Meshless Solution of the Vlasov Equation Using a Low Discrepancy Sequence

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A good method for solving the nonlinear Vlasov equation is the semi-Lagrangian algorithm, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. At each time step, orbits are followed backward from grid points. Since this method is expensive with phase space dimension D > 2, we seek a more efficient discretization of the density. Taking a cue from the theory of numerical quadrature in high dimensions, we explore the idea of replacing the grid by scattered data sites from a low-discrepancy (quasirandom) sequence. We hope to see a ... continued below

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3 pages

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Warnock, R.L.; /SLAC; Ellison, J.A.; Heinemann, K.; Zhang, G.Q. & U., /New Mexico January 28, 2009.

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A good method for solving the nonlinear Vlasov equation is the semi-Lagrangian algorithm, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. At each time step, orbits are followed backward from grid points. Since this method is expensive with phase space dimension D > 2, we seek a more efficient discretization of the density. Taking a cue from the theory of numerical quadrature in high dimensions, we explore the idea of replacing the grid by scattered data sites from a low-discrepancy (quasirandom) sequence. We hope to see a reduction in the required number of sites, especially for D > 2. In our first implementation we follow forward orbits rather than backward, and work only with D = 2. We are able to reduce the number of sites by a factor of 8, at least for a limited time of integration. A much bigger reduction is expected in higher dimensions.

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3 pages

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  • Journal Name: Conf.Proc.C0806233:tupp109,2008; Conference: EPAC'08, 11th European Particle Accelerator Conference, 23-27 June 2008, Genoa, Italy

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  • Report No.: SLAC-PUB-13519
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 946712
  • Archival Resource Key: ark:/67531/metadc894237

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  • January 28, 2009

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 29, 2016, 8 p.m.

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Warnock, R.L.; /SLAC; Ellison, J.A.; Heinemann, K.; Zhang, G.Q. & U., /New Mexico. Meshless Solution of the Vlasov Equation Using a Low Discrepancy Sequence, article, January 28, 2009; United States. (digital.library.unt.edu/ark:/67531/metadc894237/: accessed September 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.