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Wave Equation Simulation Using a Compressed Modeler

American Journal of Computational Mathematics 2013年第3期3卷 231-241页

作者： victor pereyra Energy Resources Engineering Stanford University Stanford USA

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.

关键词： Wave Equation POD Model Order Reduction Earth Imaging

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Imaging Applications with Variable Projections

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American Journal of Computational Mathematics 2019年第4期9卷 261-281页

作者： victor pereyra Godela Scherer Smart Fields Stanford University Stanford CA USA Department of Mathematics University of Reading Reading GB

We review two important fields of application for the method of Variable Projections (VARPRO): Seismic Prospecting and Medical Imaging. We cover the period since 2002 when a first review was published. Variable Projections is a method for the solution of nonlinear least squares problems where the model is a linear combination of nonlinear functions. Its success is based on the fact that the reduced functional, where the linear parameters are eliminated converges always faster than if the same method of solution is applied to the original problem. More importantly, many of these problems are very hard to solve in their original format and VARPRO has shown its value in many different applications.

关键词： Medical Imaging Geophysics Variable Projections Nonlinear Least Squares

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