Hello 👋

Welcome to my research website. I was a postdoctoral fellow at Umeå University, Sweden from Dec 2022 - Feb 2026. I received my PhD from the University of Newcastle, Australia in August 2022. I did my M.Sc (Hons) Mathematics and B.E (Hons) Mechanical Engineering from BITS Pilani Goa Campus. My interests lie in numerical methods to solve partial differential equations arising in real–life applications. You can read more about my work in my blog.

My 3 Recent Posts

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• Shape from Shading - Revisited

• Virtual element solution with Gridap

• Wrapping up GSoC

My Recent Projects

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I am currently working on

• Topology Optimization: Topology optimization of an acoustic black hole. This is joint work with
  • Martin Berggren, Umeå University, Sweden.
  • Eddie Wadbro, Karlstad University, Sweden, and
  • Seyedabbas Mousavi, KTH Royal Institute of Technology, Sweden,

  I wrote a sample tutorial on automatic differentiation (AD) in density-based topology optimization using Juila (TopOpt@github). I used Gridap.jl to handle the finite element part, and formulate the adjoint method as a reverse mode AD rule. This AD interface plays well with simple functions acting on the design, such as the penalty in the Solid Isotropic Material with Penalization technique.

• Multiscale finite element method: High-order multiscale finite element methods to solve boundary value problems with highly oscillatory/random coefficients. This is joint work with
  • Siyang Wang, Umeå University, Sweden,
  • Felix Krumbiegel, Saarland University, Germany, and
  • Roland Maier, Karlsruhe University, Germany.

  Here is the repository MsFEM.jl@github containing the code to implement the method discussed in our papers:

  • Kalyanaraman, B., Krumbiegel, F., Maier, R., & Wang, S. (2026). Enriched higher-order multiscale approaches with applications to wave propagation. Submitted arXiv [Math.NA]. Retrieved from https://arxiv.org/abs/2605.30118
    
  • Kalyanaraman, B., Krumbiegel, F., Maier, R., & Wang, S. (2025). Optimal higher-order convergence rates for parabolic multiscale problems. Submitted arXiv [Math.NA]. Retrieved from https://arxiv.org/abs/2510.09514

My Past Projects

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• PML for Elastic Waves: Perfectly Matched Layers (PML) for Elastic Waves

  Worked on the analysis and implementation of the perfectly matched layers for the elastic wave equation in a layered media. The work involved theoretically establishing the stability of the PML model and then numerically solve the governing equations using higher order summation-by-parts (SBP) finite difference methods. An example for a curvilinear domain is shown below:

  This is joint work with

  • Siyang Wang, Umeå University, Sweden,
  • Kenneth Duru, University of Texas at El Paso, USA.

  The results are discussed in this paper:

  Duru, K., Kalyanaraman, B., & Wang, S. (2025). On the stability analysis of the perfectly matched layer for the elastic wave equation in layered media. Journal of Computational Physics, 114268.

• GSoC 2021: Google Summer of Code 2021 with NumFOCUS

  Selected to be a part of GSoC 2021 with Gridap.jl and NumFOCUS. I will be working under Oriol Colomés, Santiago Badia and Eric Neiva during the program. Read more here or click the image!

• iceFEM@github: A FreeFem based open-source package to simulate a variety of linear hydro-elasticity problems.

  The algorithms are based on the papers:

  • Kalyanaraman, B., Meylan, M. H., Bennetts, L. G., & Lamichhane, B. P. (2020). A coupled fluid-elasticity model for the wave forcing of an ice-shelf. Journal of Fluids and Structures, 97, 103074.
  • Ilyas, M., Meylan, M. H., Lamichhane, B., & Bennetts, L. G. (2018). Time-domain and modal response of ice shelves to wave forcing using the finite element method. Journal of Fluids and Structures, 80, 113–131.

  This is joint work with my supervisors:

  • Mike Meylan, University of Newcastle.
  • Bishnu Lamichhane, University of Newcastle.
  • Luke Bennetts, University of Adelaide.