## Anil N. Hirani

### Research Interest

Applied and computational geometry and topology.

### PublicationsCVCitationsSoftwareDiscrete Exterior Calculus

Computational Bootcamp: Learn Python programming and computational methods in 10 days.

### News

• June 2016: Taught 2 week computational bootcamp to math grad students who were headed for summer internships.
• May 2016: Paper 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 appeared in 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 appeared in print.
• 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 Applied Geometry and Topology as part of the IMSE Symposium on Hot Topics at the Interface of Mathematics and Engineering.

Older news.

### Group Alumni

• Kaushik Kalyanaraman, Completed Ph.D. in CS, November 2015. Now a postdoc at RPI's Scientific Computation Research Center with Mark Shephard.
• Evan VanderZee, Completed Ph.D in Mathematics, December 2009. Now at Argonne National Lab.
• Andrew 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.

### Awards

• 2012 : Best Paper Award (Second Place) in Solid and Physical Modeling 2012, for paper Delaunay Hodge Star.
• 2007 : NSF CAREER Award, Division of Mathematical Sciences (Algebraic Topology and Exterior Calculus in Numerical Analysis)

### Affiliate Faculty Member of

Department of Computer Science, Computational Science and Engineering Program

### Contact

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: Wed Jan 18 10:30:51 CST 2017