Dr. Ashish Bhatt, Department of Applied Mathematics, IIT (ISM) Dhanbad, Jharkhand, 826004, India

Biography: Dr. Ashish Bhatt is an Assistant Professor at IIT (ISM) Dhanbad, India, in the department of Applied Mathematics. Before this, he was a postdoc at University of Stuttgart in Germany and he obtained his PhD from University of Central Florida in the USA. He has published several research papers in international scientific journals. His research interests include structure-preserving numerical methods, model order reduction, dynamical systems, and their interplay. To find out more about him, visit https://www.iitism.ac.in/~ashishbhatt/

Speech Title: Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces

Abstract: Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as Korteweg–de Vries, Klein–Gordon, Schrödinger, and Camassa–Holm equations, all with damping/driving terms and time-dependent coefficients. Since key features of the PDEs under consideration are described by local conservation laws, which are independent of the boundary conditions, the proposed (second-order in time) discretizations are developed with the intent of preserving those local conservation laws. The methods are respectively applied to a damped-driven nonlinear Schrödinger equation and a damped Camassa–Holm equation. Numerical experiments illustrate the structure-preserving properties of the methods, as well as favorable results over other competitive schemes.

Keywords: Conformal symplectic, Multi-symplectic, Structure-preserving algorithm, Exponential integrators, Damped-driven PDE