Anil N. Hirani
Assistant Professor of Computer Science
Publications and Preprints
My papers are available
here.
Research Interests
- Discretization of exterior calculus (DEC):
vector calculus generalizes to nonlinear manifolds as exterior
calculus in DEC we are attempting to build a complete mathematical and
computational framework in which theorems from the smooth world have
discrete analogs.
- Numerical solution of partial differential equations
(PDEs): formulation using differential forms and solution
using DEC, for PDE vector problems for which traditional vector finite
element methods are unstable, e.g. Poisson's equation in first order
form or flow in porous media.
- Computational algebraic topology: computation of
topological invariants of simplicial complexes using DEC and
computational Hodge theory, with applications e.g. in mesh topology,
machine learning, or sensor networks coverage analysis.
- Optimized triangulations: creation of optimized
triangulations for numerical PDEs and computational topology,
e.g. well-centered triangulations (in which each simplex contains its
circumcenter) and acute triangulations.
- Computational astrodynamics: adaptive
representation and computation of gravitational field of small
irregular bodies like asteroids and comets for fast trajectory
propagation; applications of dynamical systems to low thrust space
mission trajectory design.
News
May 22, 2009: Open problem solved :
dihedral acute triangulation of cube !
This seemingly simple problem had been open for
many years : triangulate a cube into tetrahedra such that each
triangle has acute angles and all angles between triangles are acute.
It was not even known if such a triangulation exists ! Our preprint
(available here, now
accepted in journal Computational Geometry: Theory and
Applications) gives the solution of this problem with the help of
algorithms and software we developed for well-centered triangulation
(WCT). WCT is described in many papers available on my publications page. This is work of my
student Evan VanderZee (co-advised with Vadim Zharnitsky) in
collaboration with Damrong Guoy. Edgar Ramos is another collaborator
in the WCT project. The vertex data and program for computing the
angles is available
here.
Awards
- 2007 :
NSF CAREER Award
(Algebraic Topology and Exterior Calculus in Numerical Analysis)
- 2003 : SIAM Student Paper Competition, Honorable Mention
(Discrete Exterior Calculus: Theory and Applications)
Teaching
Group Alumni
- John Jossey (Postdoc), September 2006 - August 2007
- Andrew Colombi,
Graduated with Ph.D in CS, August 2008
Theses
CV
- 2005-current, Assistant Professor,
University of Illinois at Urbana-Champaign,
Department of Computer Science
- 2004-05, Senior Engineer,
Jet Propulsion Laboratory Guidance, Navigation and Control Section
- 2003-04, CIMMS
Postdoctoral Scholar,
California Institute of Technology
(Caltech),
Control and Dynamical Systems
- 2003, Ph.D,
California Institute of
Technology (Caltech),
(Advisor:
Jerrold E. Marsden),
Ph.D in Computer Science with minors
in Mathematics and
Control and Dynamical Systems
Thesis :
Discrete Exterior Calculus
- 2000, M.S, Computer Science,
Caltech
- Engineer, Sony Corporation
- Software Engineer, Sun Microsystems
- M.S, Computer Science (Theoretical track),
Stanford University
- Undergraduate degree, Computer Science
Birla Institute of Technology and Science (BITS), Pilani, India 7
Affiliations
Department of Computer Science,
Computational Science and
Engineering Program,
Applied Mathematics Program
Contact
E-mail: hirani at cs dot illinois dot edu;
Office: 4320 Siebel Center;
Phone: (217) 333 2727
Address: Department of Computer Science, 201 N. Goodwin Ave., Urbana, IL 61801.
Page maintained by Anil Hirani; Last updated August 21, 2009