Wave Equation Simulation Using a Compressed Modeler

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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.

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