David M Williams

About David M Williams

I hold a PhD in Aeronautics and Astronautics from Stanford University, and an associate professorship in the mechanical engineering department at Penn State. I am an expert in developing numerical methods for solving time-dependent partial differential equations (PDEs). I also have a strong interest in computational geometry and topological data analysis (TDA). My research focuses on improving the accuracy and reliability of algorithms for computational physics, with a particular emphasis on computational fluid dynamics (CFD).My research philosophy is grounded in the following ideas (in no particular order):1.\"The future is four-dimensional.\" I believe that four-dimensional space-time methods are absolutely necessary in order to fully capitalize on the capabilities of future, high-performance computing architectures. 2.\"Math is the only solid foundation for numerical simulation.\" It is extremely important to develop numerical algorithms which are provably stable and accurate. Today\'s computer codes are too complex for us to consistently distinguish between programming errors and more insidious conceptual mistakes. 3.\"Mathematical rigor without eventual application is useless.\" I spent several years working at Boeing, and I have seen the positive impact of a well-chosen application. From my perspective, there are too few people bridging the gap between advanced mathematics and practical applications. We should not settle for beautiful math, that no one will ever implement.4. The late Steve Karman said that \"you cannot solve what you cannot resolve.\" I am devoted towards unstructured, adaptive, mesh generation techniques which are capable of optimally distributing degrees of freedom in both space and time. We must resolve all important length and time scales.5.\"Pursue integrity in all things.\" I do not believe in doing things solely for appearance or for profit. It does not matter how lucrative a particular area of research appears to be. It must be founded in valid, mathematical ideas in order for me to seriously consider it. I am not interested in chasing after the latest fads.

Experience

1. Nsf I-corps Enrollee

   Nsf I-Corps Hub Mid-Atlantic Region

   May 2025 — Present

Education

• Stanford University

  Master's degree, Aerospace, Aeronautical and Astronautical Engineering

• University of Michigan

  Bachelor's degree, Aerospace, Aeronautical and Astronautical Engineering

• Stanford University

  Doctor of Philosophy - PhD, Aerospace, Aeronautical and Astronautical Engineering