation of Finite Difference Formulas,” Mathematics of Computation, Vol. 32, 1978, pp. 955-971. doi:10.1090/S0025-5718-1978-0494848-1

has been cited by the following article:

• TITLE: Wave Equation Simulation Using a Compressed Modeler

  AUTHORS: Victor Pereyra

  KEYWORDS: Wave Equation; POD; Model Order Reduction; Earth Imaging

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3, September 5, 2013

  ABSTRACT: Repeated simulations of large scale wave propagation problems are prevalent in many fields. In oil exploration earth imaging problems, the use of full wave simulations is becoming routine and it is only hampered by the extreme computational resources required. In this contribution, we explore the feasibility of employing reduced-order modeling techniques in an attempt to significantly decrease the cost of these calculations. We consider the acoustic wave equation in two-dimensions for simplicity, but the extension to three-dimensions and to elastic or even anysotropic problems is clear. We use the proper orthogonal decomposition approach to model order reduction and describe two algorithms: the traditional one using the SVD of the matrix of snapshots and a more economical and flexible one using a progressive QR decomposition. We include also two a posteriori error estimation procedures and extensive testing and validation is presented that indicates the promise of the approach.