Leonardo Andrés Zepeda Núñez
I am a postdoctoral fellow at Lawrence Berkeley National Laboratory in the Mathematics group led by James Sethian, working primarily with Lin Lin. Before, I was a visiting assistant professor at the Department of Mathematics at the University of California at Irvine, working with Pr. Hongkai Zhao. I graduated in June 2015 from MIT with a Ph.D. in Mathematics under the direction of Pr. Laurent Demanet. I am a former student of École Polytechnique and University Pierre et Marie Curie Paris VI.
I am particularly interested in Numerical Analysis, Scientific Computing, Wave Propagation and Inverse Problems. The focus of my research is to develop fast and scalable algorithms for high-frequency computational wave propagation, i.e., algorithms with runtimes that scale linearly, or better, with respect to the number of unknowns, and that can be seamlessly parallelized.
My current projects are fast solvers for the Helmholtz equation, optimal solvers for the wave equation and new numerical methods for quantum chemistry.
The main motivation of my research comes from exploration in geophysics, where the internal properties of the earth are inverted from acoustic (or elastic) data at the surface. One popular and promising technique for inverting the properties of the crust is the full wave-form inversion (FWI). FWI recasts the inversion as the minimization of an objective function, whose gradient involves solving the wave equation (in time or in frequency) several times, which is extremely expensive for realistic applications. Within this context, my research focuses on reducing the total complexity of the bottleneck of the algorithmic pipeline of FWI.