Using 3D Voronoi grids in radiative transfer simulations

Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular, however several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. Such an unstructured grid poses new challenges in laying down the rays (straight paths) needed in RT codes. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement such a grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through the Voronoi grid with those generated by an octree grid for two synthetic models, and we perform the well-known Pascucci RT benchmark using the Voronoi grid. The presented algorithm produces correct results for our test models. Shooting photon packages through the geometrically much more complex 3D Voronoi grid is only about three times slower than the equivalent process in an octree grid with the same number of cells, while in fact the total number of Voronoi grid cells may be lower for an equally good representation of the density field. We conclude that the benefits of using a Voronoi grid in RT simulation codes will often outweigh the somewhat slower performance.Comment: 9 pages, 7 figures, accepted by A

Cosmological Simulations Using Special Purpose Computers: Implementing P3M on Grape

An adaptation of the Particle-Particle/Particle-Mesh (P3M) code to the special purpose hardware GRAPE is presented. The short range force is calculated by a four chip GRAPE-3A board, while the rest of the calculation is performed on a Sun Sparc 10/51 workstation. The limited precision of the GRAPE hardware and algorithm constraints introduce stochastic errors of the order of a few percent in the gravitational forces. Tests of this new P3MG3A code show that it is a robust tool for cosmological simulations. The code currently achieves a peak efficiency of one third the speed of the vectorized P3M code on a Cray C-90 and significant improvements are planned in the near future. Special purpose computers like GRAPE are therefore an attractive alternative to supercomputers for numerical cosmology.Comment: 9 pages (ApJS style); uuencoded compressed PostScript file (371 kb) Also available by anonymous 'ftp' to astro.Princeton.EDU [128.112.24.45] in: summers/grape/p3mg3a.ps (668 kb) and WWW at: http://astro.Princeton.EDU/~library/prep.html (as POPe-600) Send all comments, questions, requests, etc. to: [email protected]

Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods

Afivo is a framework for simulations with adaptive mesh refinement (AMR) on quadtree (2D) and octree (3D) grids. The framework comes with a geometric multigrid solver, shared-memory (OpenMP) parallelism and it supports output in Silo and VTK file formats. Afivo can be used to efficiently simulate AMR problems with up to about $10^{8}$ unknowns on desktops, workstations or single compute nodes. For larger problems, existing distributed-memory frameworks are better suited. The framework has no built-in functionality for specific physics applications, so users have to implement their own numerical methods. The included multigrid solver can be used to efficiently solve elliptic partial differential equations such as Poisson's equation. Afivo's design was kept simple, which in combination with the shared-memory parallelism facilitates modification and experimentation with AMR algorithms. The framework was already used to perform 3D simulations of streamer discharges, which required tens of millions of cells

Scalable and fast heterogeneous molecular simulation with predictive parallelization schemes

Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a permanent development of new simulation methods and optimization algorithms. In computational terms, those methods require parallelization schemes that make a productive use of computational resources for each simulation and from its genesis. Here, we introduce the heterogeneous domain decomposition approach which is a combination of an heterogeneity sensitive spatial domain decomposition with an \textit{a priori} rearrangement of subdomain-walls. Within this approach, the theoretical modeling and scaling-laws for the force computation time are proposed and studied as a function of the number of particles and the spatial resolution ratio. We also show the new approach capabilities, by comparing it to both static domain decomposition algorithms and dynamic load balancing schemes. Specifically, two representative molecular systems have been simulated and compared to the heterogeneous domain decomposition proposed in this work. These two systems comprise an adaptive resolution simulation of a biomolecule solvated in water and a phase separated binary Lennard-Jones fluid.Comment: 14 pages, 12 figure