Anil N. Hirani
Associate Professor, Department of Mathematics
University of Illinois at Urbana-Champaign
Research Interest Numerical analysis (discrete and
finite element exterior calculus) and applied and computational
on comparison of discrete Hodge star operators on surfaces has
appeared Computer-Aided Design journal and will also be presented at
the Solid and Physical Modeling conference in Berlin in June. We
show that solving PDEs using non-diagonal barycentric Hodge stars is
just as efficient using diagonal circumcentric Hodge star. This
permits the use of DEC (at least in 2D) on arbitrary meshes, not
just Delaunay meshes. This should prove to be useful for adaptive
meshing, amongst other things.
- February 2016: Navier-Stokes DEC discretization paper has
Journal of Computational Physics.
- September 2015: Paper on blood perfusion in retina using a
hierarchical porous media flow model has been accepted in the
journal Biomechanics and Modeling in Mechanobiology. The
computations were setup using our Python
library PyDEC. Our
computations show that the curvature of the retina does play a role
in blood flow in retina. Title: "Effect of ocular shape and vascular
geometry on retinal hemodynamics: a computational model".
- August 2015:
Submitted paper on
discretization of Navier-Stokes using discrete exterior calculus
(joint with Mamdouh Mohamed and Ravi Samtaney of KAUST). We
discretized the nonlinear convection term using an algebraic
discretization of contraction and a combinatorial discretization
of wedge product. These discretization formulas first appeared in
my 2003 dissertation.
- June 2015: Our Darcy
flow paper has now
- June 2014: I taught CBMG
2014: Computational Boot camp
for Mathematics Graduate
students. This was a 2 week, intensive, hands-on introduction to
computation aimed at mathematics graduate students. The boot camp
was aimed at preparing students to use computations for solving mathematical
problems in science and engineering.
- February 2014: Hal Schenck and I co-organized a workshop on
Geometry and Topology as part of the IMSE Symposium on Hot
Topics at the Interface of Mathematics and Engineering.
- Kaushik Kalyanaraman, Completed Ph.D. in CS, November 2015. Now
a postdoc at RPI's Scientific Computation Research Center with Mark Shephard.
VanderZee, Completed Ph.D in Mathematics, December
2009. Now at Argonne National
Coadvised with Vadim Zharnitsky of
Colombi, Graduated with Ph.D in CS, August 2008. Now
at Palantir in Silicon Valley.
- John Jossey
(Postdoc), September 2006 - August 2007. Now in finance
industry at RBC Capital Markets.
- 2012 : Best Paper Award (Second Place) in Solid and Physical Modeling
2012, for paper Delaunay
- 2007 : NSF CAREER Award, Division of Mathematical Sciences
(Algebraic Topology and Exterior Calculus in Numerical Analysis)
- 2013-, Associate Professor, University of Illinois at Urbana-Champaign,
Department of Mathematics
- 2005-2013, 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
California Institute of Technology
Control and Dynamical Systems
- 2003, Ph.D,
California Institute of
Jerrold E. Marsden),
Ph.D in Computer Science with minors
in Mathematics and
Control and Dynamical Systems
Ph.D Thesis, Discrete Exterior Calculus
- Engineer, Sony Corporation
- Software Engineer, Sun Microsystems
- M.S, Computer Science (Theoretical track),
- Undergraduate degree, Computer Science
Birla Institute of Technology and Science (BITS), Pilani, India
Affiliate Faculty Member of
Department of Computer Science,
Computational Science and
E-mail: hirani at illinois dot edu;
Office: 375 Altgeld Hall;
Phone: (217) 333 2727
Mailing Address: Department of Mathematics, 1409 W. Green St., M/C 382, Urbana, IL 61801.
Page maintained by Anil Hirani.
Last modified: Thu May 12 14:20:53 CST 2016