What I Do
My research is in the general area of Scientific Computing. My current interests are:1) continuous and discontinuous Galerkin methods for solving systems of nonlinear partial differential equations (see my book), 2) time-integration (multirate and HEVI), 3) adaptive mesh refinement, and 4) high-performance computing. My group works on trying to answer the question of how can we construct complex computer models that run effectively on the world's fastest computers. However, my general research interest lies in real-world problems. To this end, I have been constructing numerical models in order to better capture the behavior of atmospheric and oceanic systems. These are the goals of the projects listed below.
Welcome to my website. I am a Distinguished Professor of Applied Mathematics at the Naval Postgraduate School. I am a founding member of the Scientific Computing group and director of the Center for Computational Mathematics. I am also an Adjunct Professor of Applied Mathematics at the University of California at Santa Cruz. On this website, you will find the work of my group including that of my students and postdocs.
My Mathematics Genealogy: (click here)
Hirsch index: 31 (click here)
Erdos Number: 4
Email address: fxgirald(at)nps.edu, fgiraldo(at)ucsc.edu
Office Phone Number: 1-831-656-2293
LinkedIn Page: (click here)
ResearchGate Page: (click here)
GitHub Page: (click here)
My group and I are interested in developing a general framework for time-integration and preconditioning strategies to increase the computational performance of systems of nonlinear hyperbolic partial differential equations. Now that we have constructed such a framework, we are setting our sights on interesting applications in earth and space weather problems. In addition, my group has also been focusing on Large-Eddy Simulations (LES) to better understand which turbulence closures perform best.