• J. Xu, B. Mustapha, J.A. Nolen, P.N. Ostroumov
  ANL, Argonne

We are developing highly scalable solvers for space charge dominated beams based on both Particle-In-Cell (PIC) and direct Vlasov models. For the PIC model, particles are distributed evenly on different processors and space charge effect has been counted by solving Poisson's equation on a finite mesh. Several Poisson solvers have been developed using Fourier, Spectral Element (SEM) and Wavelet methods. Domain decomposition (DD) has been used to parallelize these solvers and all these solvers have been implemented into the PTRACK code. PTRACK is now widely used for large scale beam dynamics simulations in linear accelerators. For the Vlasov model, Semi-Lagrangian method and time splitting scheme have been employed to solve Vlasov equation directly in 1P1V and 2P2V phase spaces. 1D and 2D Poisson solvers have been developed with SEM. Similarly, DD has been used for parallelization of Poisson and Vlasov solvers. New efforts on developing Vlasov and Poisson solvers on unstructured mesh will also be reported.