Wave Equation Simulation in Two-Dimensions Using a Compressed Modeler

Repeated simulation of large scale wave propagation problems are prevalent in many fields. In oil exploration imaging problems the use of full wave simulations is becoming routinary and it is only hampered by the extreme computational resources required. In this contribution we study the feasibility of employing model order reduction techniques for the wave equation, in an attempt to decrease the cost of these calculations by at least an order of magnitude. We consider simply the acoustic wave equation in two-dimensions, but the extensions to three-dimensions and to elastic or even anysotropic problems are clear. We use the proper orthogonal decomposition approach to model order reduction and describe two algorithms: one that uses the singular value decomposition and another that uses a less expensive progressive QR decomposition. We include also two a posteriori error estimation procedures. Extensive testing and validation is performed that indicates the promise of the approach.