885 research outputs found
Semi-regular Dubuc-Deslauriers wavelet tight frames
In this paper, we construct wavelet tight frames with n vanishing moments for
Dubuc-Deslauriers 2npoint semi-regular interpolatory subdivision schemes. Our
motivation for this construction is its practical use for further regularity
analysis of wide classes of semi-regular subdivision. Our constructive tools
are local eigenvalue convergence analysis for semi-regular Dubuc-Deslauriers
subdivision, the Unitary Extension Principle and the generalization of the
Oblique Extension Principle to the irregular setting by Chui, He and
St\"ockler. This group of authors derives suitable approximation of the inverse
Gramian for irregular Bspline subdivision. Our main contribution is the
derivation of the appropriate approximation of the inverse Gramian for the
semi-regular Dubuc-Deslauriers scaling functions ensuring n vanishing moments
of the corresponding framelets
A "metric" semi-Lagrangian Vlasov-Poisson solver
We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements
of metric to follow locally the flow and its deformation, allowing one to find
quickly and accurately the initial phase-space position of any test
particle , by expanding at second order the geometry of the motion in the
vicinity of the closest element. It is thus possible to reconstruct accurately
the phase-space distribution function at any time and position by
proper interpolation of initial conditions, following Liouville theorem. When
distorsion of the elements of metric becomes too large, it is necessary to
create new initial conditions along with isotropic elements and repeat the
procedure again until next resampling. To speed up the process, interpolation
of the phase-space distribution is performed at second order during the
transport phase, while third order splines are used at the moments of
remapping. We also show how to compute accurately the region of influence of
each element of metric with the proper percolation scheme. The algorithm is
tested here in the framework of one-dimensional gravitational dynamics but is
implemented in such a way that it can be extended easily to four or
six-dimensional phase-space. It can also be trivially generalised to plasmas.Comment: 32 pages, 14 figures, accepted for publication in Journal of Plasma
Physics, Special issue: The Vlasov equation, from space to laboratory plasma
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