5,242 research outputs found
Solution of partial differential equations on vector and parallel computers
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed
Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems
We present the mixed Galerkin discretization of distributed parameter
port-Hamiltonian systems. On the prototypical example of hyperbolic systems of
two conservation laws in arbitrary spatial dimension, we derive the main
contributions: (i) A weak formulation of the underlying geometric
(Stokes-Dirac) structure with a segmented boundary according to the causality
of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac
structure by a finite-dimensional Dirac structure is realized using a mixed
Galerkin approach and power-preserving linear maps, which define minimal
discrete power variables. (iii) With a consistent approximation of the
Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models.
By the degrees of freedom in the power-preserving maps, the resulting family of
structure-preserving schemes allows for trade-offs between centered
approximations and upwinding. We illustrate the method on the example of
Whitney finite elements on a 2D simplicial triangulation and compare the
eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the
CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0
Direct Integration of the Collisionless Boltzmann Equation in Six-dimensional Phase Space: Self-gravitating Systems
We present a scheme for numerical simulations of collisionless
self-gravitating systems which directly integrates the Vlasov--Poisson
equations in six-dimensional phase space. By the results from a suite of
large-scale numerical simulations, we demonstrate that the present scheme can
simulate collisionless self-gravitating systems properly. The integration
scheme is based on the positive flux conservation method recently developed in
plasma physics. We test the accuracy of our code by performing several test
calculations including the stability of King spheres, the gravitational
instability and the Landau damping. We show that the mass and the energy are
accurately conserved for all the test cases we study. The results are in good
agreement with linear theory predictions and/or analytic solutions. The
distribution function keeps the property of positivity and remains
non-oscillatory. The largest simulations are run on 64^6 grids. The computation
speed scales well with the number of processors, and thus our code performs
efficiently on massively parallel supercomputers.Comment: 35 pages, 19 figures. Submitted to the Astrophysical Journa
Layered architecture for quantum computing
We develop a layered quantum computer architecture, which is a systematic
framework for tackling the individual challenges of developing a quantum
computer while constructing a cohesive device design. We discuss many of the
prominent techniques for implementing circuit-model quantum computing and
introduce several new methods, with an emphasis on employing surface code
quantum error correction. In doing so, we propose a new quantum computer
architecture based on optical control of quantum dots. The timescales of
physical hardware operations and logical, error-corrected quantum gates differ
by several orders of magnitude. By dividing functionality into layers, we can
design and analyze subsystems independently, demonstrating the value of our
layered architectural approach. Using this concrete hardware platform, we
provide resource analysis for executing fault-tolerant quantum algorithms for
integer factoring and quantum simulation, finding that the quantum dot
architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
VLSI Design
This book provides some recent advances in design nanometer VLSI chips. The selected topics try to present some open problems and challenges with important topics ranging from design tools, new post-silicon devices, GPU-based parallel computing, emerging 3D integration, and antenna design. The book consists of two parts, with chapters such as: VLSI design for multi-sensor smart systems on a chip, Three-dimensional integrated circuits design for thousand-core processors, Parallel symbolic analysis of large analog circuits on GPU platforms, Algorithms for CAD tools VLSI design, A multilevel memetic algorithm for large SAT-encoded problems, etc
Google matrix of the citation network of Physical Review
We study the statistical properties of spectrum and eigenstates of the Google
matrix of the citation network of Physical Review for the period 1893 - 2009.
The main fraction of complex eigenvalues with largest modulus is determined
numerically by different methods based on high precision computations with up
to binary digits that allows to resolve hard numerical problems for
small eigenvalues. The nearly nilpotent matrix structure allows to obtain a
semi-analytical computation of eigenvalues. We find that the spectrum is
characterized by the fractal Weyl law with a fractal dimension .
It is found that the majority of eigenvectors are located in a localized phase.
The statistical distribution of articles in the PageRank-CheiRank plane is
established providing a better understanding of information flows on the
network. The concept of ImpactRank is proposed to determine an influence domain
of a given article. We also discuss the properties of random matrix models of
Perron-Frobenius operators.Comment: 25 pages. 17 figures. Published in Phys. Rev.
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