Plenary Session - Friday, July 18, 9:00 am

Toward our goal of modeling strong earthquakes in seismic regions, we are interested in determining mechanical properties of sedimentary basins (such as the greater Los Angeles Basin) and descriptions of earthquake sources from seismograms of past earthquakes. This gives rise to very large inverse problems of recovering the coefficients and source of the elastic wave equation from boundary observations of the response. Our current forward simulations involve 100 million finite elements; over the next several years the desired increase in resolution and growth in basin size will require an order of magnitude increase in number of unknowns. Inversion of such forward models provides a major challenge for inverse methods. It is imperative that these methods be able to scale algorithmically to O(10^9) grid points, to highly-resolved (e.g. grid-based) elastic material models of large seismic basins, and to parallel architectures with thousands of processors.

I will discuss prototype multiscale parallel algorithms for the earthquake material and source inversion problem. Tikhonov and total variation regularization treat ill-posedness associated with rough components of the model, while multiscale grid/frequency continuation addresses multiple minima associated with smooth components. Parallel inexact Gauss-Newton-Krylov methods are used to solve the optimality conditions. CG matrix-vector products are computed via checkpointed adjoints, which involve forward and adjoint wave equation solutions at each iteration. Preconditioning is via limited memory BFGS updates, initialized with approximate inverses of the Gauss-Newton Hessian. Experience on problems with up to several million grid points suggests near mesh-independence of Newton and CG iterations, good parallel efficiency, and distinct speedups over a quasi-Newton method. However, significant difficulties remain, and I will conclude with a discussion of these, along with possible avenues for addressing them.

This work is joint with Volkan Akcelik, Jacobo Bielak, Ioannis Epanomeritakis, and Euijoong Kim at Carnegie Mellon, George Biros at Courant, and other members of the Quake Project.

Bio
Omar Ghattas is Professor of Civil & Environmental Engineering and Biomedical Engineering, and Director of the Mechanics, Algorithms, and Computing Laboratory, at Carnegie Mellon University. He received his BS, MS, and PhD from Duke University in 1984, 1986, and 1988, respectively. He joined CMU in 1989 after serving as a postdoctoral research associate at Duke. He has been a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE) at NASA-Langley Research Center; the Computer Science Research Institute (CSRI) at Sandia National Laboratories; and the Center for Applied Scientific Computing (CASC) at Lawrence Livermore National Laboratory. He has general research interests in computational science and engineering, with particular emphasis on simulation and optimization of complex multiscale systems on high performance computers.

E-mail questions and inquiries to em03@ce.washington.edu.