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 recent work here.

Recent News

Kalyanaraman, B., Krumbiegel, F., Maier, R., & Wang, S. (2025). Optimal higher-order convergence rates for parabolic multiscale problems. arXiv [Math.NA]. https://arxiv.org/abs/2510.09514

has been accepted for publication in SIAM Journal on Numerical Analysis.

Recent Projects

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 Institute of Technology (KIT), 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]. 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]. https://arxiv.org/abs/2510.09514