research
Simulated solution of the merging of two-vortices superimposed over a
satellite image of Hurricane Lili (Oct. 3, 2002).
(Photo courtesy of NOAA / National Climatic Data Center, USA).
My research is in the fields of numerical analysis and dynamical systems. I am interested in the development and analysis of numerical methods, algorithms for simulation of ordinary and partial differential equations, such as those encountered in weather prediction, climate, oceanography, and most recently energy science.
My recent focus is on the interplay between statistics, stochastics and numerical methods. The process of numerical discretization converts a continuum problem, described by ordinary or partial differential equations into a finite, discrete problem suitable for computation. However this process also typically introduces a bias into the statistics of the system being modeled. Quantifying this bias and developing methods for coping with it, are a challenging and fascinating research line.
I am also fascinated by the dynamical properties of numerical methods, such as conservation laws and symmetries, and the meaning of these for simulation. This subject is addressed in the field geometric numerical integration. In particular, the numerical solution of Hamiltonian PDEs is repleat with such considerations.
Current external collaborations:
- Onno Bokhove (Twente University) - Hamiltonian numerical methods for ideal fluid dynamics.
- Ben Leimkuhler (Edinburgh) - Thermostat methods for correcting statistical measures.
- Georg Gottwald (Sydney) - stochastic differential equations and model reduction.
- Sergiy Zhuk (IBM Research, Dublin) - data assimilation for oceanography.
- Leo Maas (NIOZ) - numerical modeling of internal wave focusing.
- Gabriël Bloemhof and Sonja Bouwman (KEMA) - electric power reliability.
- Chris Stolk (U. Amsterdam) and Wim Mulder (T.U. Delft, Shell) - geophysical inverse problems and uncertainty quantification (collaboration supported by NDNS+).
- Harald van Brummelen (T.U. Eindhoven) - adjoint methods and predictability (collaboration supported by NDNS+).
students and fellows
- Svetlana Dubinkina - PhD student, Aug 2005--July 2009. Statistical mechanics of symplectic and energy-conserving discretizations for geophysical fluid models.
- Stefan Kopecz- Masters student, Aug–Dec 2005. Wave attractors for a stratified fluid in a tilted square domain - characterisic solutions of the linear, time periodic case. Report.
- Janis Bajars - PhD student, Jan 2007–Apr 2012. Geometric integrators for wave equations; thermostat methods.
- Bob Peeters - PhD student, Oct 2006–Sep 2010. (joint project; P.I. Dr. Onno Bokhove, U. Twente). Symplectic discretization of a hydrostatic atmospheric model; the role of dissipative perturbations and forcing.
- Alex Vonk - Bachelor student, U. Amsterdam. May–Aug 2007. Statistics of projection methods for ideal fluids. Thesis.
- Halldóra Þórsdóttir - Master student, U. Amsterdam. Oct 2010–Oct. 2011. Hamiltonian marticle-mesh method for the quasi-geostrophic equation on a sphere. Thesis.
- Keith Myerscough - PhD student, Nov 2010–Oct 2014. Thermostat subgrid scale modelling of atmospheric fluids.
- Wander Wadman - PhD student, Feb 2011–Jan 2015. Electric power grid integrity under decentralized generation and storage.
- Sergiy Zhuk - ERCIM Fellow, Apr 2011–Mar 2012. Data assimilation for energy applications.