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Extra info for ACM Transactions on Graphics (January)
24, No. 1, January 2005. 46 • G. V. G. Baranoski et al. Fig. 5. A cross-section of an auroral stream, modeled by a strip of electron beams with periodic and Neuman boundary conditions, along the x-axis and y-axis, respectively. and Hockney . The perpendicular velocities and positions of the electron beams are advanced in time as follows: (1) (2) (3) (4) from the positions of the electron beams, a charge distribution (ρ) is derived; from the charge distribution, using Poisson Equation (7), the electrostatic potential is calculated; from the potential, the electric field ( E) acting on each electron beam is derived using Equation (6); Newton’s law of motion (Equation (2)), using the local electron field and the Earth’s magnetic field ( B) is then integrated resulting in a new position and velocity for each electron beam.
For the simulation of auroral dynamics, a fine grid is required to resolve the layer structure, especially when the formation of surges is simulated. Thus, an efficient linear solver is indispensable. Direct methods, such as banded Gaussian elimination (GE), can be used to exploit the banded structure of A. For matrices of size n × n, the complexity of banded GE is O(n2 ), which is still computationally impractical. Iterative methods, such as preconditioned conjugate gradient (PCG) with incomplete Cholesky factorization as preconditioner, have been successfully used in computer graphics for fluid simulations [Fedkiw et al.
However, in order to perform predictive simulations of the dynamics of plasma phenomena, one must account for their distinctive features. For example, turbulence dynamics in plasmas involve electromagnetic fields and a much larger number of relevant variables than for neutral fluids [Yoshizawa et al. 2001]. Furthermore, while the effects of global boundary conditions, such as wall boundaries, often play an important role in the growth of neutral fluid disturbances [Drazin and Reid 1981; Hinze 1975; Yoshizawa 1998], plasma turbulence is greatly affected by spatial inhomogeneities and plasma configurations.
ACM Transactions on Graphics (January) by Association for Computing Machinery