5,033 research outputs found
PyCOOL - a Cosmological Object-Oriented Lattice code written in Python
There are a number of different phenomena in the early universe that have to
be studied numerically with lattice simulations. This paper presents a graphics
processing unit (GPU) accelerated Python program called PyCOOL that solves the
evolution of scalar fields in a lattice with very precise symplectic
integrators. The program has been written with the intention to hit a sweet
spot of speed, accuracy and user friendliness. This has been achieved by using
the Python language with the PyCUDA interface to make a program that is easy to
adapt to different scalar field models. In this paper we derive the symplectic
dynamics that govern the evolution of the system and then present the
implementation of the program in Python and PyCUDA. The functionality of the
program is tested in a chaotic inflation preheating model, a single field
oscillon case and in a supersymmetric curvaton model which leads to Q-ball
production. We have also compared the performance of a consumer graphics card
to a professional Tesla compute card in these simulations. We find that the
program is not only accurate but also very fast. To further increase the
usefulness of the program we have equipped it with numerous post-processing
functions that provide useful information about the cosmological model. These
include various spectra and statistics of the fields. The program can be
additionally used to calculate the generated curvature perturbation. The
program is publicly available under GNU General Public License at
https://github.com/jtksai/PyCOOL . Some additional information can be found
from http://www.physics.utu.fi/tiedostot/theory/particlecosmology/pycool/ .Comment: 23 pages, 12 figures; some typos correcte
Space-Time Transfinite Interpolation of Volumetric Material Properties
The paper presents a novel technique based on extension of a general mathematical method of transfinite interpolation to solve an actual problem in the context of a heterogeneous volume modelling area. It deals with time-dependent changes to the volumetric material properties (material density, colour and others) as a transformation of the volumetric material distributions in space-time accompanying geometric shape transformations such as metamorphosis. The main idea is to represent the geometry of both objects by scalar fields with distance properties, to establish in a higher-dimensional space a time gap during which the geometric transformation takes place, and to use these scalar fields to apply the new space-time transfinite interpolation to volumetric material attributes within this time gap. The proposed solution is analytical in its nature, does not require heavy numerical computations and can be used in real-time applications. Applications of this technique also include texturing and displacement mapping of time-variant surfaces, and parametric design of volumetric microstructures
Geometry-Driven Detection, Tracking and Visual Analysis of Viscous and Gravitational Fingers
Viscous and gravitational flow instabilities cause a displacement front to
break up into finger-like fluids. The detection and evolutionary analysis of
these fingering instabilities are critical in multiple scientific disciplines
such as fluid mechanics and hydrogeology. However, previous detection methods
of the viscous and gravitational fingers are based on density thresholding,
which provides limited geometric information of the fingers. The geometric
structures of fingers and their evolution are important yet little studied in
the literature. In this work, we explore the geometric detection and evolution
of the fingers in detail to elucidate the dynamics of the instability. We
propose a ridge voxel detection method to guide the extraction of finger cores
from three-dimensional (3D) scalar fields. After skeletonizing finger cores
into skeletons, we design a spanning tree based approach to capture how fingers
branch spatially from the finger skeletons. Finally, we devise a novel
geometric-glyph augmented tracking graph to study how the fingers and their
branches grow, merge, and split over time. Feedback from earth scientists
demonstrates the usefulness of our approach to performing spatio-temporal
geometric analyses of fingers.Comment: Published at IEEE Transactions on Visualization and Computer Graphic
Dynamical Optimal Transport on Discrete Surfaces
We propose a technique for interpolating between probability distributions on
discrete surfaces, based on the theory of optimal transport. Unlike previous
attempts that use linear programming, our method is based on a dynamical
formulation of quadratic optimal transport proposed for flat domains by Benamou
and Brenier [2000], adapted to discrete surfaces. Our structure-preserving
construction yields a Riemannian metric on the (finite-dimensional) space of
probability distributions on a discrete surface, which translates the so-called
Otto calculus to discrete language. From a practical perspective, our technique
provides a smooth interpolation between distributions on discrete surfaces with
less diffusion than state-of-the-art algorithms involving entropic
regularization. Beyond interpolation, we show how our discrete notion of
optimal transport extends to other tasks, such as distribution-valued Dirichlet
problems and time integration of gradient flows
Lifted Wasserstein Matcher for Fast and Robust Topology Tracking
This paper presents a robust and efficient method for tracking topological
features in time-varying scalar data. Structures are tracked based on the
optimal matching between persistence diagrams with respect to the Wasserstein
metric. This fundamentally relies on solving the assignment problem, a special
case of optimal transport, for all consecutive timesteps. Our approach relies
on two main contributions. First, we revisit the seminal assignment algorithm
by Kuhn and Munkres which we specifically adapt to the problem of matching
persistence diagrams in an efficient way. Second, we propose an extension of
the Wasserstein metric that significantly improves the geometrical stability of
the matching of domain-embedded persistence pairs. We show that this
geometrical lifting has the additional positive side-effect of improving the
assignment matrix sparsity and therefore computing time. The global framework
implements a coarse-grained parallelism by computing persistence diagrams and
finding optimal matchings in parallel for every couple of consecutive
timesteps. Critical trajectories are constructed by associating successively
matched persistence pairs over time. Merging and splitting events are detected
with a geometrical threshold in a post-processing stage. Extensive experiments
on real-life datasets show that our matching approach is an order of magnitude
faster than the seminal Munkres algorithm. Moreover, compared to a modern
approximation method, our method provides competitive runtimes while yielding
exact results. We demonstrate the utility of our global framework by extracting
critical point trajectories from various simulated time-varying datasets and
compare it to the existing methods based on associated overlaps of volumes.
Robustness to noise and temporal resolution downsampling is empirically
demonstrated
Multiphysics simulations of collisionless plasmas
Collisionless plasmas, mostly present in astrophysical and space
environments, often require a kinetic treatment as given by the Vlasov
equation. Unfortunately, the six-dimensional Vlasov equation can only be solved
on very small parts of the considered spatial domain. However, in some cases,
e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a
localized domain and solve the remaining domain by appropriate fluid models. In
this paper, we describe a hierarchical treatment of collisionless plasmas in
the following way. On the finest level of description, the Vlasov equation is
solved both for ions and electrons. The next courser description treats
electrons with a 10-moment fluid model incorporating a simplified treatment of
Landau damping. At the boundary between the electron kinetic and fluid region,
the central question is how the fluid moments influence the electron
distribution function. On the next coarser level of description the ions are
treated by an 10-moment fluid model as well. It may turn out that in some
spatial regions far away from the reconnection zone the temperature tensor in
the 10-moment description is nearly isotopic. In this case it is even possible
to switch to a 5-moment description. This change can be done separately for
ions and electrons. To test this multiphysics approach, we apply this full
physics-adaptive simulations to the Geospace Environmental Modeling (GEM)
challenge of magnetic reconnection.Comment: 13 pages, 5 figure
Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
Modern graphics hardware is designed for highly parallel numerical tasks and
promises significant cost and performance benefits for many scientific
applications. One such application is lattice quantum chromodyamics (lattice
QCD), where the main computational challenge is to efficiently solve the
discretized Dirac equation in the presence of an SU(3) gauge field. Using
NVIDIA's CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector
product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double,
single and half precision respectively on NVIDIA's GeForce GTX 280 GPU. We have
developed a new mixed precision approach for Krylov solvers using reliable
updates which allows for full double precision accuracy while using only single
or half precision arithmetic for the bulk of the computation. The resulting
BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations
until convergence, perform better than the usual defect-correction approach for
mixed precision.Comment: 30 pages, 7 figure
GPU driven finite difference WENO scheme for real time solution of the shallow water equations
The shallow water equations are applicable to many common engineering problems involving modelling of waves dominated by motions in the horizontal directions (e.g. tsunami propagation, dam breaks). As such events pose substantial economic costs, as well as potential loss of life, accurate real-time simulation and visualization methods are of great importance. For this purpose, we propose a new finite difference scheme for the 2D shallow water equations that is specifically formulated to take advantage of modern GPUs. The new scheme is based on the so-called Picard integral formulation of conservation laws combined with Weighted Essentially Non-Oscillatory reconstruction. The emphasis of the work is on third order in space and second order in time solutions (in both single and double precision). Further, the scheme is well-balanced for bathymetry functions that are not surface piercing and can handle wetting and drying in a GPU-friendly manner without resorting to long and specific case-by-case procedures. We also present a fast single kernel GPU implementation with a novel boundary condition application technique that allows for simultaneous real-time visualization and single precision simulations even on large ( > 2000 × 2000) grids on consumer-level hardware - the full kernel source codes are also provided online at https://github.com/pparna/swe_pifweno3
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