Seminar in Numerical Analysis: Andreas Stock (Universität Stuttgart)

Time Domain Decomposition based on Multirate Multistep Timestepping Techniques for the Particle-In-Cell Method

In the Particle-In-Cell (PIC) method particles and electromagnetic fields are fully self-consistent coupled to solve the Vlasov equation describing the behavior of rarefied plasma flows without collisions. In the underlying physical model of the PIC method different time-scales occurs, i.e. the electromagnetic fields propagating with the speed of light and the particles moving with speeds much lower than the electromagnetic fields. Due to the CFL condition for explicit time integration schemes the time step is restricted to the largest propagating speed, yielding an inefficient time discretization for the slower particles. We developed a time domain decomposition based on a multirate multistep technique to treat each component on it's specific time-scale leading to an efficient time-integration algorithm.

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