Abhinav Jha

I'm

About

Hi! I am Dr. Abhinav Jha, currently an Assistant Professor at the Indian Institute of Technology, Gandhinagar. My research interests lie in the areas of Numerical Analysis and Scientific Computing.

During my PhD, I specialized in Stabilization Techniques for Convection-Dominated Problems, and I was also a member of the Berlin Mathematical School (BMS).

In my Postdoctoral research, I shifted focus to Computational Chemistry, working specifically on Domain Decomposition Methods for Poisson-Boltzmann Equations. For a brief overview of my work, you can check out the following presentations: AFC Schemes, ddLPB Method, and ddPB Method.

  • Birthday: 2 July 1994
  • City: Gandhinagar, India
  • Email: abhinav.jha@iitgn.ac.in
  • Age: 30
  • Degree: Dr. rer. nat
 

Publications

This is my list of publications. Most of them are available on arXiv, if you need a published version of any of the paper, do not hesitate to contact me.

  • Petr Knobloch, Dmitri Kuzmin, Abhinav Jha: Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations. In: Journal of Computational Physics, 518, (July 2024), DOI: 10.1016/j.jcp.2024.113305
  • Michele Nottoli, Michael F. Herbst, Aleksandr Mikhalev, Abhinav Jha, Filippo Lipparini, Benjamin Stamm: ddX: Polarizable Continuum Solvation from Small Molecules to Proteins. In: WIREs Computational Molecular Science, 14(4), (July 2024), DOI: 10.1002/wcms.1726
  • Abhinav Jha: Residual-Based a Posteriori Error Estimators for Algebraic Stabilizations. In: Applied Mathematics Letters, 157, (June 2024), DOI: 10.1016/j.aml.2024.109192
  • Abhinav Jha, Volker John, Petr Knobloch: Adaptive Grids in the Context of Algebraic Stabilizations for Convection-Diffusion-Reaction Equations. In: SIAM Journal on Scientific Computing, 45, (April 2023), DOI: 10.1137/21M1466360
  • Abhinav Jha, Michele Nottoli, Aleksandr Mikhalev, Chaoyu Quan, Benjamin Stamm: Linear scaling computation of forces for the domain-decomposition linear Poisson--Boltzmann method. In: The Journal of Chemical Physics, 150, (February 2023), DOI: 10.1063/5.0141025
  • Abhinav Jha, Ondrej Partl, Naveed Ahmed, Dmitri Kuzmin: An Assessment of Solvers for Algebraically Stabilized Discretizations of Convection-Diffusion-Reaction Equations. In: Journal of Numerical Mathematics, 31, (April 2022), DOI: 10.1515/jnma-2021-0123
  • Abhinav Jha: Hanging nodes for higher-order Lagrange finite elements. In: Examples and Counterexamples, 1, (November 2021), 100025, DOI: 10.1016/j.exco.2021.100025
  • Abhinav Jha: A residual based a posteriori error estimators for AFC schemes for convection-diffusion equations. In: Computers and Mathematics with Applications, 97(1), (June 2021), DOI: 10.1016/j.camwa.2021.05.031
  • Abhinav Jha, Volker John: On Basic Iteration Schemes for Nonlinear AFC Discretizations. In: Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018, 135, (January 2020), DOI: 10.1007/978-3-030-41800-7_7
  • Abhinav Jha, Volker John: A study of solvers for nonlinear AFC discretizations of convection–diffusion equations. In: Computers and Mathematics with Applications, 78(9), (May 2019), DOI: 10.1016/j.camwa.2019.04.020

    • Preprints

    These are the list of the preprints which are currently under review.

  • Thiago Carvalho Corso, Muhammad Hassan, Abhinav Jha, Benjamin Stamm: Trace estimates for harmonic functions along circular arcs with applications to domain decomposition on overlapping disks, (January 2024), arXiv: 2401.16344
  • Abhinav Jha, Benjamin Stamm: Domain decomposition method for Poisson--Boltzmann equations based on Solvent Excluded Surface, (September 2023), arXiv: 2309.06862

    • Teaching

    Winter Semester 2025, IIT Gandhinagar

    These are the courses I am offering this semester:

    • MA637: Numerical Analysis and Computing
      • Lecture Notes:
      • Assignments:

    Resume

    This is my express resume. Here is a link to my full resume.

    Summary

    Abhinav Jha

    Assistant Professor, Grade 1

    • Indian Institute of Technology, Gandhinagar, Gujarat, India
    • abhinav.jha@iitgn.ac.in

    Education

    Dr. rer. nat.

    2017 - 2020

    Freie Universität, Berlin

    Thesis: Numerical Algorithms for Algebraic Stabilizations of Scalar Convection-Dominated Problems

    Supervisor : Prof. Dr. Volker John

    M.Sc. Mathematics

    2015 - 2017

    Indian Institute of Technology, Roorkee

    Thesis: Finite Element Method for Population Balance Equation

    Supervisor : Dr. Ankik Kumar Giri

    B.Sc.(H) Mathematics

    2012 - 2015

    St. Stephen's College, University of Delhi

    Professional Experience

    Wissenschaftlicher Mitarbeiter

    September, 2022 - August, 2024

    Universität Stuttgart, Stuttgart, Germany

    Supervisor : Prof. Dr. Benjamin Stamm

    Teaching assistant for:
    • Numerische Mathematik: Winter semester 2024
    • Numerical Methods for Differential Equations: Summer semester 2023
    • Numerische Grundlagen für ernen, fmt, mach, mawie: Summer semester 2023, 2024
    • Höhere Mathematik 3: Winter semester 2022
    Supervisor for:
    • Hauptseminar Numerische Analysis und Simulation: Winter semester 2022

    Wissenschaftlicher Mitarbeiter

    November, 2020 - August, 2022

    RWTH Aachen University, Aachen, Germany

    Supervisor : Prof. Dr. Benjamin Stamm

    Teaching assistant for:
    • Numerics II: Summer semester 2022
    • Numerics V : Winter semester 2021
    • Numerics IV: Summer semester 2021

    Scholarships and Awards

    BMS Phase 2 Scholarship

    October, 2017 - September, 2020

    Berlin Mathematical School

    Dr. Gorakh Prasad Scholarship

    July, 2015 - July, 2017

    Indian Institute of Technology, Roorkee

    INSPIRE Scholarship

    July, 2012 - July, 2017

    Ministry of Human Resources and Development, India

    Workshops and Conferences

    List of workshops, internal seminars, and conferences I attended. Also, the list of mini-symposium/conferences I co-organized.

    • All
    • Conferences
    • Workshops
    • Internal Seminars
    • Organization
    Workshop on Numerical Methods and Analysis in CFD, WIAS, Berlin, Adaptive grids for algebraic stabilizations of convection-diffusion-reaction equations, 5-8 July 2022, Slides
    18th Workshop on Numerical Methods for Problems with Layer Phenomena, Hagen, Adaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations, 24-26 March 2022, Slides
    13th International Workshop on Variational Multiscale and Stabilized Finite Elements, WIAS, Berlin, Investigation of different solvers for nonlinear algebraic stabilizations of convection diffusion equations, 5-7 December 2018, Slides
    Universität Stuttgart, Domain Decomposition Methods for the Poisson‐Boltzmann Equations, 24th October 2023, Slides
    Universität Stuttgart, Overview of the Domain Decomposition Method for the Linear Poisson Boltzmann Equations, 8th December 2022, Slides
    RWTH Aachen University, Adaptive Grids for Algebraic Stabilizations of Convection‐Diffusion‐Reaction Equations, 5th April 2022, Slides
    RWTH Aachen University, Numerical Algorithms for Algebraic Stabilizations of Scalar Convection‐Dominated Problems, 26th January 2021, Slides
    93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics Dresden, Domain Decomposition Methods for the Poisson-Boltzmann Equations, 30 May - 2 June 2023, Slides
    SIAM Conference on Computational Science and Engineering (CSE23) Amsterdam, Adaptive Grids for Algebraic Stabilizations of Convection-Diffusion-Reaction Equations, 26 February - 3 March 2023, Slides
    92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics Aachen, Computation of Forces Arising from the Linear Poisson‐Boltzmann Method in the Domain Decomposition Paradigm, 15 - 18 August 2022, Slides
    15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics (WCCM-APCOM 2022) (Online), A Residual based a Posteriori Error Estimators for Algebraic Flux Correction Scheme, 31 July - 5 August 2022, Slides
    Chemnitz Finite Element Symposium, 2021 (Online), Residual based a Posteriori Error Estimators for Algebraic Flux Correction Scheme, 6-8 September 2021, Slides
    Bound-Preserving Space and Time Discretizations for Convection-Dominated Problems, BIRS & CMO (Online), Residual based a Posteriori Error Estimators for Algebraic Flux Correction Scheme, 22-27 August 2021, Slides
    ESCO 2020, 7th International Congress of Computational Engineering and Sciences (Online), Towards A Posteriori Error Estimators for Algebraic Flux Correction Scheme, 8-12 June 2020
    The 28th Biennial Numerical Analysis Conference, Glasgow, On Numerical Simulations and a Posteriori Analysis for Algebraic Flux Correction Schemes, 25-28 June 2019
    MAFELAP 2019, The Mathematics of Finite Elements and Applications 2019, London, On Numerical Simulations and a Posteriori Analysis for Algebraic Flux Correction Schemes, 17-21 June 2019
    BAIL 2018, International Conference on Boundary and Interior Layers, Glasgow, Study of Iterative Methods for Nonlinear AFC Discretizations on Convection-Diffusion Equations, 18-22 June 2018, Slides
    15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics (WCCM-APCOM 2022), Yokohoma, Minisymposium: Special Methods in Computational Fluid Mechanics, Co-Organiser with Dr. Matthias Kirchhart, 31 July - 5 August, 2022
    8th BMS Student Conference, TU Berlin, Co-Organiser, Conference Page, 19-22 February, 2020

    Software

    I have co-developed and currently working on the following software packages.

    ddX

    Domain Decomposition Paradigm for Continuum Solvation Models

  • Language: Fortran
  • Developed the Domain Decomposition Linear Poisson Boltzmann (ddLPB) sub-module
  • Co-developed the general framework of the package
    •  

    ParMooN

    Parallel Mathematics and object-oriented Numerics

  • Language: C++
  • Developed the Algebraic Flux Correction package for Steady-State and Time-Dependent Convection-Diffusion Equations
  • Co-developed the a Posteriori Estimator package

    • Miscellaneous

    Here are some general information that might be useful to you. I list some books that I really like, some non-mathematical stuff that interests me, and some stuff that I like!

    Mathematical Books

    Numerical Analysis

  • Numerical Analysis, Richard L. Burden, J. Douglas Faires: Covers all the sections of introductory Numerical Analysis
  • Numerical Solution of Partial Differential Equations by the Finite Element Method, Claes Johnson: Best introductory book for FEM
  • Theory and Practice of Finite Elements, Alexandre Ern and Jean-Luc Guermond: Covers advanced FEM
  • A Posteriori Error Estimation in Finite Element Analysis, J. Tinsley Oden and Mark Ainsworth: Covers important topics in Adaptive FEM
    •  

    Functional Analysis

  • Sobolev Spaces, John J. F. Fournier and Robert A. Adams: Covers Functional Analysis
  • Topics in Functional Analysis and Applications, S. Kesavan: Covers Functional Analysis required for FEM
    •  

    Computational Fluid Dynamics

  • Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems, Hans-Görg Roos, Lutz Tobiska, and Martin Stynes: Essential for CDR Equations
  • Finite Element Methods for Incompressible Flow Problems, Volker John: Covers important topics in CFD analysis
    •  

    Non-Mathematical Books

    Comic Books

  • Dark Knight Returns, Frank Miller
  • Batman: New 52, Scott Snyder
  • Batman: The Killing Joke, Alan Moore
  • JLA: Tower of Babel, Mark Waid
  • Identity Crisis, Brad Meltzer
  • Doctor Strange: The Oath, Brian K. Vaughan
    •  

    Other stuff

  • Blink: The Power of Thinking Without Thinking, Malcolm Gladwell
    •  

    TV Series

    Anime

  • Death Note, Tsugumi Ohba
  • Naruto, Masashi Kishimoto
    •  

    Non-Anime

  • Dark, Netflix
  • Sex Education, Netflix
  • Stranger Things, Netflix
  • Kim's Convenience, Netflix
  • The Boys, Amazon Prime
    •  

    General Interests

    Apart from the aforementioned things, I am also a big football fan and support Chelsea FC. I am also a TCG player and enjoy Magic: The Gathering and Flesh and Blood. I also like listening to podcasts and two of my all time favorite are: 44Two and TISS.

    Contact

    If you have any questions, please feel free to write to me. If I don't respond, don't feel guilty and send me a reminder.

    Location:

    Indian Institute of Technology, Gandhinagar, Gujarat, India

    Call:

    +91 123 456 7890