A New Finite Element Method for Radiation Transport on Spherical Geodesic Grids

Dr. Maitraya Bhattacharyya
Dr. Maitraya Bhattacharyya

Abstract: We present a new numerical method to solve the Boltzmann equation based on a finite element approach in angle, that combines the advantages of the discrete ordinate method (SN) and the filtered spherical harmonics method (FPN) while avoiding their disadvantages. The scheme uses a finite element basis to represent functions of angular variables on a geodesic grid along with a simple limiting strategy to ensure non-negativity of solutions. We then compare this new method with SN and FPN schemes using four test problems and find it to perform well when one of the other methods fails.

Please see https://arxiv.org/abs/2212.01409 for the technical paper.

Speaker’s Bio: Dr. Bhattacharyya received their Ph.D. from the Indian Institute of Science Education Research Kolkata, India where they worked on non-linear black hole perturbation theory with the numerical relativity code 'bamps'. After graduating in 2021, they joined Penn State as a post-doc in Prof. David Radice's group where they are developing a new Boltzmann transport code for neutrinos in general relativity within AthenaK, a new numerical relativity code designed to work on both central processing unit and graphics processing unit architectures.

Last Updated: March 8, 2023 - 8:47 am