scholarly journals 3+1 covariant suite of numerical relativity evolution systems

2002 ◽  
Vol 66 (8) ◽  
Author(s):  
C. Bona ◽  
T. Ledvinka ◽  
C. Palenzuela
Keyword(s):  
Numerical Relativity ◽  
Evolution Systems

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 Action principle for numerical-relativity evolution systems

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
C. Bona ◽  
C. Bona-Casas ◽  
C. Palenzuela
Keyword(s):  
Numerical Relativity ◽  
Action Principle ◽  
Evolution Systems

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

scholarly journals Constraint-preserving boundary conditions in numerical relativity

2002 ◽  
Vol 65 (10) ◽  
Author(s):  
Gioel Calabrese ◽  
Luis Lehner ◽  
Manuel Tiglio
Keyword(s):  
Boundary Conditions ◽  
Numerical Relativity
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