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Center for Nonlinear Studies |
Prominent among the many challenges in simulating kinetic plasma phenomena is the high-dimensionality of the kinetic PDE to be solved. We will discuss the use of the sparse grid combination technique as a method for circumventing the curse of dimensionality in this context. The combination technique uses a linear combination of grids – each of which is fine in some coordinate directions and coarse in others – to mimic a single grid which is fine in every direction. The method has drawbacks – most notably, it is very sensitive to the coordinate system on which the grid is based – but we will show that kinetic equations for plasmas, and especially strongly magnetized plasmas, are in many ways ideally suited to overcome these drawbacks. We will present work on using sparse grids with both PIC and continuum finite-volume schemes, with theory and results from test problems for each. This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics Program under Contract DE-AC5207NA27344 at Lawrence Livermore National Laboratory.
Host: William Taitano