Robert Kirby

Current Contact Information

Associate Professor
Department Mathematics and Statistics
College of Arts and Sciences
Texas Tech University
Math/Stat Building, Room 243
Phone: (806)742-2580x243
Fax: (806)742-1112
Email: string.join( map( lambda x:string.join(x,".") , [ [ "robert" , "c" , "kirby" ] , [ "ttu" , "edu" ] ] ) , "@" )

Previous Positions

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

This spring I'm teaching Numerical Analysis (Math 4312-001). Previously, I've taught Linear Algebra (Math 2360), Classical and Applied Analysis (Math 5310), Functional Analysis (Math 5340/1), Differential Equations (Math 3354), Calculus I and II (Math 1351/2), Analysis for Applications (Math 5399), Numerical Analysis (Math 5334/5) and topics classes on finite elements and finite volumes. At UC, I taught a variety of introductory programming and computer science classes, plus graduate numerical linear algebra.

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

• V. Howle, R. Kirby, and G. Dillon, "Block Preconditioners for Coupled Physics Problems", submitted to SIAM J. Scientific Computing.
• J. Benk, K. Long, R. Kirby, and M. Mehl, "Adaptive parallel Cartesian mesh in a FEM PDE-toolbox environment," submitted to ACM Trans. Math. Software
• R. C. Kirby and T. T. Kieu, "Symplectic-mixed finite element approximation of linear wave equations," submitted to SIAM J. Numerical Analysis. (pdf)

Accepted

• P. Bochev, H. C. Edwards, R. C. Kirby, K. Peterson, and D. Ridzal, "Solving PDEs with Intrepid," to appear, Scientific Programming.
• B. Brennan, V. E. Howle, K. Kennedy, R. C. Kirby, and K. R. Long, "Playa: High-performance programmable linear algebra," to appear, Scientific Programming.

Appeared

• R. C. Kirby, and T. T. Kieu, "Fast simplicial quadrature-based finite element operators using Bernstein polynomials," Numerische Mathematik 121(2): 261 -- 279 (2012). (pdf)
• V. E. Howle and R. C. Kirby, "Block preconditioners for finite element discretization of incompressible flow with thermal convection," Numerical Linear Algebra with Applications 19(2): 427 -- 440 (2012). (pdf)
• R. C. Kirby, "Fast simplicial finite element algorithms using Bernstein polynomials," Numerische Mathematik 117(4): 631 -- 652 (2011). (pdf)
• K. R. Long, R. C. Kirby, and B. van Bloemen Waanders, "Unified embedded parallel finite element computations via software-based Frechet differentiation," SIAM J. Scientific Computing 32(6):3323 -- 3351 (2010). (pdf)
• R. C. Kirby, "From functional analysis to iterative methods," SIAM Review 52(2): 269 -- 293 (2010). (pdf)
• R. C. Kirby, "Singularity-free evaluation of collapsed-coordinate orthogonal polynomials," ACM Trans. Math Software 37(1): 1 -- 16 (2010). (pdf)
• M. E. Rognes, R. C. Kirby, and A. Logg, "Efficient assembly of H(div) and H(curl) conforming finite elements," SIAM J. Scientific Computing 31(6):4130--4151 (2009). (pdf)
• A. R. Terrell, L. R. Scott, M. G. Knepley and R. C. Kirby, "Automated FEM Discretizations of the Stokes equations," BIT Numerical Mathematics, 48(2):389--404 (2008).
• R. C. Kirby and A. Logg, "Benchmarking domain-specific compiler optimizations for variational forms," ACM Trans. Math. Software 35(2):1--18 (2008). (pdf)
• R. C. Kirby and L. R. Scott, "Geometric optimization of the evaluation of finite element operators", SIAM J. Scientific Computing 29:827--841 (2007). (pdf)
• R. C. Kirby and A. Logg, "Efficient compilation of a class of variational forms", ACM Trans. Math. Software 33(3):1 -- 20 (2007). (pdf)
• R. C. Kirby and A. Logg, "A compiler for variational forms," ACM Trans. Math. Software. 32:417-444 (2006). (pdf)
• R. C. Kirby, A. Logg, L. R. Scott, and A. Terrel, "Topological optimization of the evaluation of finite element matrices," SIAM J. Scientific Computing 28:224-240 (2006). (pdf)
• R. C. Kirby, "Optimizing FIAT with Level 3 BLAS," ACM Trans. Math. Software. 32:223--235 (2006). (pdf)
• R. C. Kirby, M. G. Knepley, A. Logg, and L. R. Scott, "Optimizing the evaluation of finite element matrices," SIAM J. Scientific Computing 27:741-758 (2005). (pdf)
• R. C. Kirby, "FIAT: A new paradigm for computing finite element basis functions," ACM Trans. Math. Software. 30:502-516 (2004). (pdf)
• R. C. Kirby, "A new look at expression templates for matrix computation," IEEE Computing in Science and Engineering, 5:66-70 (2003).
• R. Kirby, "A Posteriori Error Estimates for the Mixed Hybrid Finite Element Method," Computational Geosciences. 7:197-214 (2003).
• R. Kirby, "On the convergence of high resolution methods with multiple time scales for hyperbolic conservation laws", Math. Comp. 72:1239-1250 (2003). (pdf)
• C. Dawson and R. Kirby, "High resolution schemes for conservation laws with locally varying time steps", SIAM J. Sci. Comput. 22:2256-2281 (2001). (pdf)
• C. Dawson and R. Kirby, "Solution of parabolic equations by backward-Euler mixed finite elements on a dynamically changing mesh", SIAM J. Numer. Anal. 37:423-442 (2000). (pdf)
• C. Dawson, S. Bryant, and R. Kirby, "Dynamically adaptive upwind finite volume methods for contaminant transport," Computational Methods in Water Resources XII, vol. 2, 641-648 (1998).

Students

Ph.D. students

Brian Brennan (in progress): working on B-spline finite elements. 2011 Summer Internship at Argonne.
Geoffrey Dillon (in progress): Schur complements and block preconditioners for coupled diffusion systems
Kieu Tri Thinh (in progress): Bernstein-based finite elements, spectra of Bernstein-based FEM operators

M.S. Students

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