Each entry links to the version of record where one exists. Links marked arXiv or PDF are freely readable; DOI may be behind a publisher paywall. PDFs of most papers are available here. Every entry has a BibTeX toggle, and the whole list is in publications.bib.
@phdthesis{Hirani2003_PhD_Caltech,
author = {Hirani, Anil N.},
title = {{Discrete Exterior Calculus}},
school = {California Institute of Technology},
year = {2003},
month = {5},
doi = {10.7907/ZHY8-V329},
url = {https://resolver.caltech.edu/CaltechETD:etd-05202003-095403}}@misc{GuHiLiPo2026_arXiv,
author = {Guzm{\'a}n, Johnny and Hirani, Anil N. and Liu, Bingyan and Potu, Pratyush},
title = {{Discrete Poincar{\'e} and Bogovskii Operators on Cochains and Whitney Forms}},
year = {2026},
eprint = {2603.29018},
archivePrefix = {arXiv},
primaryClass = {math.NA},
url = {https://arxiv.org/abs/2603.29018}}@misc{ZhChHuHi2025_arXiv,
author = {Zhu, Chengbin and Christiansen, Snorre H. and Hu, Kaibo and Hirani, Anil N.},
title = {{Convergence and Stability of Discrete Exterior Calculus for the Hodge Laplace Problem in Two Dimensions}},
year = {2025},
eprint = {2505.08966},
archivePrefix = {arXiv},
primaryClass = {math.NA},
note = {Accepted for publication in IMA Journal of Numerical Analysis},
url = {https://arxiv.org/abs/2505.08966}}@inproceedings{LiElHi2025_TRL,
author = {Liu, Bingyan and Elkan, Charles and Hirani, Anil N.},
title = {{Embeddings for Numerical Features Using tanh Activation}},
booktitle = {Proceedings of the 4th Table Representation Learning Workshop at ACL 2025},
pages = {208--216},
year = {2025},
address = {Vienna, Austria},
url = {https://aclanthology.org/2025.trl-1.18/}}@article{ScBeHi2024_ACOM,
author = {Schubel, Mark D. and Berwick-Evans, Daniel and Hirani, Anil N.},
title = {{Averaging property of wedge product and naturality in discrete exterior calculus}},
journal = {Advances in Computational Mathematics},
volume = {50},
number = {4},
year = {2024},
month = July,
publisher = {Springer Science and Business Media LLC},
ISSN = {1572-9044},
DOI = {10.1007/s10444-024-10179-8},
url = {https://doi.org/10.1007/s10444-024-10179-8}}@article{HiWaWo2024_JCD,
author = {Hirani, Anil N. and Wan, Andy T. S. and Wojtalewicz, Nikolas},
title = {{Conservative integrators for piecewise smooth systems with transversal dynamics}},
journal = {Journal of Computational Dynamics},
volume = {11},
number = {2},
pages = {135--152},
year = {2024},
publisher = {American Institute of Mathematical Sciences (AIMS)},
ISSN = {2158-2505},
DOI = {10.3934/jcd.2023009},
url = {https://doi.org/10.3934/jcd.2023009}}@article{WaJaHiSa2023_JCP,
author = {Wang, Minmiao and Jagad, Pankaj and Hirani, Anil N. and Samtaney, Ravi},
title = {{Discrete exterior calculus discretization of two-phase incompressible Navier-Stokes equations with a conservative phase field method}},
journal = {Journal of Computational Physics},
volume = {488},
pages = {112245},
year = {2023},
month = Sept,
publisher = {Elsevier BV},
ISSN = {0021-9991},
DOI = {10.1016/j.jcp.2023.112245},
url = {https://doi.org/10.1016/j.jcp.2023.112245}}@article{HiKaWaWa2023_CGTA,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik and Wang, Han and Watts, Seth},
title = {{Computing discrete harmonic differential forms in a given cohomology class using finite element exterior calculus}},
journal = {Computational Geometry},
volume = {109},
pages = {101937},
year = {2023},
month = Feb,
publisher = {Elsevier BV},
ISSN = {0925-7721},
DOI = {10.1016/j.comgeo.2022.101937},
url = {https://doi.org/10.1016/j.comgeo.2022.101937}}@misc{BeHiSc2021_arXiv,
author = {Berwick-Evans, Daniel and Hirani, Anil N. and Schubel, Mark D.},
title = {{Discrete Vector Bundles with Connection}},
year = {2021},
eprint = {2104.10277},
archivePrefix = {arXiv},
primaryClass = {math.DG},
note = {Originally posted in 2021 as \emph{Discrete vector bundles with connection and Bianchi identity}; major update posted April 2026},
url = {https://arxiv.org/abs/2104.10277}}@misc{KaHi2021_arXiv,
author = {Karve, Vaibhav and Hirani, Anil N.},
title = {{GraphSAT --- a Decision Problem Connecting Satisfiability and Graph Theory}},
year = {2021},
eprint = {2105.11390},
archivePrefix = {arXiv},
primaryClass = {math.CO},
url = {https://arxiv.org/abs/2105.11390}}@article{KaHi2020_DAM,
author = {Karve, Vaibhav and Hirani, Anil N.},
title = {{The complete set of minimal simple graphs that support unsatisfiable 2-CNFs}},
journal = {Discrete Applied Mathematics},
volume = {283},
pages = {123--132},
year = {2020},
month = Sept,
publisher = {Elsevier BV},
ISSN = {0166-218X},
DOI = {10.1016/j.dam.2019.12.017},
url = {https://doi.org/10.1016/j.dam.2019.12.017}}@article{MoHiSa2018_IJCMESM,
author = {Mohamed, Mamdouh S. and Hirani, Anil N. and Samtaney, Ravi},
title = {{Numerical convergence of discrete exterior calculus on arbitrary surface meshes}},
journal = {International Journal for Computational Methods in Engineering Science and Mechanics},
volume = {19},
number = {3},
pages = {194--206},
year = {2018},
month = Apr,
publisher = {Informa UK Limited},
ISSN = {1550-2295},
DOI = {10.1080/15502287.2018.1446196},
url = {https://doi.org/10.1080/15502287.2018.1446196}}@article{MoHiSa2016a_CAD,
author = {Mohamed, Mamdouh S. and Hirani, Anil N. and Samtaney, Ravi},
title = {{Comparison of discrete Hodge star operators for surfaces}},
journal = {Computer-Aided Design},
volume = {78},
pages = {118--125},
year = {2016},
month = Sept,
publisher = {Elsevier BV},
ISSN = {0010-4485},
DOI = {10.1016/j.cad.2016.05.002},
url = {https://doi.org/10.1016/j.cad.2016.05.002}}@article{MoHiSa2016_JCP,
author = {Mohamed, Mamdouh S. and Hirani, Anil N. and Samtaney, Ravi},
title = {{Discrete exterior calculus discretization of incompressible Navier--Stokes equations over surface simplicial meshes}},
journal = {Journal of Computational Physics},
volume = {312},
pages = {175--191},
year = {2016},
month = May,
publisher = {Elsevier BV},
ISSN = {0021-9991},
DOI = {10.1016/j.jcp.2016.02.028},
url = {https://doi.org/10.1016/j.jcp.2016.02.028}}@article{DzGuHaHiRuTh2015_BMM,
author = {Dziubek, Andrea and Guidoboni, Giovanna and Harris, Alon and Hirani, Anil N. and Rusjan, Edmond and Thistleton, William},
title = {{Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model}},
journal = {Biomechanics and Modeling in Mechanobiology},
volume = {15},
number = {4},
pages = {893--907},
year = {2016},
month = Oct,
publisher = {Springer Science and Business Media LLC},
ISSN = {1617-7940},
DOI = {10.1007/s10237-015-0731-8},
url = {https://doi.org/10.1007/s10237-015-0731-8}}@article{HiNaCh2015_IJCMESM,
author = {Hirani, A. N. and Nakshatrala, K. B. and Chaudhry, J. H.},
title = {{Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus}},
journal = {International Journal for Computational Methods in Engineering Science and Mechanics},
volume = {16},
number = {3},
pages = {151--169},
year = {2015},
month = May,
publisher = {Informa UK Limited},
ISSN = {1550-2295},
DOI = {10.1080/15502287.2014.977500},
url = {https://doi.org/10.1080/15502287.2014.977500}}@inproceedings{HiKaWa2015_GABB,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik and Watts, Seth},
title = {{Graph Laplacians and Least Squares on Graphs}},
booktitle = {2015 IEEE International Parallel and Distributed Processing Symposium Workshop},
pages = {812--821},
year = {2015},
month = May,
publisher = {IEEE},
DOI = {10.1109/ipdpsw.2015.73},
url = {https://doi.org/10.1109/IPDPSW.2015.73}}@article{DeHi2014_FOCM,
author = {Demlow, Alan and Hirani, Anil N.},
title = {{A Posteriori Error Estimates for Finite Element Exterior Calculus: The de Rham Complex}},
journal = {Foundations of Computational Mathematics},
volume = {14},
number = {6},
pages = {1337--1371},
year = {2014},
month = May,
publisher = {Springer Science and Business Media LLC},
ISSN = {1615-3383},
DOI = {10.1007/s10208-014-9203-2},
url = {https://doi.org/10.1007/s10208-014-9203-2}}@article{VaHiGuZhRa2013_CGTA,
author = {VanderZee, Evan and Hirani, Anil N. and Guoy, Damrong and Zharnitsky, Vadim and Ramos, Edgar A.},
title = {{Geometric and combinatorial properties of well-centered triangulations in three and higher dimensions}},
journal = {Computational Geometry},
volume = {46},
number = {6},
pages = {700--724},
year = {2013},
month = Aug,
publisher = {Elsevier BV},
ISSN = {0925-7721},
DOI = {10.1016/j.comgeo.2012.11.003},
url = {https://doi.org/10.1016/j.comgeo.2012.11.003}}@article{HiKaVa2013_CAD,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik and VanderZee, Evan B.},
title = {{Delaunay Hodge star}},
journal = {Computer-Aided Design},
volume = {45},
number = {2},
pages = {540--544},
year = {2013},
month = Feb,
publisher = {Elsevier BV},
ISSN = {0010-4485},
DOI = {10.1016/j.cad.2012.10.038},
url = {https://doi.org/10.1016/j.cad.2012.10.038}}@article{BeHi2012_TOMS,
author = {Bell, Nathan and Hirani, Anil N.},
title = {{PyDEC: Software and Algorithms for Discretization of Exterior Calculus}},
journal = {ACM Transactions on Mathematical Software},
volume = {39},
number = {1},
pages = {1--41},
year = {2012},
month = Nov,
publisher = {Association for Computing Machinery (ACM)},
ISSN = {1557-7295},
DOI = {10.1145/2382585.2382588},
url = {https://doi.org/10.1145/2382585.2382588}}@misc{HiKaWaWa2011_arXiv,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik and Wang, Han and Watts, Seth},
title = {{Cohomologous Harmonic Cochains}},
year = {2011},
eprint = {1012.2835},
archivePrefix = {arXiv},
primaryClass = {cs.CG},
url = {https://arxiv.org/abs/1012.2835}}@misc{HiKaWa2011_arXiv,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik and Watts, Seth},
title = {{Least Squares Ranking on Graphs}},
year = {2011},
eprint = {1011.1716},
archivePrefix = {arXiv},
primaryClass = {cs.NA},
url = {https://arxiv.org/abs/1011.1716}}@misc{HiKa2011_arXiv,
author = {Hirani, Anil N. and Kalyanaraman, Kaushik},
title = {{Numerical Experiments for Darcy Flow on a Surface Using Mixed Exterior Calculus Methods}},
year = {2011},
eprint = {1103.4865},
archivePrefix = {arXiv},
primaryClass = {cs.NA},
url = {https://arxiv.org/abs/1103.4865}}@article{DeHiKr2011_SICOMP,
author = {Dey, Tamal K. and Hirani, Anil N. and Krishnamoorthy, Bala},
title = {{Optimal Homologous Cycles, Total Unimodularity, and Linear Programming}},
journal = {SIAM Journal on Computing},
volume = {40},
number = {4},
pages = {1026--1044},
year = {2011},
month = Jan,
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
ISSN = {1095-7111},
DOI = {10.1137/100800245},
url = {https://doi.org/10.1137/100800245}}@inproceedings{DuHi2011_SOCG,
author = {Dunfield, Nathan M. and Hirani, Anil N.},
title = {{The least spanning area of a knot and the optimal bounding chain problem}},
booktitle = {Proceedings of the twenty-seventh annual symposium on Computational geometry},
series = {SoCG ’11},
pages = {135--144},
year = {2011},
month = June,
publisher = {ACM},
DOI = {10.1145/1998196.1998218},
url = {https://doi.org/10.1145/1998196.1998218}}@inproceedings{DeHiKr2010_STOC,
author = {Dey, Tamal K. and Hirani, Anil N. and Krishnamoorthy, Bala},
title = {{Optimal homologous cycles, total unimodularity, and linear programming}},
booktitle = {Proceedings of the forty-second ACM symposium on Theory of computing},
series = {STOC′10},
pages = {221--230},
year = {2010},
month = June,
publisher = {ACM},
DOI = {10.1145/1806689.1806721},
url = {https://doi.org/10.1145/1806689.1806721}}@article{VaHiGuRa2010_SISC,
author = {VanderZee, Evan and Hirani, Anil N. and Guoy, Damrong and Ramos, Edgar A.},
title = {{Well-Centered Triangulation}},
journal = {SIAM Journal on Scientific Computing},
volume = {31},
number = {6},
pages = {4497--4523},
year = {2010},
month = Jan,
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
ISSN = {1095-7197},
DOI = {10.1137/090748214},
url = {https://doi.org/10.1137/090748214}}@article{VaHiZhGu2010_CGTA,
author = {VanderZee, Evan and Hirani, Anil N. and Zharnitsky, Vadim and Guoy, Damrong},
title = {{A dihedral acute triangulation of the cube}},
journal = {Computational Geometry},
volume = {43},
number = {5},
pages = {445--452},
year = {2010},
month = July,
publisher = {Elsevier BV},
ISSN = {0925-7721},
DOI = {10.1016/j.comgeo.2009.09.001},
url = {https://doi.org/10.1016/j.comgeo.2009.09.001}}@article{CoHiVi2009_JGCD,
author = {Colombi, Andrew and Hirani, Anil N. and Villac, Benjamin F.},
title = {{Structure Preserving Approximations of Conservative Forces for Application to Small-Body Dynamics}},
journal = {Journal of Guidance, Control, and Dynamics},
volume = {32},
number = {6},
pages = {1847--1858},
year = {2009},
month = Nov,
publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
ISSN = {1533-3884},
DOI = {10.2514/1.42067},
url = {https://doi.org/10.2514/1.42067}}@inbook{VaHiGu2008_IMR,
author = {VanderZee, Evan and Hirani, Anil N. and Guoy, Damrong},
title = {{Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra}},
booktitle = {Proceedings of the 17th International Meshing Roundtable},
pages = {19--35},
year = {2008},
publisher = {Springer Berlin Heidelberg},
ISBN = {9783540879213},
DOI = {10.1007/978-3-540-87921-3_2},
url = {https://doi.org/10.1007/978-3-540-87921-3_2}}@inproceedings{CoHiVi2008a_ASC,
author = {Colombi, Andrew and Hirani, Anil N. and Villac, Benjamin F.},
title = {{Structure Preserving Approximations of Conservative Forces for Application to Small Body Dynamics}},
booktitle = {Proceedings of the AAS/AIAA Astrodynamics Specialist Conference},
year = {2008},
note = {Paper AIAA 2008-7205}}@article{CoHiVi2008_JGCD,
author = {Colombi, Andrew and Hirani, Anil N. and Villac, Benjamin F.},
title = {{Adaptive Gravitational Force Representation for Fast Trajectory Propagation Near Small Bodies}},
journal = {Journal of Guidance, Control, and Dynamics},
volume = {31},
number = {4},
pages = {1041--1051},
year = {2008},
month = July,
publisher = {American Institute of Aeronautics and Astronautics (AIAA)},
ISSN = {1533-3884},
DOI = {10.2514/1.32559},
url = {https://doi.org/10.2514/1.32559}}@article{WaScHiDe2007_ACM,
author = {Warren, Joe and Schaefer, Scott and Hirani, Anil N. and Desbrun, Mathieu},
title = {{Barycentric coordinates for convex sets}},
journal = {Advances in Computational Mathematics},
volume = {27},
number = {3},
pages = {319--338},
year = {2007},
month = Dec,
publisher = {Springer Science and Business Media LLC},
ISSN = {1572-9044},
DOI = {10.1007/s10444-005-9008-6},
url = {https://doi.org/10.1007/s10444-005-9008-6}}@inbook{VaHiGuRa2007_IMR,
author = {VanderZee, Evan and Hirani, Anil N. and Guoy, Damrong and Ramos, Edgar},
title = {{Well-centered Planar Triangulation -- An Iterative Approach}},
booktitle = {Proceedings of the 16th International Meshing Roundtable},
pages = {121--138},
year = {2007},
publisher = {Springer Berlin Heidelberg},
ISBN = {9783540751021},
DOI = {10.1007/978-3-540-75103-8_7},
url = {https://doi.org/10.1007/978-3-540-75103-8_7}}@misc{JoHi2007_arXiv,
author = {Jossey, John and Hirani, Anil N.},
title = {{Equivalence Theorems in Numerical Analysis: Integration, Differentiation and Interpolation}},
year = {2007},
eprint = {0709.4046},
archivePrefix = {arXiv},
primaryClass = {math.NA},
url = {https://arxiv.org/abs/0709.4046}}@inproceedings{CoHiVi2007_SFM,
author = {Colombi, Andrew and Hirani, Anil N. and Villac, Benjamin F.},
title = {{Efficient Gravity Field Computation for Trajectory Propagation Near Small Bodies}},
booktitle = {Proceedings of the 17th AAS/AIAA Space Flight Mechanics Meeting},
year = {2007},
note = {Paper AAS 07-223}}@inproceedings{HiRu2006_SFM,
author = {Hirani, Anil N. and Russell, Ryan P.},
title = {{Approximations of Distant Retrograde Orbits for Mission Design}},
booktitle = {Proceedings of the 16th AAS/AIAA Space Flight Mechanics Meeting},
year = {2006},
note = {Paper AAS 06-116}}@inproceedings{LaHiKa2006_SFM,
author = {Lam, Try and Hirani, Anil N. and Kangas, Julie A.},
title = {{Characteristics of Transfers to and Captures at Europa}},
booktitle = {Proceedings of the 16th AAS/AIAA Space Flight Mechanics Meeting},
year = {2006},
note = {Paper AAS 06-188}}@inproceedings{HiLo2005_ASC,
author = {Hirani, Anil N. and Lo, Martin W.},
title = {{Surface Structure of an Invariant Manifold of a Halo Orbit}},
booktitle = {Proceedings of the 2005 AAS/AIAA Astrodynamics Specialists Conference},
year = {2005},
note = {Paper AAS 05-379}}@misc{DeHiLeMa2005_arXiv,
author = {Desbrun, Mathieu and Hirani, Anil N. and Leok, Melvin and Marsden, Jerrold E.},
title = {{Discrete Exterior Calculus}},
year = {2005},
eprint = {math/0508341},
archivePrefix = {arXiv},
primaryClass = {math.DG},
url = {https://arxiv.org/abs/math/0508341}}@inproceedings{DeHiMa2003_CDC,
author = {Desbrun, M. and Hirani, A.N. and Marsden, J.E.},
title = {{Discrete exterior calculus for variational problems in computer vision and graphics}},
booktitle = {42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)},
series = {CDC-03},
pages = {4902--4907},
year = {2003},
publisher = {IEEE},
DOI = {10.1109/cdc.2003.1272393},
url = {https://doi.org/10.1109/CDC.2003.1272393}}@inproceedings{GrHiDeSc2003_SCA,
author = {Grinspun, Eitan and Hirani, Anil N. and Desbrun, Mathieu and Schr\"{o}der, Peter},
title = {{Discrete Shells}},
booktitle = {SCA '03: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation},
pages = {62--67},
year = {2003},
publisher = {Eurographics Association},
url = {https://diglib.eg.org/handle/10.2312/SCA.SCA03.062-067}}@article{ToLoHiDe2003_SIGGRAPH,
author = {Tong, Yiying and Lombeyda, Santiago and Hirani, Anil N. and Desbrun, Mathieu},
title = {{Discrete multiscale vector field decomposition}},
journal = {ACM Transactions on Graphics},
volume = {22},
number = {3},
pages = {445--452},
year = {2003},
month = July,
publisher = {Association for Computing Machinery (ACM)},
ISSN = {1557-7368},
DOI = {10.1145/882262.882290},
url = {https://doi.org/10.1145/882262.882290}}@inbook{HiMaAr2001_EMMCVPR,
author = {Hirani, Anil N. and Marsden, Jerrold E. and Arvo, James},
title = {{Averaged Template Matching Equations}},
booktitle = {Energy Minimization Methods in Computer Vision and Pattern Recognition},
pages = {528--543},
year = {2001},
publisher = {Springer Berlin Heidelberg},
ISBN = {9783540447450},
ISSN = {0302-9743},
DOI = {10.1007/3-540-44745-8_35},
url = {https://doi.org/10.1007/3-540-44745-8_35}}@inproceedings{HiTo1996_SIGGRAPH,
author = {Hirani, Anil N. and Totsuka, Takashi},
title = {{Combining frequency and spatial domain information for fast interactive image noise removal}},
booktitle = {Proceedings of the 23rd annual conference on Computer graphics and interactive techniques},
series = {SIGGRAPH96},
pages = {269--276},
year = {1996},
month = Aug,
publisher = {ACM},
DOI = {10.1145/237170.237264},
url = {https://doi.org/10.1145/237170.237264}}@inproceedings{HiTo1996_ICIP,
author = {Hirani, A.N. and Totsuka, T.},
title = {{Dual domain interactive image restoration: basic algorithm}},
booktitle = {Proceedings of 3rd IEEE International Conference on Image Processing},
series = {ICIP-96},
volume = {1},
pages = {797--800},
year = {1996},
publisher = {IEEE},
DOI = {10.1109/icip.1996.559619},
url = {https://doi.org/10.1109/ICIP.1996.559619}}@article{HiSu1990_FI,
author = {Hirani, Anil and Subrahmanian, V.S.},
title = {{Algebraic Foundations of Logic Programming, I: The Distributive Lattice of Logic Programs}},
journal = {Fundamenta Informaticae},
volume = {13},
number = {3},
pages = {317--332},
year = {1990},
month = July,
publisher = {SAGE Publications},
ISSN = {0169-2968},
DOI = {10.3233/fi-1990-13306},
url = {https://doi.org/10.3233/FI-1990-13306}}@mastersthesis{Hirani2000_MS,
author = {Hirani, Anil N.},
title = {{Linearization Methods for Variational Integrators and Euler-Lagrange Equations}},
school = {California Institute of Technology},
year = {2000},
month = {4},
note = {Advisors: James R. Arvo and Jerrold E. Marsden}}