During my B.S. and Masters I worked at UNAM with Paco Sanchez-Sesma and Paco Luzon in Integral Equations applied to wave propagation. I developed Paco's idea on an approximate Green's function for a constant gradient in velocity (Master's thesis). In addition, I studied and developed a fluid-solid interaction algorithm to study the seismic response of dams (B.S. thesis).
Finite Elements
In order to solve realistic problems in wave propagation I started to learn Finite Elements with Gustavo Ayala at UNAM. As a civil engineer I used and developed standard structural analysis codes in order to explore the torsion problem in buildings. In wave propagation, I worked 2D SH and P-SV cases.
At CMU, I have mastered Finite Elements. This technique is the tool I use to simulate large scale problem and Dynamic Rupture. I am one of the main developers ( with Tiankai Tu, Julio Lopez and Ricardo Taborda) of Hercules, a finite element toolchain tailored for big simulations.
This is my PhD topic. I develop new high order Finite Elements and stress glut type methods to handle the dynamic rupture problem. With Hiroyuki Goto, I develop an integral equation and finite elements hybrid method.
Quake project.- I am an active member of the Quake project. The objective is the development of computational tools useful for analyzing the wave propagation due to earthquakes. Los Angeles basin has been the main target, although there are plans to study some other regions.
Mexico city project.- Moises Contreras and I initiated the development of the first Central Mexico data base of soil properties. Soon it will be available. The objective is to have a model that can be used with tools developed by the Quake team.