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arXiv · 1611.02757

Integer Lattice Dynamics for Vlasov-Poisson

Philip Mocz·Sauro Succi
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Abstract

We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N^4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.

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Philip Mocz, Sauro Succi. 2016-11-08. Integer Lattice Dynamics for Vlasov-Poisson. https://doi.org/10.1093/mnras%2Fstw2928

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