# Publications

## Journals

Gaik Ambartsoumian and Venkateswaran P. Krishnan, "Inversion of a class of circular and elliptical Radon transforms", Contemporary Mathematics, American Mathematical Society, Proceedings of the international conference on Complex Analysis and Dynamical Systems VI, 2013 Preprint

Venkateswaran P. Krishnan and Eric Todd Quinto, "Microlocal analysis in tomography", in

*Handbook of Mathematical Methods in Imaging*, 2, In Press. PreprintSouvik Roy, Venkateswaran P. Krishnan, Praveen. C and A. S. Vasudevamurthy, "An efficient numerical algorithm for the inversion of an integral transform arising in ultrasound imaging",

*Journal of Mathematical Imaging and Vision*, 53 (2015), no.1, 78-91.Preprint- Praveen C and C. Klingenberg, "A second order well-balanced finite volume scheme for Euler equations with gravity", SIAM J. Sci. Comp., vol. 37, Issue 3, pp. 382-402.
Anupam Pal Choudhury and Venkateswaran P. Krishnan, "Stability estimates for the inverse boundary value problem for the biharmonic operator with bounded potentials",

*Journal of Mathematical Analysis and Applications*, 431 (2015), no.1, 300-316.. PreprintKevin Schaal, Andreas Bauer, Praveen Chandrashekar, Rüdiger Pakmor, Christian Klingenberg, Volker Springel, "Astrophysical hydrodynamics with a high-order discontinuous Galerkin scheme and adaptive mesh refinement", Monthly Notices of the Royal Astronomical Society - Main Journal, vol. 453, issue 4, Nov 2015, pp. 4278-4300. Preprint

Raluca Felea, Venkateswaran P. Krishnan, Clifford Nolan and Eric Todd Quinto, "Common midpoint versus common offset acquisition geometry in seismic imaging",

*Inverse Problems and Imaging*, 10 (2016), no. 1, 87–102.PreprintTuhin Ghosh and Venkateswaran P. Krishnan, "Determination of lower order perturbations of the polyharmonic operator from partial boundary data", Applicable Analysis, 95 (2016), no. 11, 2444–2463. Preprint

Ulrik S. Fjordholm and Deep Ray, "A sign preserving WENO reconstruction method", accepted in J. Sci. Comp. Preprint, Journal

- Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes on two-dimensional unstructured grids for Euler equations", Communications in Computational Physics, vol. 19, issue 5, May 2016, pp. 1111-1140.
Praveen C and C. Klingenberg, "Entropy stable finite volume scheme for ideal compressible MHD on 2-D Cartesian meshes", SIAM J. Numerical Analysis., vol. 54, issue 2, pp. 1313-1340. Preprint

- Parish, E., Duraisamy, K., and Chandrashekar, P., "Generalized Riemann Problem-based Upwind Scheme for the Vorticity Transport Equations", Computers and Fluids, Vol. 132, pp. 10-18, June 2016.
- Juan Pablo Gallego-Valencia, Christian Klingenberg, Praveen Chandrashekar, "On limiting for higher order discontinuous Galerkin method for 2D Euler equations", Bulletin of the Brazilian Math Society, New Series, 47(1), pp. 335-354, March 2016.
Praveen. C, "Finite volume discretization of heat equation and compressible Navier-Stokes equations with weak Dirichlet boundary condition on triangular grids", International Journal of Advances in Engineering Sciences and Applied Mathematics, vol. 8, issue 3, pp. 174-193, Sep. 2016 Journal

- Debanjana Mitra, Mythily Ramaswamy and Jean-Pierre Raymond, "Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension", Math. Control Relat. Fields, 5 (2015), no. 2, 259-290.
- Shirshendu Chowdhury, Debayan Maity and Jean-Pierre Raymond, "Local Stabilization of Compressible Navier Stokes System around a null velocity in One Dimension", Jl. Differential Equns. 259 (2015) 371-407.
- Gaik Ambartsoumian and Souvik Roy, “Numerical inversion of a class of broken ray transforms with partial radial data in a disc”, IEEE Transactions on Computational Imaging: Vol 2, Issue 2, Pages: 166-173, doi: 10.1109/TCI.2016.2531581
- Souvik Roy, Mario Annunziato and Alfio Borzi, “A Fokker-Planck feedback control constrained approach for modelling crowd motion”, accepted for publication
Andreas Bauer, Kevin Schaal, Volker Springel, Praveen Chandrashekar, Rudiger Pakmor and Christian Klingenberg, "Simulating turbulence using the astrophysical discontinuous Galerkin code TENET", in Software for Exascale Computing - SPPEXA 2013-2015, Lecture Notes in Computational Science and Engineering, Springer, 2016. Arxiv, Journal

- Souvik Roy, Praveen Chandrashekar, A. S. Vasudeva Murthy, "A variational approach to estimate incompressible fluid flows", Proc. Indian Acad. Sci. (Math. Sci.), Vol. 127, No. 1, Feb 2017, pp. 175-201.
Praveen Chandrashekar and Markus Zenk, "Well-balanced nodal discontinuous Galerkin method for Euler equations with gravity", J. Sci. Comp., Vol. 71, Issue 3, pp. 1062-1093, June 2017. Arxiv, Journal

Asha Meena, Harish Kumar, Praveen Chandrashekar, "Positivity preserving high-order discontinuous Galerkin schemes for 10-moment Gaussian closure equations", Journal of Comp. Physics, Vol. 339, No. 15, pp. 370-395, June 2017. Journal

Debayan Maity, Takéo Takahashi, Marius Tucsnak, "Analysis of a system modelling the motion of a piston in a viscous gas", Journal of Mathematical Fluid Mechanics, 19 (2017), no. 3, 551–579. Preprint

- Debayan Maity; Jean-Pierre Raymond, Feedback stabilization of the incompressible Navier-Stokes equations coupled with a damped elastic system in two dimensions. J. Math. Fluid Mech. 19 (2017), no. 4, 773–805.
- A. Mitra, A. Apte, R. Govindarajan, V. Vasan and S. Vadlamani, "A discrete view of the Indian monsoon to identify spatial patterns of rainfall", Dynamics and Statistics of the Climate Systems, Vol. 3, No. 1, 2019
- A. Mitra, A. Apte, R. Govindarajan, V. Vasan and S. Vadlamani, "Spatio-temporal patterns of daily Indian summer monsoon rainfall", Dynamics and Statistics of the Climate Systems, Vol. 3, No. 1, 2019
- S. Panigrahi, J. Taylor and S. Vadlamani, "Kinematic formula for heterogeneous Gaussian related fields", To appear in Stoch. Proc. Appl., 2019
Shirshendu Chowdhury, Debanjana Mitra, Mythily Ramaswamy and Michael Renardy, Null Controllability of the Linearized Compressible Navier Stokes System in One Dimension, Jl. Differential Equns. 257 (2014) , page 3813--3849. Journal

Shirshendu Chowdhury, Debanjana Mitra, Mythily Ramaswamy and Michael Renardy, Approximate Controllability results for Linearized visco-elastic flows, Jl. Math. Fl. Mech. 19 (2017), No. 3, 529-549. Journal

Debanjana Mitra, Local null controllability of viscous Camassa-Holm equation, Journal of Evolution equations, 18 (2018), 627–657. Journal

- Numerical inversion of arc Radon transform, Syed Tabish Abbas, Venkateswaran P. Krishnan and Jayanthi Sivaswamy, IEEE Transactions on Computational Imaging 2 (2016), no. 4, 540–549.
- Gaik Ambartsoumian, Raluca Felea, Venkateswaran P. Krishnan, Cliff Nolan and Eric Todd Quinto, Singular FIOs in SAR imaging, II: Transmitter and receiver at different speeds, SIAM Journal on Mathematical Analysis 50 (2018), no. 1, 591–621.
- Gaik Ambartsoumian, Rim Gouia-Zarrad,Venkateswaran P. Krishnan, Souvik Roy, Image reconstruction from radially incomplete spherical Radon data, European Journal of Applied Mathemaics, 29 (2018), no. 3, 470–493.
Bolaji Adesokan, Kim Knudsen, Venkateswaran P. Krishnan and Souvik Roy, A fully non-linear optimization approach to acousto-electric tomography, Inverse Problems 34 (2018), no. 10. Arxiv

- Tuhin Ghosh, Venkateswaran P. Krishnan and M. Vanninathan, Inverse diffusivity problem via homogenization theory, Preprint
- Venkateswaran P. Krishnan and Rohit Kumar Mishra, Microlocal analysis of a restricted ray transform on symmetric m-tensor fields in R^n, SIAM Journal on Mathematical Analysis, 50(6), 6230–6254, 2019.
- Venkateswaran P. Krishnan, Suman Kumar Sahoo, Ramesh Manna and Vladimir Sharafutdinov, Momentum ray transforms, Inverse Problems and Imaging, 13(3): 679-701, 2019.
- Venkateswaran P. Krishnan and Manmohan Vashisth, An inverse problem for the relativistic Schrödinger equation with partial boundary data, Accepted for publication in Applicable Analysis.
Deepak Varma and Praveen Chandrashekar, "A second order, discretely well-balanced finite volume scheme for Euler equations with gravity", Computers and Fluids, Vol. 181, pp. 292-313, March 2019. Journal

Praveen Chandrashekar, "A global divergence conforming DG method for hyperbolic conservation laws with divergence constraint", Journal of Scientific Computing, Vol. 79, pp, 79-102, April 2019. Journal

Thomas Guillet, Rudiger Pakmor, Volker Springel, Praveen Chandrashekar, Christian Klingenberg, "High-order Magnetohydrodynamics for Astrophysics with an Adaptive Mesh Refinement Discontinuous Galerkin Scheme", MNRAS, Volume 485, Issue 3, May 2019. Journal

Arijit Hazra, Praveen Chandrashekar, Dinshaw S Balsara, "Globally constraint-preserving FR/DG scheme for Maxwell's equations at all orders", J. Comp. Phy., Vol. 394, pp. 298-328, October 2019. Journal

Jonas Berberich, Praveen Chandrashekar, Christian Klingenberg, Fritz Roepke, "Second order finite volume scheme for Euler equations with gravity which is well-balanced for general equations of state and grid systems", Commun. Comput. Phys., vol. 26, issue 2, pp. 599-630, 2019. Journal

Praveen Chandrashekar, Boniface Nkonga, Ashish Bhole, "A discontinuous Galerkin method for a reduced resistive MHD model", Comp. Fluids, vol. 190, pp. 178-191, August 2019. Journal

- Arijit Hazra, Praveen Chandrashekar, Dinshaw S Balsara, "Globally constraint-preserving FR/DG scheme for Maxwell's equations at all orders", J. Comp. Phy., Vol. 394, pp. 298-328, October 2019.
- Jayesh Badwaik, Praveen Chandrashekar and Christian Klingenberg, "Single-step Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for 1-D Euler equations", Communications on Applied Mathematics and Computation, Vol. 2, pp. 541-579, January 2020.

## Conferences/Workshops

Anupam Pal Choudhary, "Delta Waves and Explicit Formulae for Spherically Symmetric Solutions of the Multi-dimensional Zero-Pressure Gas Dynamics System", XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications, IMPA, Brazil, July 2014 Slides

Imran Biswas, "Conservation laws driven by Levy white noise", XV International Conference on Hyperbolic Problems: Theory, Numerics, Applications, IMPA, Brazil, July 2014. Slides

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes for compressible flows on unstructured meshes", Poster presented at the Workshop on the Analysis and Numerical Approximation of PDEs, ETH Zurich, 8th-10th September, 2014 Poster

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes for compressible flows on unstructured meshes", Speaker at the the 5th International Conference on Scientific Computing and Partial Differential Equations, Hong Kong, 8th-12th December, 2014 Slides

Praveen. C, "Well-balanced schemes for Euler equations with gravity", Conference on Partial Differential Equations LNMIIT Jaipur, 10-11 December, 2014 Slides

- Venkateswaran P. Krishnan, Exact and approximate inversion methods in some imaging reconstruction problems, Recent and Emerging Trends in Computer and Computational Sciences (RETCOMP) 2015, PESIT South Campus, Bangalore, India, 08 January 2015.
- Venkateswaran P. Krishnan, Inversion of integral transforms arising in ultrasound imaging and related fields: Theory and Numerics, International Conference on Mathematical and Computational Biology (ICMCB), 2015, IIT Kanpur, India, 01 March, 2015
Praveen C, “Well-balanced discontinuous Galerkin method for the Euler equations with gravity”, Workshop on Higher Order Numerical Methods for Evolutionary PDEs: Applied Mathematics Meets Astrophysical Applications (15w5134), BIRS, Banff, Canada, 10-15 May 2015 Slides

- Venkateswaran P. Krishnan, Inversion of circular, elliptical and spherical Radon transforms: Theory and Numerics, Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May, 2015.
- Rohit Kumar Mishra, Microlocal analysis of restricted ray transform in 3-dimensional Euclidean space, Contributed talk at Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May 2015.
- Sombuddha Bhattacharyya, Recovering second order isotropic perturbation of a biharmonic operator from boundary data, Poster presentation at Applied Inverse Problems Conference, Helsinki, Finland, 25-29 May 2015.
Sreekar Vadlamani, "￼￼￼￼￼￼￼CLT for Lipschitz-Killing curvatures of excursion sets of Gaussian random fields", Conference on Extreme Values and Analysis, U. of Michigan, Ann Arbor, June 17, 2015 Slides

Mythily Ramaswamy, "Stabilization of one dimensional Compressible Navier-Stokes system”, Workshop on Fluid-Structure Interaction Problems, 29 June - 1 July, 2015, TIFR CAM, Bangalore. Slides

Praveen C, "Numerical implementation of feedback stabilization for Boussinesq model", Workshop on Fluid-Structure Interaction Problems, 29 June - 1 July, 2015, TIFR CAM, Bangalore. Slides

- Rohit Kumar Mishra, Exact inversion for restricted ray transform of symmetric m-tensor field in n-dimensional Euclidean space, Poster presentation in a topical workshop, Computational and Analytical Aspects of Image Reconstruction, ICERM, Brown University, Rhode Island, USA, 13-17 July 2015.
Deep Ray, "A sign preserving WENO reconstruction", International Conference on Industrial and Applied Mathematics, 10-14 Aug 2015, Beijing, China. Slides

- Venkateswaran P. Krishnan, Singular Fourier integral operators arising in some imaging problems, International Conference on Industrial and Applied Mathematics, 10-14 August 2015, Beijing, China.
Jayesh Badwaik, "Arbitrary Lagrangian Eulerian Discontinuous Galerkin Method for 1-D Euler Equations", Conference on Computational PDE, TIFR-CAM, Bangalore, 21-23 Dec, 2015. Slides

- Rohit Kumar Mishra, “Explicit and microlocal inversion of restricted ray transform in n-dimensional Euclidean space”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
- Sombuddha Bhattacharyya, “Calderon type inverse problems on Riemannian manifolds”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
- Manmohan Vashisth, “Inverse problems for the wave equation with underdetermined data”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey
Souvik Roy, “Inversion of spherical Radon transform in a spherical shell”, 8’th International Conference, Inverse Problems: Modeling and Simulation, May 23-28, 2016, Fethiye, Turkey Slides

- Praveen Chandrashekar, "Structure preserving schemes for conservation laws", International Conference on Advances in Scientific Computing, IIT Madras, 28-30 November, 2016. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin method for rotating shallow water equation on the sphere", International Conference on Recent Advances in Theoretical and Computational PDE with Applications, Univ. Institute of Engineering and Technology, Panjab University, Chandigarh, 5-9 December, 2016. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin and spectral element method for rotating shallow water equation on the sphere", Computational Science Symposium, Dept. of Computational and Data Sciences, IISc, Bangalore, 16-18 March, 2017. [Slides]
- Praveen Chandrashekar, "Discontinuous Galerkin and spectral element method for rotating shallow water equation on the sphere", PDES on the Sphere 2017, ENS, Paris, 3-7 April, 2017.
- S. Vadlamani, "An adaptive scheme for MCMC in infinite dimensions." 13th EnKF Workshop, Bergen, Norway, May 2018

## Reports

Deep Ray, Praveen Chandrashekar, Ulrik S. Fjordholm and Siddhartha Mishra, "Entropy stable schemes on two-dimensional unstructured grids", Report number 2014-28, SAM, ETH Zurich, October 2014

## Master theses

- Sourav Mitra, "Feedback Stabilization of density dependent N-S equations”.
- Rohit Kumar Mishra, "Microlocal analysis of restricted Doppler transform in n-dimensional Euclidean space", July 2014
- Sombuddha Bhattacharyya, "Recovering second order Isotropic perturbation of a biharmonic operator from full boundary data", June 2014
- Manmohan Vashisth, "Inverse problems related to hyperbolic PDEs and hybrid imaging", July 2015

## PhD Theses

- Souvik Roy, Ph. D., 2015, Joint advisors: A. S. Vasudeva Murthy, Praveen Chandrashekar and Venkateswaran P. Krishnan, Thesis title: "Reconstruction of a class of fluid flows by variational methods and inversion of integral transforms in tomography"
- Deep Ray, "Entropy stable finite difference and finite volume schemes for compressible flows", TIFR-CAM, May 2017.
- Madhuresh, "Bayesian approach to ill-posed inverse problems", TIFR-CAM, 2017.
- Rohit Kumar Mishra, Ph. D., 2017, Advisor: Venkateswaran P. Krishnan, Thesis title: "Some uniqueness results in tensor tomography"
- Sombuddha Bhattacharyya, Ph. D. 2017, Advisor: Venkateswaran P. Krishnan, Thesis title: "Inverse problems on Riemannian manifolds"
- Manmohan Vashisth, Ph.D., 2018, Advisor: Venkateswaran P. Krishnan, Thesis title: "Some inverse problems in hyperbolic partial differential equations"
- Anuj Abhishek, Ph.D., 2018 from Tufts University, USA, Joint Advisors: Eric Todd Quinto and Venkateswaran P. Krishnan, Thesis title: "Support theorems for certain ray transforms"