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Numerical modeling of ultra-high intensity laser-plasma physics demands a kinetic approach to handle the extreme nonlinearities, wave-particle interactions and accelerated particle beams which may be produced. Mathematically this requires the ab initio solution of the relativistic Vlasov-Boltzmann equation for the plasma constituents together with the appropriate Maxwell equations for the electromagnetic fields. Currently the model of choice is the particle-in-cell code: a highly versatile, finite-difference discretization of the Vlasov equation for the particle distribution function f(x,p). State of the art three dimensional PIC simulations include up to 1012 particles on 105 cores.
In dense, colder plasma regions, PIC simulation is less suitable because it cannot model collisions accurately. Recently a new modeling paradigm has been established - mesh-free plasma simulation - in which fast summation techniques replace the solution of the field equations on the mesh. The key innovation behind this development is the hierarchical tree algorithm, a rapid O(N log N) technique for evaluating mutual (Coulomb) forces due to an ensemble of charged particles. At JSC we have developed a parallel tree-code (PEPC) capable of running on the entire 294912 processors of the BlueGene/P supercomputer Jugene, a milestone which makes it feasible to perform first principles simulations of transport processes in strongly coupled plasmas using well over 109 particles. Over the past two years, a road map has emerged which, despite stagnating processor clock speeds, foresees the advent of exascale machines capable of 1018 floating-point operations per second by 2020. This can only be achieved by a combination of increased concurrency, drastic reductions in power consumption, and a complete redesign of processor memory access. For the computational scientist, these new architectures necessitate a major paradigm shift from pure distributed memory algorithms (MPI) to more complex program structures featuring concepts such as hybrid communication layouts, asynchronous tasking and non-blocking I/O. Some of these emerging trends will be reviewed and demonstrated using the PIC and tree-code algorithms as examples. |
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