• A. N. Hirani, A. T. S. Wan, N. Wojtalewicz. Conservative integrators for piecewise smooth systems with transversal dynamics. Journal of Computational Dynamics (2023) 10.3934/jcd.2023009.
• M. D. Schubel, D. Berwick-Evans, A. N. Hirani. Averaging Property of Wedge Product and Naturality in Discrete Exterior Calculus. arXiv:2310.00725 [math.NA] (2023), 12 pages.
• (UPDATED) D. Berwick-Evans, A. N. Hirani, and M. D. Schubel. Discrete vector bundles with connection and the Bianchi identity. arXiv:2104.10277 [math.DG] (2023, 2021), 37 pages. We recently (July 2023) posted a major update.
• M. Wang, P. Jagad, A. N. Hirani, R. Samtaney. Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method. Journal of Computational Physics. Vol. 488 (2023) 10.1016/j.jcp.2023.112245.
• A. N. Hirani, K. Kalyanaraman, H. Wang, S. Watts. Computing discrete harmonic differential forms in a given cohomology class using finite element exterior calculus. Computational Geometry: Theory and Applications 10.1016/j.comgeo.2022.101937 (2022).
• V. Karve and A. N. Hirani. GraphSAT - a decision problem connecting satisfiability and graph theory. arXiv:2105.11390 [math.CO] (2021), 31 pages.
• V. Karve, A. N. Hirani. The complete set of minimal simple graphs that support unsatisfiable 2-CNFs.Discrete Applied Mathematics Vol. 283 (2020), 123-132. 10.1016/j.dam.2019.12.017
• M. S. Mohamed, A. N. Hirani, R. Samtaney. Numerical convergence of discrete exterior calculus on arbitrary surface meshes. International Journal for Computational Methods in Engineering Science & Mechanics Vol. 19 (2018), 194-206. 10.1080/15502287.2018.1446196
• M. S. Mohamed, A. N. Hirani, R. Samtaney. Comparison of discrete Hodge star operators for surfaces. Computer-Aided Design Vol. 78 (2016), 118-125. 10.1016/j.cad.2016.05.002
• M. S. Mohamed, A. N. Hirani, R. Samtaney. Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes. Journal of Computational Physics Vol. 312 (2016), 175-191.
  10.1016/j.jcp.2016.02.028
• A. Dziubek, G. Guidoboni, A. Harris, A. N. Hirani, E. Rusjan, W. Thistleton. Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model. Biomechanics and Modeling in Mechanobiology Vol. 15 (2016), 893-907. 10.1007/s10237-015-0731-8
• A. N. Hirani, K. B. Nakshatrala, J. H. Chaudhry. Numerical method for Darcy flow derived using Discrete Exterior Calculus. International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 16 (2015), 151-169. 10.1080/15502287.2014.977500
• A. N. Hirani, K. Kalyanaraman, S. Watts. Graph Laplacians and Least Squares on Graphs. GABB’2015: Proceedings of Graph Algorithms Building Blocks workshop at the IEEE International Parallel and Distributed Processing Symposium, 812-821, 2015. 10.1109/IPDPSW.2015.73
• A. Demlow and A. N. Hirani. A posteriori error estimates for finite element exterior calculus: The de Rham complex . Foundations of Computational Mathematics Vol. 14 (2014), 1337-1371. 10.1007/s10208-014-9203-2.
• E. VanderZee, A. N. Hirani, D. Guoy, V. Zharnitsky, E. Ramos. Geometric and Combinatorial Properties of Well-Centered Triangulations in Three and Higher Dimensions. Computational Geometry: Theory and Applications, Vol. 46 (2013), 700-724. 10.1016/j.comgeo.2012.11.003,
• N. Bell and A. N. Hirani. PyDEC: Software and Algorithms for Discretization of Exterior Calculus. ACM Transactions on Mathematical Software, Vol. 39 (2012), 3:1-3:41. 10.1145/2382585.2382588
• A. N. Hirani, K. Kalyanaraman, and E. VanderZee Delaunay Hodge Star. Computer-Aided Design, Vol. 45 (2013), 540-544. 10.1016/j.cad.2012.10.038. Corrigendum 10.1016/j.cad.2017.09.005
• A. N. Hirani, K. Kalyanaraman, H. Wang, and S. Watts. Cohomologous Harmonic Cochains. arXiv:1012.2835 [cs.CG] (2011), 16 pages.
• A. N. Hirani, K. Kalyanaraman, and S. Watts. Least Squares Ranking on Graphs. arXiv:1011.1716 [cs.NA] (2011).
• A. N. Hirani and K. Kalyanaraman. Numerical Experiments for Darcy Flow on a Surface Using Mixed Exterior Calculus Methods. arXiv:1103.4865 [cs.NA] (2011).
• T. K. Dey, A. N. Hirani and B. Krishnamoorthy. Optimal Homologous Cycles, Total Unimodularity, and Linear Programming. SIAM Journal on Computing Vol. 40 (2011), 1026-1044. This is a journal version of the preliminary results that appeared in our STOC 2010 paper and contains additional results. 10.1137/100800245
• N. M. Dunfield and A. N. Hirani. The Least Spanning Area of a Knot and the Optimal Bounding Chain Problem. SoCG ’11: Proceedings of the 27th annual ACM symposium on Computational geometry (2011), 135–144. 10.1145/1998196.1998218
• T. K. Dey, A. N. Hirani and B. Krishnamoorthy. Optimal Homologous Cycles, Total Unimodularity, and Linear Programming. STOC '10 : 42nd ACM Symposium on Theory of Computing (2010), 221-230. 10.1145/1806689.1806721
• E. VanderZee, A. N. Hirani, D. Guoy, E. Ramos. Well-Centered Triangulation. SIAM Journal on Scientific Computing Vol. 31 (2010), 4497-4523. 10.1137/090748214
• E. VanderZee, A. N. Hirani, V. Zharnitsky, D. Guoy. A Dihedral Acute Triangulation of the Cube. Computational Geometry: Theory and Applications Vol. 43 (2010), 445-452. 10.1016/j.comgeo.2009.09.001
• A. Colombi, A. N. Hirani, B. F. Villac. Structure preserving approximations of conservative forces for application to small body dynamics. Journal of Guidance, Control, and Dynamics Vol. 32 (2009), 1847-1858. 10.2514/1.42067
• E. VanderZee, A. N. Hirani, D. Guoy. Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra. Proceedings of the 17th International Meshing Roundtable (2008), 19-35. 10.1007/978-3-540-87921-3_2
• A. Colombi, A. N. Hirani, B. F. Villac. Structure preserving approximations of conservative forces for application to small body dynamics. Proceedings of AAS/AIAA Astrodynamics Specialist Conference (2008), Paper AIAA 2008-7205. PDF
• A. Colombi, A. N. Hirani, B. F. Villac. Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies. Journal of Guidance, Control, and Dynamics Vol. 31 (2008), 1041-1051. 10.2514/1.32559
• J. Warren, S. Schaefer, A. N. Hirani, M. Desbrun. Barycentric Coordinates for Convex Sets. Advances in Computational Mathematics Vol. 27 (2007), 319-338. 10.1007/s10444-005-9008-6
• E. VanderZee, A. N. Hirani, D. Guoy, E. Ramos. Well-Centered Planar Triangulation - an Iterative Approach. Proceedings of the 16th International Meshing Roundtable (2007), 121-138. 10.1007/978-3-540-75103-8_7
• J. Jossey, A. N. Hirani. Equivalence Theorems in Numerical Analysis : Integration, Differentiation and Interpolation. arXiv:0709.4046 [math.NA] (2007).
• A. Colombi, A. N. Hirani, B. F. Villac. Efficient Gravity Field Computation for Trajectory Propagation Near Small Bodies. Proceedings of 17th AAS/AIAA Space Flight Mechanics Meeting (2007), Paper AAS 07-223. PDF
• A. N. Hirani, R. P. Russell. Approximations of Distant Retrograde Orbits for Mission Design. Proceedings of 16th AAS/AIAA Space Flight Mechanics Meeting (2006), Paper AAS 06-116 PDF
• T. Lam, A. N. Hirani, J. A. Kangas. Characteristics of Transfers to and Captures at Europa. Proceedings of 16th AAS/AIAA Space Flight Mechanics Meeting (2006), Paper AAS 06-188. PDF
• A. N. Hirani, M. W. Lo. Surface Structure of an Invariant Manifold of a Halo Orbit. Proceedings of 2005 AAS/AIAA Astrodynamics Specialists Conference (2005), Paper AAS 05-379. PDF
• M. Desbrun, A. N. Hirani, M. Leok, J. E. Marsden. Discrete Exterior Calculus. arXiv:math/0508341 [math.DG] (2005).
• M. Desbrun, A. N. Hirani, J. E. Marsden. Discrete Exterior Calculus for Variational Problems in Computer Graphics and Vision. (Invited paper). Proceedings of the 42nd IEEE Conference on Decision and Control (2003), 4902-4907. 10.1109/CDC.2003.1272393
• E. Grinspun, A. N. Hirani, M. Desbrun, P. Schröder. Discrete Shells. SCA '03: Proceedings of the 2003 ACM SIGGRAPH / Eurographics Symposium on Computer Animation (2003), 62-67. 10.5555/846276.846284
• Y. Tong, S. Lombeyda, A. N. Hirani, M. Desbrun. Discrete Multiscale Vector Field Decomposition. ACM Transactions on Graphics, Vol. 22 (2003), 445-452. 10.1145/882262.882290
• A. N. Hirani, J. E. Marsden, J. Arvo. Averaged Template Matching Equations. Proceedings of Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2001), Springer Verlag Lecture Notes in Computer Science LNCS 2134, 2001, 528-543. 10.1007/3-540-44745-8_35
• A. N. Hirani, T. Totsuka. Combining Frequency and Spatial Domain Information for Fast Interactive Image Noise Removal. Proceedings of ACM SIGGRAPH 1996, 1996, 269-276. 10.1145/237170.237264
• A. N. Hirani, T. Totsuka, Dual Domain Interactive Image Restoration: Basic Algorithm., Proceedings of the IEEE International Conference on Image Processing, (1996), Vol. 1,, 797-800. 10.1109/ICIP.1996.559619
• A. N. Hirani, V. S. Subrahmanian, Algebraic Foundations of Logic Programming I: The Distributive Lattice of Logic Programs. Fundamenta Informaticae Vol. 13 (1990), 317-332. 10.3233/FI-1990-13306

Ph.D. Thesis