相关论文: Using 3D Voronoi grids in radiative transfer simul…

We present RAYTHEIA, a high-performance reverse ray-tracing algorithm designed to efficiently solve three-dimensional direction-dependent equations in astronomical simulations. The algorithm uses a dual-grid framework in which the native…

We extend the Geometric Refinement Transform (GRT) by introducing centroidal Voronoi tessellations (CVTs) into the refinement process, enhancing symmetry, reconstruction accuracy, and numerical stability. By applying Lloyds algorithm at…

Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…

Volumetric shape representations have become ubiquitous in multi-view reconstruction tasks. They often build on regular voxel grids as discrete representations of 3D shape functions, such as SDF or radiance fields, either as the full shape…

We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures which include dense regions of high optical depth like in dense molecular clouds, circumstellar disks, envelopes of evolved…

Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…

A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in {\it ab-initio} electronic-structure calculations. We combine a weighted Voronoi tessellation with…

Unstructured Voronoi mesh simulations offer many advantages for simulating self-gravitating gas dynamics on galactic scales. Adaptive mesh refinement (AMR) can be a powerful tool for simulating the details of star cluster formation and gas…

Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…

We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…

The development of radiation hydrodynamical methods that are able to follow gas dynamics and radiative transfer self-consistently is key to the solution of many problems in numerical astrophysics. Such fluid flows are highly complex, rarely…

A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…

Overset methods are commonly employed to enable the effective simulation of problems involving complex geometries and moving objects such as rotorcraft. This paper presents a novel overset domain connectivity algorithm based upon the direct…

Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…

The manuscript describes fast and scalable architectures and associated algorithms for computing convolutions and cross-correlations. The basic idea is to map 2D convolutions and cross-correlations to a collection of 1D convolutions and…

In this work we investigate numerically the reconstruction approach proposed in Goncharov, Novikov, 2016, for weighted ray transforms (weighted Radon transforms along oriented straight lines) in 3D. In particular, the approach is based on a…

The broadband line-by-line analysis of radiative transfer in the atmosphere is extremely demanding with regard to computational resources. As a remedy, we present here the calculation of uniform error bounds for approximating the classical…

We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all…

3D detailed radiative transfer is computationally taxing, since the solution of the radiative transfer equation involves traversing the six dimensional phase space of the 3D domain. With modern supercomputers the hardware available for…

Adaptive binning is a crucial step in the analysis of large astronomical datasets, such as those from integral-field spectroscopy, to ensure a sufficient signal-to-noise ratio (S/N) for reliable model fitting. However, the widely used…