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CONTACT INFORMATION:

Department of Mathematical Science,

Room 318 Bell Hall Bldg,

University of Texas at El Paso, El Paso.

email address : nssharma@utep.edu

   

Welcome to my webpage!

About me:

  • I am an associate professor with tenure at Department of Mathematical Sciences, at UTEP.

  • Between June and August 2023, I have been a participant in the Sustainable Research Pathways Program. During this ten-week program, I gained research experience at the Lawrence Livermore National Laboratory with my DOE mentor Dr. Andrew K. Gillette.

  • Till the Fall of 2014, I was a post-doctoral fellow in the working group Mathematical Methods of Simulation headed by Prof. Guido Kanschat , University of Heidelberg, Heidelberg, Germany.

  • In December 2011, I completed my Ph.D. from the University of Houston, Houston Texas under the guidance of Prof. Ronald Hoppe.

  • Before my time in Houston, I obtained my Bachelors's and Master's in Mathematics from the University of Delhi, New Delhi, India.

    • Research Interests:

    My research interests are in numerical analysis, with a focus on developing efficient, accurate, convergent, and easy-to-compute numerical methods to solve mathematical models arising in material sciences, specifically crystal growth and applications in the design of sustainable drug delivery systems. To improve efficiency, my research relies on adaptive mesh and time step size refinement techniques that are oftentimes data-driven.

    Funding 

    DOE NNSA/MSIPP (Grant Number: GRANT13584020): The Rio Grande Consortium for Advanced Research on Exascale Simulation (Grande CARES), 2022-2027; Co-PI (with participating institutes: UNM (Lead, Vorobieff - PI, Poroseva), UTEP (Kumar PI, Co-PIs: Bronson, Tandon, Tosh, Sharma), NMSU (Kota), NMT (Hargather), PVAMU (Radhakrishnan) and Sandia (Tezaur), DOE NNSA/MSIPP). Funded $5M.

    DOE ASCR (Grant Number DE-SC0022957): Broadening National Science on Advanced Modeling and Simulations, 2022-2023; Senior Personnel (with PI Vinod Kumar, University of Texas at El Paso). Funded $44000.

    NSF DMS 2110774: Collaborative Research: Numerical Methods and Adaptive Algorithms for Sixth-Order Phase Field Models, 2021-2024; PI (with PI at participating institute Amanda Diegel, Mississippi State University).

    NSF DMS 1520862: Collaborative Research: Numerical Simulation of the Morphosynthesis of Polycrystalline Biominerals, 2015-2018; PI (with PI at participating institute Ronald Hoppe, University of Houston)

    Publications

  • A.E. Diegel, D. Bond, & N.S.Sharma, Stability and Error Analysis for a C Interior Penalty Method for the Modified Phase Field Crystal Equation. La Matematica 2024. Link to download.
  • A. E. Diegel and N. S. Sharma, Unconditional Energy Stability and Solvability for a C0 Interior Penalty Method for a Sixth-Order Equation Modeling Microemulsions. International Journal of Numerical Analysis and Modeling, 20, pp. 459-477, 2023. Link to download.
  • A. E. Diegel and N. S. Sharma, A C0 Interior Penalty Method for the Phase Field Crystal Equation, Accepted with Numerical Methods for Partial Differential Equations, 2022.
  • N. Sharma, Robust a-posteriori error estimates for weak Galerkin method for the convection-diffusion problem. Applied Numerical Mathematics Volume 170, December 2021, pp. 384-397
  • N. S. Sharma and G. Kanschat, A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem, Journal of Numerical Mathematics, 26(4), pp. 209-232, 2018.

  • S. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack, N. Sharma, A C0 interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints, Topics in Numerical Partial Differential Equations and Scientific Computing, IMA Volumes in Mathematics and Its Applications, 160, 2016.

  • Guido Kanschat and Natasha Sharma, Divergence-conforming Discontinuous Galerkin Methods and C0 Interior Penalty Methods, SIAM, Journal of Numerical Analysis, Vol. 52, Issue 4

  • R.H.W. Hoppe. and N. Sharma, Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method for the Helmholtz Equation, IMA Journal of Numerical Analysis,Volume 33, Issue 3, 2013.

  • C. Carstensen, R.H.W. Hoppe, N. Sharma and T. Warburton, Adaptive hybridized Interior Penalty Discontinuous Galerkin methods for H(curl)-elliptic problems. Numer. Math. Theor. Meth. Appl. 4, 13--37, 2011.

    Manuscript Under Review

  • N. S. Sharma and G. Tierra, Unconditionally Energy Stable Second Order Numerical Scheme for a Microemulsion model.

    Conference Proceedings

  • N.S Sharma (Joint work with R.H.W Hoppe). Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method for the Helmholtz Equation. Oberwolfach Reports, Workshop on Theory and Applications of Discontinuous Galerkin Methods, 2012.

  • N.S Sharma (Joint work with Dr. R.H.W Hoppe and Dr. Tim Warburton). A posteriori error analysis for hybridized Interior Penalty Discontinuous Galerkin Method for H(curl)-elliptic problems. Oberwolfach Reports, Workshop on Computational Electromagnetism and Acoustics, Springer, Berlin-Heidelberg-New York 2010.