I am a postdoctoral researcher working with Prof. Dr. Mária Lukáčová-Medviďová, in the Numerical Mathematics group at Johannes Gutenberg Universität Mainz. Prior to my current role, I was a PhD student at the Indian Institute of Science, and was awarded the Prime Minister's Research Fellowship by the Ministry of Education, Government of India, to pursue my PhD. I am interested in the development and numerical analysis of structure-preserving methods for hyperbolic systems and multiscale kinetic equations.

The hyperbolic systems of partial differential equations (PDEs) tend to develop discontinuous solutions even for smooth initial data. Furthermore, infinitely many weak entropy solutions can be constructed for multidimensional systems governing fluid motion, such as compressible and incompressible Euler systems. This opens an important question on admissibility criteria to select a physically reasonable, unique solution. Incidentally, many standard numerical methods pick up the correct physically relevant solution, and it is interesting to identify the underlying structural properties, such as positivity preservation and entropy inequality. Moreover, it is of fundamental importance that the schemes satisfy structure-preserving properties in order to analyze the convergence of numerical schemes.

I'm also interested in developing efficient methods for multiscale PDEs. Standard explicit methods are inefficient for such systems, as the time step scales with the small parameters. Fully implicit methods for such nonlinear systems are also inefficient due to the need for iterative solvers at each time step. Therefore, efficient and clever implicit-explicit (IMEX) methods with a reasonable time step condition that is independent of the small parameters are required. Furthermore, these methods must be consistent with the asymptotic limits of the PDEs, and hence it is important to develop asymptotic preserving IMEX methods for multiscale PDEs.

Journal publications and full-length conference proceedings

  1. Megala Anandan, Benjamin Boutin, Nicolas Crouseilles, "Uniformly higher order accurate schemes for dynamics of charged particles under fast oscillating magnetic fields", IMA Journal of Numerical Analysis, 2025. [Published article], [Preprint].
  2. Megala Anandan, Mária Lukáčová-Medviďová, S. V. Raghurama Rao, "An asymptotic preserving scheme satisfying entropy stability for the barotropic Euler system", SeMA Journal, 2025. [Published article], [Preprint].
  3. Megala Anandan, S. V. Raghurama Rao, "On Lattice Boltzmann Methods based on vector-kinetic models for hyperbolic partial differential equations", Computers and Fluids, 2024. [Published article], [Preprint].
  4. Megala Anandan, Benjamin Boutin, Nicolas Crouseilles, "High order asymptotic preserving scheme for diffusive scaled linear kinetic equations with general initial conditions", ESAIM: Mathematical Modelling and Numerical Analysis, 2024. [Published article], [Preprint].
  5. Megala Anandan, S. V. Raghurama Rao, "Entropy conserving/stable schemes for a vector-kinetic model of hyperbolic systems", Applied Mathematics and Computation, 2024. [Published article], [Preprint].
  6. Megala A, S. V. Raghurama Rao, "D2Q9 model of upwind lattice Boltzmann scheme for hyperbolic scalar conservation laws", Proceedings of the ECCOMAS Congress 2022 - 8th European Congress on Computational Methods in Applied Sciences and Engineering. [Published article].

Talks

  1. Megala Anandan, Mária Lukáčová-Medviďová, S. V. Raghurama Rao, "Asymptotic preserving and energy stable numerical schemes for barotropic Euler equations", numhyp25: Numerical Methods for Hyperbolic Problems, Darmstadt, Germany.
  2. Megala Anandan, S. V. Raghurama Rao, "Entropy conserving and stable schemes for vector-kinetic and macroscopic models", Kompaktseminar 2024, Prien am Chiemsee, Germany.
  3. Megala Anandan, S. V. Raghurama Rao, "A study of Lattice Boltzmann methods based on vector-kinetic models", 33rd International Conference on Discrete Simulation of Fluid Dynamics (DSFD), ETH Zurich, Switzerland (2024).
  4. Megala Anandan, S. V. Raghurama Rao, "Entropy conserving/stable schemes for vector-kinetic and macroscopic models", 19th International Conference on Hyperbolic Problems: Theory, Numerics and Applications (HYP2024), Shanghai, China.
  5. Megala Anandan, S. V. Raghurama Rao, "A discrete-kinetic entropy conserving and exact discontinuity capturing scheme for scalar conservation laws", XVIII International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2022), Málaga, Spain.
  6. Megala Anandan, S. V. Raghurama Rao, "D2Q9 model of upwind lattice Boltzmann scheme for hyperbolic scalar conservation laws", ECCOMAS Congress 2022, Oslo, Norway.
  7. Megala Anandan, S. V. Raghurama Rao, "An entropy conservative and exact discontinuity capturing discrete kinetic scheme for scalar conservation laws", Oberseminar Numerik, Institut für Mathematik, Johannes Gutenberg Universität Mainz, Germany (2022). [Abstract].

Thesis

Teaching

As a part of my Prime Minister's Research Fellowship, I lectured full courses at different private institutions in India.

Mentoring

Curriculum Vitae

You can view or download my CV below.

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