Mathematics Seminar - 10/22/21

Abstract: Many time-dependent problems in science and engineering can be modeled by differential equations (ODEs, PDEs). They usually involve multiple physical processes, where their complex interactions can result in dynamics over a wide range of time and spatial scales. Since it is typically impossible to solve these problems analytically, numerical methods are constructed to discretize the problems in space and time in order to provide an approximation to the true solution. For time simulation, the major challenge lies in a significantly growing number of changing time scales in the dynamics of problems. A prominent example is the existence of vastly differing time scales in atmospheric phenomena, ranging from a relatively slow advection to very fast gravity waves, which poses significant difficulties for real-time simulation of weather conditions. Therefore, developing accurate and efficient time integration techniques is crucial for many applications. The aim of this talk is to give an introduction to time discretization (from classical to advanced methods) for differential equations and to demonstrate their performance on applications in numerical weather prediction and in computer graphics.

The talk is designed for audiences with different backgrounds (beginners + experts) and should be understandable for both undergraduate and graduate students. As such, everyone is welcome to attend the talk.