scholarly journals Optimization of Finite-Differencing Kernels for Numerical Relativity Applications

2018 ◽  
Author(s):  
Roberto Alfieri ◽  
Sebastiano Bernuzzi ◽  
Albino Perego ◽  
David Radice
Keyword(s):  
Shared Memory ◽  
Numerical Relativity ◽  
High Order ◽  
Optimization Strategy ◽  
Stencil Computations ◽  
Main Application ◽  
Finite Differencing

A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes.

A Multilevel Parallelization Framework for High-Order Stencil Computations

2009 ◽  
pp. 642-653 ◽  
Author(s):  
Hikmet Dursun ◽  
Ken-ichi Nomura ◽  
Liu Peng ◽  
Richard Seymour ◽  
Weiqiang Wang ◽  
...  
Keyword(s):  
High Order ◽  
Stencil Computations

scholarly journals Applied Mathematics of Space-time & Space+time: Problems in General Relativity and Cosmology

2021 ◽  
Author(s):  
◽  
Celine Cattoen
Keyword(s):  
Variational Formulation ◽  
Numerical Relativity ◽  
Cosmological Parameters ◽  
Spectral Element ◽  
Space Time ◽  
High Order ◽  
Einstein Equations ◽  
Element Discretization ◽  
Friedmann Equations ◽  
Hubble Flow

<p>Cosmography is the part of cosmology that proceeds by making minimal dynamic assumptions. That is, one does not assume the Friedmann equations (Einstein equations) unless and until absolutely necessary. On the other hand, cosmodynamics is the part of cosmology that relates the geometry to the density and pressure using the Friedmann equations. In both frameworks, we consider the amount of information and the nature of the constraints we can obtain from the Hubble flow in a FLRW universe. Indeed, the cosmological parameters contained in the Hubble relation between distance and redshift provide information on the behaviour of the universe (expansion, acceleration etc...). In the first framework, it is possible to concentrate more directly on the observational situation in a model-independent manner. We perform a number of inter-related cosmographic fits to supernova datasets, and pay particular attention to the extent to which the choice of distance scale and manner of representing the redshift scale affect the cosmological parameters. In the second framework, we use the class of w-parameter models which has become increasingly popular in the last decade. We explore the extent to which a constraint on the w-parameter leads to useful and non-trivial constraints on the Hubble flow in terms of cosmological parameters H(z), density p(z), density parameter O(z), distance scales d(z), and lookback time T(z). On another front, Numerical Relativity has experienced many breakthroughs since 2005, with full inspiral-merger-ringdown simulations now possible. One of the main goals is to provide very accurate templates of gravitational waves for ground-based and space-based interferometers. We explore the potential of a very recent and accurate numerical method, the Spectral Element Method (SEM), for Numerical Relativity, by treating a singular Schwarszchild black hole evolution as a test case. Spectral elements combine the theory of spectral and pseudo-spectral methods for high order polynomials and the variational formulation of finite elements and the associated geometric flexibility. We use the BSSN formulation of the Einstein equations with the method of the moving punctures. After applying the variational formulation to the BSSN system, we present several possible weak forms of this system and its spectral element discretization in space. We use a Runge-Kutta fourth order time discretization. The accuracy of high order methods can deteriorate in the presence of discontinuities or sharp gradients. We show that we can treat the element that contains the puncture with a filtering method to avoid artificial and spurious oscillations. These might form and propagate into the domain coming from discontinuous initial data from the BSSN system.</p>

scholarly journals Novel finite-differencing techniques for numerical relativity: application to black-hole excision

2003 ◽  
Vol 20 (20) ◽  
pp. L245-L251 ◽  
Author(s):  
Gioel Calabrese ◽  
Luis Lehner ◽  
David Neilsen ◽  
Jorge Pullin ◽  
Oscar Reula ◽  
...  
Keyword(s):  
Black Hole ◽  
Numerical Relativity ◽  
Finite Differencing

scholarly journals Compression of Extreme-Ultraviolet Ultrashort Pulses by Grating Configurations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Fabio Frassetto ◽  
Paolo Miotti ◽  
Luca Poletto
Keyword(s):  
Free Electron ◽  
Extreme Ultraviolet ◽  
Ultrashort Pulses ◽  
Spectral Phase ◽  
High Order ◽  
Free Electron Lasers ◽  
Main Application ◽  
Temporal Compression ◽  
Fourier Limit ◽  
Compression Of Pulses

The design and realization of grating instruments to condition the spectral phase of ultrashort extreme-ultraviolet pulses are discussed. The main application of such configurations is the temporal compression of pulses by compensating the phase chirp and getting close to the Fourier limit. We discuss the two configurations useful for the realization of ultrafast grating compressors, namely, the classical diffraction mount and the off-plane one. The configuration may be applied to free-electron lasers and high-order laser harmonics.

High order accurate simulation of compressible flows on GPU clusters over Software Distributed Shared Memory

2014 ◽  
Vol 93 ◽  
pp. 18-29 ◽  
Author(s):  
Konstantinos I. Karantasis ◽  
Eleftherios D. Polychronopoulos ◽  
John A. Ekaterinaris
Keyword(s):  
Shared Memory ◽  
Compressible Flows ◽  
Distributed Shared Memory ◽  
High Order ◽  
Gpu Clusters ◽  
Software Distributed Shared Memory
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