An influence matrix particle-particle particle-mesh algorithm with exact particle-particle correction. (English) Zbl 1063.78026
Well-established methods for the solution of the \(N\)-body problem occurring in chemistry, fluid dynamics and astrophysics are the particle-particle (PP) method, the particle-mesh (PM) method and the particle-particle particle-mesh (PPPM) method. PPPM algorithms are applied for particle systems with non-smooth density fields where the exact force field will contain sub-grid scales not resolved by PM algorithms but by an explicit PP correction. In this paper the author gives a new approach to the PPPM algorithm. The goal of the presented method is the application of an accurate influence matrix technique. It allows specific cancellations of the anisotropic sub-grid scales not using Fourier space. Hence the application of other fast field solvers than FFT based algorithms is possible. The proposed influence matrix PPPM algorithm improves the overall accuracy of the method compared to other approaches at the same computational costs.
Reviewer: Ursula van Rienen (Rostock)
MSC:
| 78M25 | Numerical methods in optics (MSC2010) |
| 78A30 | Electro- and magnetostatics |
Keywords:
particle-particle particle-mesh algorithm; particle methods; N-body problem; Coulomb interaction; electrostatic interaction; influence matrixReferences:
| [1] | Allen, M. P.; Tildesley, D. J., Computer Simulation of Liquids (1987), Clarendon Press Oxford: Clarendon Press Oxford Oxford · Zbl 0703.68099 |
| [2] | Anderson, C. R., A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys., 62, 1, 111-123 (1986) · Zbl 0575.76031 |
| [3] | Barnes, J.; Hut, P., A hierarchical \(O(N\) log \(N)\) force-calculation algorithm, Nature, 324, 4, 446-449 (1986) |
| [4] | Beckers, J. V.L.; Lowe, C. P.; De Leeuw, S. W., An iterative PPPM method for simulating Coulombic systems on distributed memory parallel computers, Mol. Sim., 20, 6, 369-383 (1998) · Zbl 0961.81500 |
| [5] | Cottet, G.-H.; Koumoutsakos, P., Vortex Methods—Theory and Practice (2000), Cambridge University Press: Cambridge University Press New York |
| [6] | Eastwood, J. W.; Brownrigg, D. R.K., Remarks on the solution of Poisson’s equation for isolated systems, J. Comput. Phys., 32, 24-38 (1979) · Zbl 0407.65050 |
| [7] | Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J. Comput. Phys., 73, 325-348 (1987) · Zbl 0629.65005 |
| [8] | Hockney, R. W., The potential calculation and some applications, Methods Comput. Phys., 9, 136-210 (1970) |
| [9] | Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1988), IOP · Zbl 0662.76002 |
| [10] | Monaghan, J. J., Particle methods for hydrodynamics, Comp. Phys. Repts., 3, 71-123 (1985) |
| [11] | Walther, J. H.; Morgenthal, G., An immersed interface method for the vortex-in-cell algorithm, J. Turbul., 3, 1-9 (2002) · Zbl 1082.76587 |
| [12] | Pereyra, V., On improving the approximate solution of a functional equation by deferred corrections, Numer. Math., 8, 376-391 (1966) · Zbl 0173.18103 |
| [13] | Green Mountain Software, Crayfishpak, User’s guide, P.O. Box 86124, Madeira Beach, Florida 33738, USA, 1990; Green Mountain Software, Crayfishpak, User’s guide, P.O. Box 86124, Madeira Beach, Florida 33738, USA, 1990 |
| [14] | Theuns, T., Parallel P3M with exact calculation of short range forces, Comp. Phys. Commun., 78, 238-246 (1994) |
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