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What's New
  • For a detailed discussion on my research, please visit Research News.

  • The 3rd  North American High Order Methods Conference (NAHOMCon) will be held on June 17-19, 2024 at Dartmouth College where I will be one of the plenary speakers. Looking forward to meeting many of you.

What I Do

I surf every day but also try to do some math. 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 (e.g., multirate, HEVI, implicit); and 3) applications in fluid dynamics. My group works on how best to construct complex computer models that run effectively on the world's fastest computers. My general research interest lies in real-world problems. To this end, I have been constructing numerical models 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 and founding member of the Scientific Computing group of Applied Mathematics at the Naval Postgraduate School.  I am currently serving as Chair of the department. 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.

General Information

My Mathematics Genealogy: (click here)

Hirsch Index: 36 (click here)

Scopus Profile: (click here)

Erdos Number: 4

Email address: fxgirald(at), fgiraldo(at)

Office Phone Number: 1-831-656-2207

LinkedIn Page: (click here)

ResearchGate Page: (click here)

GitHub Page: (click here)

GitLab Page: (click here)

Surfline: (click here)

Carmel ClamCam: (click here)

Recent Interests

My group focuses on the development of a general modeling framework  for systems of nonlinear hyperbolic partial differential equations (e.g., Navier-Stokes).  With this framework in place, we seek to tackle interesting applications in earth and space weather problems. My group has also been focusing on Large-Eddy Simulations (LES) to better understand the fine-scale structures of meteorological processes, such as hurricanes. This work includes exploiting static/dynamic mesh refinement, multi-scale modeling, scientific machine learning, and high-performance computing on GPUs. For more information on this work visit the NUMA and xNUMA pages. NUMA is the general Navier-Stokes solver whereas xNUMA is the multi-scale modeling framework component. 

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