Spectral collocation, domain decomposition and their parallel implementation for the Vlasov equations in one-D
- Univ. of Michigan, Ann Arbor, MI (United States)
Spectral collocation methods provide an attractive method for the accurate numerical solution of problems without artificial numerical dissipation or dispersion, but their reliance on global stencils determined by polynomial interpolation impose some penalty in their use as the basis for a Vlasov solver. Because the derivative at any grid point depends on the distribution function value at all other grid points, the computational cost of a derivative grows rapidly with the number of grid points, and they do not always perform well if the distribution function is zero in some regions of phase space. They do however provide very good--even exact--numerical conservation properties, they provide excellent behavior at system boundaries, and they offered very high accuracy. To overcome their faults while retaining these strengths, a domain decomposition method has been developed wherein phase space is broken into a relatively few nodes, inside each of which a spectral collocation method is used to compute derivatives. The time stepping is accomplished by an explicit scheme that is second order accurate in time overall, and provides exact conservation of particles and energy, independent of time step size or collocation order. It further ensures that the error in momentum conservation is independent of the number of interpolation points used--it only depends on the time step size. Spectral methods for hyperbolic problems are known to be sensitive to non-physical (non-characteristic) boundary conditions. Some care must therefore be taken in coupling the phase space sub-domains together. Two methods have been examined, both of which use the single particle trajectories to define upwind points from which subdomain boundary data must come.
- OSTI ID:
- 63089
- Report Number(s):
- CONF-940604-; ISBN 0-7803-2006-9; TRN: IM9527%%140
- Resource Relation:
- Conference: 1994 Institute of Electrical and Electronic Engineers (IEEE) international conference on plasma science, Santa Fe, NM (United States), 6-8 Jun 1994; Other Information: PBD: 1994; Related Information: Is Part Of 1994 IEEE international conference on plasma science; PB: 252 p.
- Country of Publication:
- United States
- Language:
- English
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