dispersive waves

A Dichotomy of Continuous Finite Element Spaces and Its Application to Energy-Conservative Galerkin Methods for Nonlinear and Dispersive Wave Equations

Dimitrios Mitsotakis, Reader/Associate Professor, Engineering Mathematics, School of Mathematics and Statistics, Victoria University of Wellington (VUW)

Feb 17, 14:30 - 15:30

B1 L3 R3119

dispersive waves optimization Finite elements

This talk illustrates why energy-conservative Galerkin methods for nonlinear and dispersive wave equations achieve optimal convergence rate with odd-degree polynomials.

Nonlinear and dispersive waves: Theory, computations and applications

Dr. Dimitrios Mitsotakis, Senior Lecturer, Victoria University of Wellington

Sep 30, 12:00 - 13:00

KAUST

oceanic waves dispersive waves

The study of waves in fluids is one of the most significant branches of fluid mechanics. Part of this study is the theory of nonlinear and dispersive waves which has recently emerged and is still under development. Nonlinear and dispersive waves appear in fluids of any form and have significant role in the fields of oceanic waves (surface and internal), atmospheric modelling, electromagnetism, nonlinear optics, ultra-cold matter and even in blood flow problems. In this presentation we will review relevant applications, such as tsunami waves, the El Nino southern oscillation, blood flow in arteries and solitons propagating in optical fibres. Mathematical modelling techniques for deriving equations that describe such phenomena will be introduced in the context of surface water waves. We will also review the minimum required theoretical background in order to proceed with safe numerical simulations. Finally, we will discuss the numerical modelling of such problems where methods such as standard and mixed Galerkin / Finite element methods are of central focus. We close this presentation by showcasing a topic of much current interest, namely, the development of modern mathematical models for nonlinear and dispersive waves by combining machine learning techniques with classical methodologies.

David Ketcheson

Professor, Applied Mathematics and Computational Science

numerical methods numerical analysis PDE nonlinear waves heterogenouse media dispersive waves optimization software development

Professor Ketcheson is an expert in numerical analysis and computational science, specializing in the study of numerical methods for differential equations and the modeling and analysis of time-dependent nonlinear wave phenomena.