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5 fine grid vectors are needed in our implementation, which requires even less memory than CG. For the interested reader, an iteration count comparison between our multigrid method and PCG can be found in the original technical report written by the authors [Baranoski et al. 2002]. 4 Velocity and Position Update. The electric field Ei, j is defined on the Eulerian grid whose value is given by numerical differentiation of φi, j . However, electron beams are located on the Lagrangian grid, which, in general, does not overlap with the Eulerian.

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 [1968]. 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.

Comput. Graph. For. 22, 1, 1–7. WARREN, J. AND SCHAEFER, S. 2003. A factored approach to subdivision surfaces. Submitted to Comput. Graph. Applicat. WARREN, J. AND WEIMER, H. 2001. Subdivision Methods for Geometric Design. Morgan Kaufmann. ZORIN, D. 2000. Smoothness of subdivision on irregular meshes. Construt. Approx. 16, 3, 359–397. ¨ ZORIN, D. AND SCHRODER , P. 2001. A unified framework for primal/dual quadrilateral subdivision schemes. Comput. Aided Geomet. Design 18, 5, 429–454. Received September 2003; revised May 2004; accepted August 2004 ACM Transactions on Graphics, Vol.

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ACM Transactions on Graphics (January) by Association for Computing Machinery

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