The Appelö High Order Group focuses on the development of novel high order accurate discretization of partial differential equations modeling problems form science and engineering.

Daniel's primary research interest is the development, analysis and implementation of fast, stable and accurate numerical algorithms for approximation of partial differential equations arising in engineering and natural sciences. Another research topic Daniel has focused on is the development of artificial boundary conditions that are required to solve time dependent partial differential equations on unbounded domains.

Before joining University of Colorado Daniel was an Associate Professor at The University of New Mexico in Albuquerque. Before that Daniel was a postdoc in Mechanical Engineering at Caltech with Tim Colonius. Prior to Caltech Daniel 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 massively parallel numerical methods for seismology. Together with Anders I also developed a fourth order accurate embedded boundary method for the wave equation. At LLNL I also worked with Bill Henshaw on simulations of converging shocks and on a parallel overset grid solver for solid mechanics.

Daniel was a Hans Werthen (the founder of Electrolux) Prize postdoc at the Department of Mathematics and Statistics at UNM where he worked with Tom Hagstrom on a general formulation of perfectly matched layer models for hyperbolic-parabolic systems and Hermite methods.

Daniel obtained a PhD in Numerical Analysis at NADA, KTH under the supervision of Gunilla Kreiss. The thesis considered different aspects of the perfectly matched layer method. It turned out that the well-posedness of general pml models could always be guaranteed by a parabolic complex frequency shift and that stability can be established for a certain class of hyperbolic systems.