Model Reduction for Wave Equations and Its Applications to Inversion
Abstract
In high resolution seismic imaging or medical imaging, one deals with models or media with large degrees of freedoms. During the inversion process, the forward problem is solved repeatedly using many different inputs, and this process is prohibitively expensive. In this talk, the speaker will present a new model reduction methodology for wave equations in heterogeneous media. The main idea of the proposed approach is to obtain the important scales among all scales within the solution. In the first step, the speaker will construct local snapshots by solving local problems, and the local snapshots represent some features of the solution. This process is also a way to learn about the effect on the media to the solution. In the next step, the speaker will perform a dimension reduction procedure, and construct the dominant modes within the snapshot space. This is achieved by some carefully designed spectral problems. The resulting generalized multiscale finite element method is able to solve wave equations in heterogeneous media with a good accuracy and a reduced computational cost.
About the speaker
Prof. Eric Chung received his PhD from the University of California at Los Angeles in 2005. Prior to joining the Chinese University of Hong Kong (CUHK) in 2008, he held the positions of Visiting Assistant Professor in the University of California at Irvine in 2005 – 2006 and von-Karman Instructor in the California Institute of Technology in 2006 – 2008. He is currently an Associate Professor in the Department of Mathematics at CUHK and an Adjunct Associate Professor in the Department of Mathematics at the Texas A&M University.
Prof. Chung’s research interests are numerical analysis and scientific computing. Specifically, he works on computational partial differential equations, numerical methods for wave propagation, flows in heterogeneous media, model reduction for multiscale problems, multiscale finite element methods, domain decomposition methods, inverse problems and traveltime tomography.
About the program
For more information, please refer to the program website http://iasprogram.ust.hk/inverseproblems for details.
