Tag Archives: Computational Geometry

PSI: Constructing ad-hoc Simplices to Interpolate High-Dimensional Unstructured Data [IMA]

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http://arxiv.org/abs/2109.13926


Interpolating unstructured data using barycentric coordinates becomes infeasible at high dimensions due to the prohibitive memory requirements of building a Delaunay triangulation. We present a new algorithm to construct ad-hoc simplices that are empirically guaranteed to contain the target coordinates, based on a nearest neighbor heuristic and an iterative dimensionality reduction through projection. We use these simplices to interpolate the astrophysical cooling function $\Lambda$ and show that this new approach clearly outperforms our previous implementation at high dimensions.

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S. Lüders and K. Dolag
Thu, 30 Sep 21
51/82

Comments: 4 pages, 2 figures

The Cosmic Spiderweb and General Origami Tessellation Design [CEA]

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http://arxiv.org/abs/1809.00015


The cosmic web (the arrangement of matter in the universe), spider’s webs, and origami tessellations are linked by their geometry (specifically, of sectional-Voronoi tessellations). This motivates origami and textile artistic representations of the cosmic web. It also relates to the scientific insights origami can bring to the cosmic web; we show results of some cosmological computer simulations, with some origami-tessellation properties. We also adapt software developed for cosmic-web research to provide an interactive tool for general origami-tessellation design.

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M. Neyrinck
Wed, 5 Sep 18
56/133

Comments: Accepted to Origami$^7$, proceedings of 7OSME, the 7th meeting of Origami, Science, Mathematics and Education, Oxford, Sep 2018. Software at this https URL

ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation [CL]

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http://arxiv.org/abs/1509.07720


Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\’e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

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T. Sousbie and S. Colombi
Mon, 28 Sep 15
57/67

Comments: Code and illustration movies available at: this http URL – Article submitted to Journal of Computational Physics