Comparative Analysis of Numerical Methods for Solving 3D Continuation Problem for Wave Equation
Speaker
Sobolev Institute of Mathematics, Novosibirsk, Russia
Host
Session Moderator
Dr. Azhar Yousuf
Abstract
This talk presents an explicit finite difference method (FDM) for solving an ill-posed Cauchy continuation problem for the three-dimensional acoustic wave equation in the time domain, where data are prescribed on only a part of the boundary of a cubic domain. The finite difference method is a widely used numerical technique for solving hyperbolic partial differential equations (PDEs) by discretizing the computational domain into a finite number of regions, thereby transforming the governing PDE into a system of linear algebraic equations (SLAE). The talk will discuss the theoretical formulation of the proposed approach and its numerical implementation in MATLAB (R2023a). Emphasis will be placed on the efficient solution of the resulting dense system of linear equations through several iterative techniques. Specifically, the Jacobi, Gauss–Seidel, and Successive Over-Relaxation (SOR) methods are extended and employed to improve computational efficiency while investigating the convergence properties of the proposed numerical scheme. Finally, numerical experiments will be presented to demonstrate the effectiveness of the method. The numerical results will be compared with analytical solutions for different time-dependent scenarios, illustrating the accuracy and convergence behavior of the proposed approach.
About the Speaker
Dr Sreelatha Chandragiri completed her PhD in Mathematics from the Department of Theory of Functions and Complex Analysis, Siberian Federal University, Russia (now the Krasnoyarsk Mathematical Centre), under the supervision of Prof. Evgeniy K. Leinartas. Her doctoral thesis was titled “The Cauchy Problem for Difference Equations in Lattice Cones and Generating Functions for Its Solutions.” She previously earned a master’s degree in engineering from Vels University, Chennai, India. She worked as a postdoctoral researcher at the Laboratory of Applied Inverse Problems, Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk State University, where she worked under the joint supervision of Prof. Sergey I. Kabanikhin and Prof. Maxim A. Shishlenin. Her current research focuses on the Cauchy problem for three-dimensional Poisson, parabolic, and hyperbolic (telegraph and acoustic wave) equations using finite difference methods and iterative techniques in MATLAB, as well as numerical solutions of elliptic equations using the finite element method with Python and FreeFEM++. Her research interests include partial differential equations, inverse problems, numerical analysis, mathematical modelling, and combinatorics.