Ylva Rydin
TDB, IT, UU
Wave problems appear in many fields of science such as acoustics, quantum mechanics, geophysics and electromagnetics. High order finite difference methods are known to be well suited for problems of this type. However, it has historically been difficult to achieve a stable boundary treatment and accurate treatment of non-smooth features such as point sources. Using summation-by-parts (SBP) finite different operators combined with imposing the boundary conditions with a penalty (SAT) technique provides a framework that makes it possible to construct stable discretisations of wave problems in a systematic way.
In this seminar, the SBP-SAT framework will be introduced. Further, I will present my own research in the area by briefly presenting two projects. The first project is in acoustics, the main focus in this part will be accurate treatment of point sources. The second project is in quantum-mechanics, here a scheme for solving the time-dependent Schrödinger equation on deforming domains will be presented.