Daniel Appelö
I am working as a postdoc with Oscar Bruno and Nathan Albin at Applied and Computational Mathematics on high-order unconditionally stable embedded boundary PDE solvers. Previously I was a postdoc in Mechanical Engineering at Caltech with Tim Colonius. With Tim I developed a high order version of the Super-Grid-Scale method, which is a flexible, accurate and robust technique for truncating unbounded computational domains. We were also developing computational models to predict thermal behavior of Montgolfier aerobots for exploration of Titan under a subcontract with JPL, including some modeling of double walled balloons.
Before I came to Caltech I worked at Lawrence Livermore National Laboratory in the Applied Math. group at the Center for Applied Scientific Computing. At LLNL I was a part of the Serpentine project where Anders Petersson, Bjorn Sjögreen and I developed numerical methods for seismic modeling. We also wrote a massively parallel code for simulation of seismic wave propagation. At LLNL I also collaborated with Bill Henshaw on simulations of converging shocks. With Bill I am currently working on a parallel overset grid solver for solid mechanics computations on complex geometries. Together with Anders I am developing a fourth order accurate embedded boundary method for the wave equation.
After my dissertation I spent six months as a Hans Werthen (the founder of Electrolux) Prize postdoc at the Department of Mathematics and Statistics at UNM. There I worked with Tom Hagstrom on a general formulation of perfectly matched layer models for hyperbolic-parabolic systems. Tom has come up with new and very exiting discretization methods of arbitrary order based on Hermite interpolation and Taylor time series expansion. As a part of my postdoc we considered the application of these methods to compressible flows, specifically we looked at Runge-Kutta time stepping schemes and absorbing layers. Currently we are interested in comparing our Hermite-Runge-Kutta methods with more conventional methods in simulation of homogeneous compressible turbulence. Here is an example of a computation with a Hermite method with absorbing layers. The upper solution has layers on all sides, in the lower the (unphysical) acoustic disturbances create a feedback and lead to an instability.
I did my PhD in Numerical Analysis at NADA, KTH under the supervision of Gunilla Kreiss. During my thesis work I also had the fortune to be able to visit Tom Hagstrom in New Mexico at several occasions and he became a co-adviser of sorts. In my thesis I looked at different aspects of the perfectly matched layer method. One result we got was that well-posedness of a general pml model we developed could always be guaranteed by a parabolic complex frequency shift. We were also able to establish stability results for a certain class of hyperbolic systems, the details can be found in my thesis.