75 research outputs found
A multidomain spectral method for solving elliptic equations
We present a new solver for coupled nonlinear elliptic partial differential
equations (PDEs). The solver is based on pseudo-spectral collocation with
domain decomposition and can handle one- to three-dimensional problems. It has
three distinct features. First, the combined problem of solving the PDE,
satisfying the boundary conditions, and matching between different subdomains
is cast into one set of equations readily accessible to standard linear and
nonlinear solvers. Second, touching as well as overlapping subdomains are
supported; both rectangular blocks with Chebyshev basis functions as well as
spherical shells with an expansion in spherical harmonics are implemented.
Third, the code is very flexible: The domain decomposition as well as the
distribution of collocation points in each domain can be chosen at run time,
and the solver is easily adaptable to new PDEs. The code has been used to solve
the equations of the initial value problem of general relativity and should be
useful in many other problems. We compare the new method to finite difference
codes and find it superior in both runtime and accuracy, at least for the
smooth problems considered here.Comment: 31 pages, 8 figure
A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements
A parallel fast direct solver for rank-compressible block tridiagonal linear
systems is presented. Algorithmic synergies between Cyclic Reduction and
Hierarchical matrix arithmetic operations result in a solver with arithmetic complexity and memory footprint. We provide a
baseline for performance and applicability by comparing with well known
implementations of the -LU factorization and algebraic multigrid
with a parallel implementation that leverages the concurrency features of the
method. Numerical experiments reveal that this method is comparable with other
fast direct solvers based on Hierarchical Matrices such as -LU and
that it can tackle problems where algebraic multigrid fails to converge
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
Revisiting Event Horizon Finders
Event horizons are the defining physical features of black hole spacetimes,
and are of considerable interest in studying black hole dynamics. Here, we
reconsider three techniques to localise event horizons in numerical spacetimes:
integrating geodesics, integrating a surface, and integrating a level-set of
surfaces over a volume. We implement the first two techniques and find that
straightforward integration of geodesics backward in time to be most robust. We
find that the exponential rate of approach of a null surface towards the event
horizon of a spinning black hole equals the surface gravity of the black hole.
In head-on mergers we are able to track quasi-normal ringing of the merged
black hole through seven oscillations, covering a dynamic range of about 10^5.
Both at late times (when the final black hole has settled down) and at early
times (before the merger), the apparent horizon is found to be an excellent
approximation of the event horizon. In the head-on binary black hole merger,
only {\em some} of the future null generators of the horizon are found to start
from past null infinity; the others approach the event horizons of the
individual black holes at times far before merger.Comment: 30 pages, 15 figures, revision
A comparison of 3D particle, fluid and hybrid simulations for negative streamers
In the high field region at the head of a discharge streamer, the electron
energy distribution develops a long tail. In negative streamers, these
electrons can run away and contribute to energetic processes such as
terrestrial gamma-ray and electron flashes. Moreover, electron density
fluctuations can accelerate streamer branching. To track energies and locations
of single electrons in relevant regions, we have developed a 3D hybrid model
that couples a particle model in the region of high fields and low electron
densities with a fluid model in the rest of the domain. Here we validate our 3D
hybrid model on a 3D (super-)particle model for negative streamers in
overvolted gaps, and we show that it almost reaches the computational
efficiency of a 3D fluid model. We also show that the extended fluid model
approximates the particle and the hybrid model well until stochastic
fluctuations become important, while the classical fluid model underestimates
velocities and ionization densities. We compare density fluctuations and the
onset of branching between the models, and we compare the front velocities with
an analytical approximation
Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes
We report the first theoretical study of hydroxyl vacancies in
aluminosilicate and aluminogermanate single-walled metal-oxide nanotubes. The
defects are modeled on both sides of the tube walls and lead to occupied and
empty states in the band gap which are highly localized both in energy and in
real space. We find different magnetization states depending on both the
chemical composition and the specific side with respect to the tube cavity. The
defect-induced perturbations to the pristine electronic structure are related
to the electrostatic polarization across the tube walls and the ensuing change
in Br{\o}nsted acid-base reactivity. Finally, the capacity to counterbalance
local charge accumulations, a characteristic feature of these systems, is
discussed in view of their potential application as insulating coatings for
one-dimensional conducting nanodevices.Comment: manuscript: 4 pages, 4 figure
A computational study of the effect of windscreen shape and flow resistivity on turbulent wind noise reduction
This is the published version. Copyright 2011 Acoustical Society of AmericaIn this paper, numerical simulations are used to study the turbulentwind noise reduction effect of microphone windscreens with varying shapes and flow resistivities. Typical windscreen shapes consisting of circular, elliptical, and rectangular cylinders are investigated. A turbulent environment is generated by placing a solid circular cylinder upstream of the microphone. An immersed-boundary method with a fifth-order weighted essentially non-oscillatory scheme is implemented to enhance the simulation accuracy for high-Reynolds number flow around the solid cylinder as well as at the interface between the open air and the porous material comprising the windscreen. The Navier–Stokes equations for incompressible flow are solved in the open air. For the flow inside the porous material, a modified form of the Zwikker–Kosten equation is solved. The results show that, on average, the circular and horizontal ellipse windscreens have similar overall wind noise reduction performance, while the horizontal ellipse windscreen with medium flow resistivity provides the most effective wind noise reduction among all the considered cases. The vertical ellipse windscreen with high flow resistivity, in particular, increases the wind noise because of increased self-generation of turbulence
DWM07 global empirical model of upper thermospheric storm-induced disturbance winds
We present a global empirical disturbance wind model (DWM07) that represents average geospace-storm-induced perturbations of upper thermospheric (200-600 km altitude) neutral winds. DWM07 depends on the following three parameters: magnetic latitude, magnetic local time, and the 3-h Kp geomagnetic activity index. The latitude and local time dependences are represented by vector spherical harmonic functions ( up to degree 10 in latitude and order 3 in local time), and the Kp dependence is represented by quadratic B-splines. DWM07 is the storm time thermospheric component of the new Horizontal Wind Model (HWM07), which is described in a companion paper. DWM07 is based on data from the Wind Imaging Interferometer on board the Upper Atmosphere Research Satellite, the Wind and Temperature Spectrometer on board Dynamics Explorer 2, and seven ground-based Fabry-Perot interferometers. The perturbation winds derived from the three data sets are in good mutual agreement under most conditions, and the model captures most of the climatological variations evident in the data
Dynamics of the speed changes control device with differential gear and closed-loop hydraulic system through the sun gear
Розглянуті та досліджені динамічні процеси у пристрої для керування змінамишвидкості з зубчастою диференціальноюпередачеюі замкнутою гідросистемою через сонячне зубчасте колесо, коли ведучою ланкою є водило, а веденою – епіцикл. Розроблена математична модель та розв’язані рівняння динаміки таких пристроїв залежно від умов їх роботи. Отримані результати є підґрунтям для подальшого комп’ютерного моделювання та проведення кількісного аналізу з метоюоцінки роботи гідромеханічного приводу та вибору необхідної замкнутої гідросистеми для керування змінамишвидкості.Dynamic processes in speed changes control device with differential gear transmission and closed loop hydraulic system have been considered and investigated for the case when the sun gear is a control link, carrier is a driving link and the ring gear is driven. The motion of the system has been modeled in a formalized form using the Lagrange’s equation of the second kind. For this purpose, the expression for the energy of such speed changes control device has been derived. Then, based on the Lagrange’s equation of second kind, a system of differential equations for the motion of the links has been obtained and solved. The solution of the system of equations of dynamics of such devices is the basis for further computer simulation and quantitative analysis in order to evaluate the operation of such devices and to select the necessary closed loop hydraulic system to control changes in speed, when the load changes periodically over a long time; or when the magnitude of the shock load after a sharp increase remains unchanged for either a long time or a small time; or the actuator stops immediately because of a significant overload
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