Akash Anand

Akash Anand

Email: akasha at iitk.ac.in
Phone: +91-512-259-7880
Office: Room 327, Faculty Building
Address: IIT Kanpur, Kanpur, UP 208016, India

Overview

Much of my work is centered around the computational wave scattering problem, where the goal is to develop accurate and efficient algorithms for solving time-harmonic wave equations. In particular, I work with integral equation based methods, which are well-suited for handling unbounded domains and complex geometries. My contributions include the design and analysis of fast algorithms for high-frequency scattering, as well as the development of robust solvers that combine mathematical rigor with computational efficiency.

In addition to this, I have actively collaborated with experts and students on the solution of certain moment problems. These investigations have led to progress on open questions in functional analysis and operator theory, illustrating my broader interest in both applied and theoretical aspects of mathematical research.

Research Themes

1. Computational Wave Scattering

I design high-order integral equation solvers for acoustic and electromagnetic wave problems. Key contributions include:

2. Numerical Analysis of Computational Algorithms

I analyze the stability, convergence, and error estimates of high-order methods, ensuring that computational algorithms are reliable and practically effective.

3. Broader Interests

I am also interested in inverse scattering, imaging, and high-order PDE solvers applied to problems requiring large-scale simulations in physics and engineering.

Computational Tools & Software

To facilitate research and education in high-order numerical methods, we develop interactive computational tools that make advanced techniques accessible to the broader research community. These platforms allow researchers to test their own algorithmic ideas and benchmark them against established methods.

HighFIE Lab - Fourier Extension Research Platform

HighFIE Lab is an interactive benchmarking platform for high-order Fourier interpolation and extension methods. The tool enables researchers to:

  • Test and validate custom Fourier extension algorithms
  • Compare performance against implemented baseline methods (FC-Gram, with more coming)
  • Visualize spectral convergence properties and approximation errors
  • Interactively explore parameter sensitivity and method behavior

The platform is designed as an open research tool for the computational mathematics community, with ongoing development to include additional extension methods for comprehensive comparison and benchmarking.

Visit Software page for details and access

Research Group

Past Graduate Students

Current Postdoctoral Fellows

Past Postdoctoral Fellows

Selected Publications

Publications

  1. (with S. Tomar and A. K. Verma) An effective computational technique for solving nonlinear boundary value problems arising in various physical phenomena, Mathematical Methods in the Applied Sciences, Online (2026).
  2. (with P. Nainwal) A modified FC-Gram approximation algorithm with provable error bounds, Journal of Scientific Computing, Volume 105, Article Number 8 (2025).
  3. (with S. Chavan and R. Nailwal) Complete monotonicity of rational functions in two variables and toral m-isometric pairs, Journal of Operator Theory, Volume 92, Issue 1, Pages 101-130 (2024).
  4. (with J. Paul, A. Pandey and B. V. R. Kumar) Fast rapidly convergent penetrable scattering computations, Advanced Modeling and Simulation in Engineering Sciences, Volume 11, Article Number 2 (2024).
  5. (with A. K. Tiwari and A. Pandey) A fast, rapidly convergent Nyström solver for electromagnetic scattering from orthotropic media, Computers and Mathematics with Applications, Volume 154, Pages 58-64 (2024).
  6. (with A. K. Tiwari, A. Pandey and J. Paul) A fast rapidly convergent method for approximation of convolutions with applications to wave scattering and some other problems, Journal of Computational Physics, Volume 459, 111119 (2022).
  7. (with Y. Boubendir, F. Ecevit and S. Lazergui) Spectral Galerkin boundary element methods for high-frequency sound-hard scattering problems, Numerische Mathematik, Volume 150, Pages 803-847 (2022).
  8. (with S. Chavan, Z. J. Jabłoński and J. Stochel) The Cauchy dual subnormality problem for cyclic 2-isometries, Advances in Operator Theory, Volume 5, Issue 3, Pages 1061–1077 (2020).
  9. (with J. Ovall, S. Reynolds and S. Weisser) Trefftz finite elements on curvilinear polygons, SIAM Journal on Scientific Computing, Volume 42, Issue 2, Pages A1289-A1316 (2020).
  10. (with S. Chavan and S. Trivedi) Analytic m-isometries without the wandering subspace property, Proceedings of the American Mathematical Society, Volume 148, Number 5, Pages 2129-2142 (2020).
  11. (with F. Ecevit and Y. Boubendir) Galerkin boundary element methods for high-frequency multiple-scattering problems, Journal of Scientific Computing, Volume 83 (2020).
  12. (with S. Chavan, Z. J. Jabłoński and J. Stochel) A solution to the Cauchy dual subnormality problem for 2-isometries, Journal of Functional Analysis, Volume 277, Issue 12, 108292 (2019).
  13. (with A. K. Tiwari) A Fourier extension based numerical integration scheme for fast and high-order approximation of convolutions with weakly singular kernels, SIAM Journal on Scientific Computing, Volume 41, Issue 5, Pages A2772–A2794 (2019).
  14. (with S. Chavan, Z. J. Jabłoński and J. Stochel) Complete systems of unitary invariants for some classes of 2-isometries, Banach Journal of Mathematical Analysis, Volume 13, Pages 359-385 (2019).
  15. (with A. Pandey) Improved convergence of fast integral equation solvers for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface, Journal of Computational Physics, Volume 376, Pages 767-785 (2019).
  16. (with J. Ovall and S. Weisser) A Nyström-based finite element method on polygonal elements, Computers and Mathematics with Applications, Volume 75, Issue 11, Pages 3971-3986 (2018).
  17. (with S. Chavan) Module tensor product of subnormal modules need not be subnormal, Journal of Functional Analysis, Volume 272, Issue 11, Pages 4752-4761 (2017).
  18. (with S. Chavan) A Moment Problem and Joint q-isometry Tuples, Complex Analysis and Operator Theory, Volume 11, Issue 4, Pages 785-810 (2017).
  19. (with A. Pandey, B. V. R. Kumar and J. Paul) An efficient high-order Nyström scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface, Journal of Computational Physics, Volume 311, Pages 258-274 (2016).
  20. (with J. Ovall and C. Turc) Well-conditioned boundary integral equations for two-dimensional sound-hard scattering problems in domains with corners, Journal of Integral Equations and Applications, Volume 24, Issue 3, Pages 1-38 (2012).
  21. (with R. Dalmeya, I. Sharma and C. Upadhyay) Contact of a rigid cylindrical punch with an adhesive elastic layer, Journal of Adhesion, Volume 88, Issue 1, Pages 1-31 (2012).
  22. (with Y. Boubendir, F. Reitich and F. Ecevit) Analysis of multiple scattering iterations for high-frequency scattering problems. II: The three-dimensional scalar case, Numerische Mathematik, Vol. 114, No. 3, Pages 373-427 (2010).
  23. (with F. Reitich) An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions, Journal of Acoustical Society of America, Volume 121, Issue 5, Pages 2503-2514 (2007).

Proceedings

  1. (with F. Ecevit, Y. Boubendir and S. Lazergui) Galerkin boundary element methods for high-frequency sound-hard scattering problems. 14th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), August 25-30, 2019, Vienna University of Technology (TU Wien), Vienna, Austria.
  2. (with J. Paul and B. V. R. Kumar) Acoustic scattering by inhomogeneous media with piecewise smooth material properties. 13th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), May 15-19, 2017, University of Minnesota, Twin Cities, USA.
  3. (with A. Pandey and B. V. R. Kumar) A high-order Nyström scheme for acoustic scattering by inhomogeneous penetrable media in three dimensions. 12th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), July 20-24, 2015, Karlsruhe Institute of Technology, Germany.
  4. (with A. K. Tiwari and A. Pandey) A high-order Nyström solver for electromagnetic scattering from orthotropic media. 12th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), July 20-24, 2015, Karlsruhe Institute of Technology, Germany.
  5. (with J. Paul, A. Pandey and B. V. R. Kumar) A high-order solver for inhomogeneous penetrable scattering in two dimensions. 12th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), July 20-24, 2015, Karlsruhe Institute of Technology, Germany.
  6. (with A. Pandey and J. Paul) A high-order Nyström scheme for acoustic scattering by inhomogeneous penetrable media in two dimensions. 11th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), June 3-7, 2013, Gammarth, Tunisia.
  7. (with U. Anand and J. Singh) A fast and robust star identification algorithm for star tracker. National Conference on Applications and Challenges in Space Based Navigation, April 17-18, 2013.
  8. (with J. Singh, J. Rammohan and A. Pandey) The earth gravitational field model for inertial navigation of space vehicle. National Conference on Applications and Challenges in Space Based Navigation, April 17-18, 2013.
  9. (with C. Turc, O. Bruno and J. Chaubell) Efficient solution of three-dimensional problems of acoustic and electromagnetic scattering by open surfaces. 10th International Conference on Mathematical and Numerical Aspects of Waves (WAVES), July 25-29, 2011, Vancouver, Canada.

Others

  1. (with A. Pandey) Fourier smoothed pre-corrected trapezoidal rule for solution of Lippmann-Schwinger integral equation, Preprint (2020).
  2. A Fourier continuation framework for high-order approximations, Preprint (2018).

A complete list of publications is available on Google Scholar.