scholarly journals Robust evolution system for numerical relativity

1999 ◽  
Vol 60 (10) ◽  
Author(s):  
A. Arbona ◽  
C. Bona ◽  
J. Massó ◽  
J. Stela
Keyword(s):  
Numerical Relativity ◽  
Evolution System

scholarly journals Hyperbolic evolution system for numerical relativity

1992 ◽  
Vol 68 (8) ◽  
pp. 1097-1099 ◽  
Author(s):  
C. Bona ◽  
J. Massó
Keyword(s):  
Numerical Relativity ◽  
Evolution System

NUMERICAL RELATIVITY: EVOLVING SPACETIME

1993 ◽  
Vol 04 (04) ◽  
pp. 883-907 ◽  
Author(s):  
C. BONA ◽  
J. MASSÓ
Keyword(s):  
Ad Hoc ◽  
Numerical Solutions ◽  
Numerical Relativity ◽  
Historical Review ◽  
Evolution System ◽  
Field Equations ◽  
Metric Tensor ◽  
New Family ◽  
Mandatory Use ◽  
Evolution Systems

The construction of numerical solutions of Einstein's General Relativity equations is formulated as an initial-value problem. The space-plus-time (3 + 1) decomposition of the spacetime metric tensor is used to discuss the structure of the field equations. The resulting evolution system is shown to depend in a crucial way on the coordinate gauge. The mandatory use of singularity avoiding coordinate conditions (like maximal slicing or similar gauges) is explained. A brief historical review of Numerical Relativity is included, showing the enormous effort in constructing codes based in these gauges, which lead to non-hyperbolic evolution systems, using "ad hoc" numerical techniques. A new family of first order hyperbolic evolution systems for the vacuum Einstein field equations in the harmonic slicing gauge is presented. This family depends on a symmetric 3 × 3 array of parameters which can be used to scale the dynamical variables in future numerical applications.

scholarly journals THE BSSN FORMULATION IS A PARTIALLY CONSTRAINED EVOLUTION SYSTEM

2010 ◽  
Vol 19 (02) ◽  
pp. 153-158
Author(s):  
ADRIAN P. GENTLE
Keyword(s):  
Numerical Relativity ◽  
Einstein Equations ◽  
Evolution System ◽  
Connection Coefficients ◽  
Constrained Evolution ◽  
Conformal Connection

It is shown that the BSSN formulation of the Einstein equations, which forms the basis of most simulations in numerical relativity, explicitly uses the momentum constraints to evolve the conformal connection coefficients.

scholarly journals Up-down instability of binary black holes in numerical relativity

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Vijay Varma ◽  
Matthew Mould ◽  
Davide Gerosa ◽  
Mark A. Scheel ◽  
Lawrence E. Kidder ◽  
...  
Keyword(s):  
Black Holes ◽  
Numerical Relativity ◽  
Binary Black Holes

scholarly journals On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

scholarly journals Constraint-preserving boundary conditions in the Z4 numerical relativity formalism

2005 ◽  
Vol 22 (13) ◽  
pp. 2615-2633 ◽  
Author(s):  
C Bona ◽  
T Ledvinka ◽  
C Palenzuela-Luque ◽  
M Žáček
Keyword(s):  
Boundary Conditions ◽  
Numerical Relativity

A Study on Development of Urbanization in Western Region under the Ecological Environment Restriction

2012 ◽  
Vol 518-523 ◽  
pp. 5853-5858
Author(s):  
Lu Feng Duan
Keyword(s):  
Sustainable Development ◽  
Urban Development ◽  
Regional Economy ◽  
Development Planning ◽  
External Condition ◽  
Ecological Environment ◽  
Western Region ◽  
Evolution System ◽  
Industrial Transformation ◽  
Organic Combination

Ecological environment is an important external condition for subsistence and development of human being, and urbanization is an important engine to promote regional economy and social development, and whether they can become an organic combination would be crucial for the western region to ensure sustainable development in economy and society. The paper presents the corresponding solution including change of idea about ecology, improvement of environment for urban development, planning in a scientific and reasonable way, upgrading urban evolution system, carrying on industrial transformation, enhancement of the momentum for urban development, building “Two Oriented” society so as to increase urban development quality after analysis of various restrictive factors in development of urbanization in western region under the ecological environment restriction.

Sign in / Sign up

Export Citation Format

Share Document