Graduate Student Seminar

Speaker 1: Nadeesri Wijekoon

Title

An Introduction to Julia software

Abstract

Julia is a new scientific programming language which has high-performance where syntax that is familiar to users of other technical computing environments. Some of Julia's features are the sophisticated compiler, distributed parallel execution, high numerical accuracy and the extensive mathematical function library. In the presentation, we will give a brief introduction about Julia software and evaluate its performance with use of few examples.

Speaker 2: Joshua Hudson

Title

Data assimilation for the 2D MHD using feedback control algorithms

Abstract

In the study of a differential equation, dY = F(Y), subject to certain boundary conditions, theory usually is developed to show that unique solutions will arise given an initial value Y(0) = Y_0, and that the solution will change in a continuous way with respect to changes in the initial value. However, in practice the initial value may not be known accurately enough to appeal to this continuity. Data assimilation is the attempt to compensate for this lower bound on the accuracy of the measured initial condition by taking measurements as time goes on and feeding them back into the differential equation.

There are various ways of doing in this, and in this talk we will discuss a few algorithms for the Magneto-Hydrodynamic equations (MHD), which is a system of partial differential equations that govern the movement of a fluid in presence of a magnetic field. 

We will see that the in 2D, algorithms exist which give exponential convergence of the data assimilation solutions to the true value of the observable, including some that collect measurements on less variables than the total number of unknowns in the system.