Current Contact Information
Department Mathematics and Statistics
College of Arts and Sciences
Texas Tech University
Math/Stat Building, Room 243
Email: string.join( map( lambda x:string.join(x,".") , [ [ "robert" , "c" , "kirby" ] , [ "ttu" , "edu" ] ] ) , "@" )
Assistant Professor, University of Chicago, 2002-2006.
Dickson Instructor, University of Chicago, 2000-2002.
Ph.D., University of Texas at Austin, 2000.
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
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
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.
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.
I have contributed nine peer-reviewed chapters to the
book on the FEniCS project:
Solution of Differential Equations by the Finite Element Method
(Logg, Mardal, Wells, eds). Coming soon
to a bestseller list near you!
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.
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.
R. C. Kirby, and T. T. Kieu, "Fast simplicial quadrature-based finite element operators using
Bernstein polynomials," Numerische Mathematik 121(2):
261 -- 279 (2012).
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).
R. C. Kirby, "Fast simplicial finite element algorithms using
Bernstein polynomials," Numerische Mathematik 117(4):
631 -- 652 (2011).
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
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).
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).
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).
R. C. Kirby, "Optimizing FIAT with Level 3 BLAS," ACM
Trans. Math. Software. 32:223--235 (2006).
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).
R. C. Kirby, "FIAT: A new paradigm for computing finite element
basis functions," ACM Trans. Math. Software. 30:502-516
R. C. Kirby, "A new look at expression templates for matrix
computation," IEEE Computing in Science and Engineering,
R. Kirby, "A Posteriori Error Estimates for the Mixed Hybrid
Finite Element Method," Computational Geosciences. 7:197-214
R. Kirby, "On the convergence of high resolution methods with
multiple time scales for hyperbolic conservation laws",
Math. Comp. 72:1239-1250 (2003).
C. Dawson and R. Kirby, "High resolution schemes for
conservation laws with locally varying time steps", SIAM
J. Sci. Comput. 22:2256-2281 (2001).
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).
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).
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
Andy Terrel (joint with Ridg Scott, 2007), now at TACC.