Our primary research interest is the development, analysis and implementation of fast, stable and accurate numerical algorithms for approximation of differential equations arising in engineering and natural sciences. We are interested in forward and inverse problems governed by acoustic, elastic and electromagnetic waves in the time and frequency domain. We are also developing and analyzing computational tools for qunatum computing applications. Another research topic of interest is the development of artificial boundary conditions that are required to solve time dependent partial differential equations on unbounded domains.
Before joining CMSE and the Department of Mathematics at MSU Daniel was an Associate Professor at the University of Colorado Boulder and 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 he was a part of the Serpentine project where he and Anders Petersson, Bjorn Sjögreen developed massively parallel numerical methods for seismology. Together with Anders he also developed high order accurate embedded boundary methods for the wave equation. While at LLNL Daniel 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. His 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.