Title of the talk: Bridging Physics and Numerics: The Port-Hamiltonian Way

Date & Time: 22 July 2025, 11:00 AM , Seminar Hall, Dept. of Mathematics

Abstract: The port-Hamiltonian (pH) system framework provides a geometric foundation for modelling conservation laws in physical systems, particularly those with energy exchange through boundaries. In this talk, I will introduce a novel discontinuous Galerkin (DG) framework for discretizing distributed parameter pH systems, i.e, the port-Hamiltonian discontinuous Galerkin Finite Element Method. This approach yields structure-preserving semi-discrete formulations while offering flexibility in geometry and function spaces. The explicit treatment of boundary ports in the pH formulation simplifies the design of power-preserving numerical fluxes. Thus, this method has a twofold advantage, first it provides a flexible structure preserving discretization technique for pH systems and second it provides a solution to the challenge of dissipative numerical flux in discontinuous finite element methods.

About the Speaker: Dr. Nishant Kumar is a Research Geophysicist at Shell India, working in the Imaging and Inversion R&D group, where he develops hybrid methods that combine data science and computational physics to solve PDEs governing geophysical processes. He has completed his Ph.D. at the University of Twente in the Mathematics of Computational Science group, focusing on structure-preserving numerical methods, developing the novel port-Hamiltonian discontinuous Galerkin method. His interests lie at the intersection of physics-informed machine learning, structure preserving finite element methods, and inverse problems, with a strong drive to bridge theoretical insights with real-world applications.