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We have developed a new parallel tree method which will be called the forest method hereafter. This new method uses the sectional Voronoi tessellation (SVT) for the domain decomposition. The SVT decomposes a whole space into polyhedra and allows their flat borders to move by assigning different weights. The forest method determines these weights based on the load balancing among processors by means of the over-load diffusion (OLD). Moreover, since all the borders are flat, before receiving the data from other processors, each processor can collect enough data to calculate the gravity force with precision. Both the SVT and the OLD are coded in a highly vectorizable manner to accommodate on vector parallel processors. The parallel code based on the forest method with the Message Passing Interface is run on various platforms so that a wide portability is guaranteed. Extensive calculations with 15 processors of Fujitsu VPP300/16R indicate that the code can calculate the gravity force exerted on 10^5 particles in each second for some ideal dark halo. This code is found to enable an N-body simulation with 10^7 or more particles for a wide dynamic range and is therefore a very powerful tool for the study of galaxy formation and large-scale structure in the universe.
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several serial Vo
The typical cell of a Voronoi tessellation generated by $n+1$ uniformly distributed random points on the $d$-dimensional unit sphere $mathbb S^d$ is studied. Its $f$-vector is identified in distribution with the $f$-vector of a beta polytope generate
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting scheme on
We have developed a highly-tuned software library that accelerates the calculation of quadrupole terms in the Barnes-Hut tree code by use of a SIMD instruction set on the x86 architecture, Advanced Vector eXtensions 2 (AVX2). Our code is implemented
A homogeneous Poisson-Voronoi tessellation of intensity $gamma$ is observed in a convex body $W$. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and in