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Extra info for ACM Transactions on Graphics (January)
It also worth noting that Weimer and Warren  used a full multigrid approach for fluid flow which is appropriate for solving nonlinear equations. In our implementation, we used a V-cycle multigrid which is more appropriate for solving linear equations such as those arising in our simulations. ACM Transactions on Graphics, Vol. 24, No. 1, January 2005. 40 • G. V. G. Baranoski et al. Fig. 1. Satellite snapshot of an auroral oval around the Earth’s north magnetic pole. a) Viewed from the satellite position and b) viewed from a position normal to the Earth’s north pole.
These regions are called the auroral ovals. Figure 1 shows a satellite snapshot of an aurora oval around the Earth’s north magnetic pole. The shape of an aurora is determined by the energy and density of the electrons entering the atmosphere as well as the local variations in the Earth’s magnetic and electric fields. The most common aurorae can be thought of as “curtains” of light emissions from “sheets” of falling electrons, which move along the Earth’s magnetic field. As the electrons travel down along the Earth’s magnetic field lines, they suffer many random deflections which are caused by collisions with atoms of atmospheric gases such as oxygen and nitrogen.
2003]. This algorithm takes into account the spatial inhomogeneity of auroral electrons and their initial energy to compute the deflection points and the displacements of an electron beam along the magnetic field lines. ACM Transactions on Graphics, Vol. 24, No. 1, January 2005. Simulating the Dynamics of Auroral Phenomena • 49 Fig. 8. Sketch showing that the apparent surface brightness of an auroral display is proportional to the number of emissions along the line of sight represented by the vector s.
ACM Transactions on Graphics (January) by Association for Computing Machinery