Wave Equation Simulation Using a Compressed Modeler
- 1 Energy Resources Engineering, Stanford University, Stanford, USA
Abstract
Repeated simulation s 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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