- 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:
**C**omputational**B**oot camp for**M**athematics**G**raduate 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.

- Fall 2015: MATH 285 Introduction to Differential Equations
- Spring 2015: MATH 286 Introduction to Differential Equations Plus
- Fall 2014: MATH 595 TTA Top 10 Algorithms of 20th and 21st Century (with Y. Baryshnikov)
- Summer 2014: CBMG 2014 Computational Boot camp for Mathematics Graduate Students
- Fall 2013: MATH 285 Introduction to Differential Equations
- Spring 2013: CS 450 / CSE 401 / ECE 491 / MATH 450 Numerical Analysis
- Fall 2012: CS 357 / MATH 357 Numerical Methods I
- Spring 2012: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
- Fall 2011: CS 450 / CSE 401 / ECE 491 / MATH 450 Numerical Analysis
- Fall 2011: CS 199ANH (Discovery Course) What is Shape ? A Computer Based Exploration
- Spring 2011: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
- Fall 2010: CS 357 / MATH 357 Numerical Methods I
- Spring 2010: CS 555 / MATH 552 / CSE 510 Numerical Methods for PDEs
- Fall 2009: CS 558 / CSE 513 Laplacians on Networks and Meshes (Topics in Numerical Analysis)
- Spring 2009: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
- Fall 2008: CS 558 / CSE 513 Calculus on Meshes (Topics in Numerical Analysis)
- Spring 2008: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
- Fall 2007: CS 257 / MATH 257 Numerical Methods
- Spring 2007: CS 257 / MATH 257 Numerical Methods
- Fall 2006: CS 598ANH Symplectic Integrators and Discrete Mechanics
- Spring 2006: CS 450 / CSE 401 / MATH 450 / ECE 491 Introduction to Numerical Analysis
- Fall 2005: CS 598ANH Calculus on Meshes

- 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.

Coadvised with Vadim Zharnitsky of Mathematics department. - 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.

- 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*)

- 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 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

Ph.D Thesis,**Discrete Exterior Calculus**( Abstract, PDF, BibTeX) - 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

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