Robert Kirby

Current Contact Information

Associate Professor
Department Mathematics
Baylor University
Sid Richardson Building, Room 320
Phone: (254)710-4846
Fax: (254)710-3569
Email: reduce( operator.add , ["Robert","_","Kirby","@","baylor",".","edu"] , "" )

Previous Positions

Associate Professor, Texas Tech University, 2006-20012.
Assistant Professor, University of Chicago, 2002-2006.
Dickson Instructor, University of Chicago, 2000-2002.
Ph.D., University of Texas at Austin, 2000.


Research Interests

Computers were invented to automate tedious and error-prone tasks, like the vast hoards of arithemtic operations required to perform advanced numerical simulations of science and engineering problems. However, programming computers is itself a tedious and error-prone task. So, why not get a computer to do it?

At the intersection of mathematics and computer science, one finds "metanumerical computing" - the use of mathematical structure to generate, manipulate, and optimize numerical software. I have contributed to several large software projects, such as Trilinos (especially Sundance and Intrepid) and the FEniCS project (especially FIAT and FErari, although I did some early conceptual work on ffc). Basically, the goal is to fuse together aspects of domain-specific languages with structural and algorithmic aspects of finite elements to produce easy-to-use yet highly efficient code systems that provide efficient implementations of state-of-the-art numerical methods. Or, you can call it "numerical methods with a universal quantifier".

While these tools are still under development and yet widely used in applications, it is also important to continue pressing forward the state of the art for basic research. One ongoing project is to develop low-complexity simplicial finite element methods based on Bernstein polynomials. These will keep the same of generality with respect to unstructured geometry and high-order approximation currently offered by automated PDE codes like Sundance and FEniCS, but also have run-time costs comparable to tensor-product spectral elements and similarly support efficient multicore implementations. Fresh results extending these techniques to the Finite Element Exterior Calculus coming soon.

Also, given the ability to solve one problem well, how do we solve two problems glued together? Vicki Howle and I are using Sundance as a suite to develop block preconditioners for multiphysics problems. These problems employ some new mathematical insights based on PDE theory and compact operators.

Teaching

Spring 2014, I am teaching:

My students should check Blackboard as the semester begins for course information.

Publications

Book Chapters

I have contributed nine peer-reviewed chapters to the newly-released Springer book on the FEniCS project: Automated Solution of Differential Equations by the Finite Element Method (Logg, Mardal, Wells, eds). Coming soon to a bestseller list near you!

Submitted

To appear

Appeared

Students

Ph.D. students

Brian Brennan (in progress at Baylor): finite element modeling of trace gas sensors
Geoffrey Dillon (in progress at TTU): Schur complements and block preconditioners for coupled systems
Thinh Tri Kieu (in progress at TTU): Finite element methods for nonlinear wave equations.

M.S. Students

Andy Terrel (joint with Ridg Scott, 2007), now at Continuum Analytics.