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(* ::Package:: *)
(* Copyright 2004 Sascha Husa, Ian Hinder, Christiane Lechner, Barry Wardell
This file is part of Kranc.
Kranc is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
Kranc is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with Foobar; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*)
$KrancTensorPackage="xTensorKranc`";
Get["KrancTensor`"];
PrependTo[$Path, "../../EinsteinExact/m"];
Check[Get["Metrics`LoadMetric`"],
Print["Cannot load Metrics package"]; Quit[1],
Get::noopen];
Print["Using Metrics database at ", FindFile["Metrics`LoadMetric`"]];
$DefInfoQ=False;
$CVVerbose=False;
$PrePrint=ScreenDollarIndices;
(**************************************************************************************)
(* Derivatives *)
(**************************************************************************************)
derivatives =
{
PDstandard2nd[i_] -> StandardCenteredDifferenceOperator[1,1,i],
PDstandard2nd[i_, i_] -> StandardCenteredDifferenceOperator[2,1,i],
PDstandard2nd[i_, j_] -> StandardCenteredDifferenceOperator[1,1,i] *
StandardCenteredDifferenceOperator[1,1,j],
PDstandard4th[i_] -> StandardCenteredDifferenceOperator[1,2,i],
PDstandard4th[i_, i_] -> StandardCenteredDifferenceOperator[2,2,i],
PDstandard4th[i_, j_] -> StandardCenteredDifferenceOperator[1,2,i] *
StandardCenteredDifferenceOperator[1,2,j]
};
(**************************************************************************************)
(* Tensors *)
(**************************************************************************************)
(* Load Euclidean metric and set components of g, epsilon and gamma *)
LoadMetric["Euclidean"];
MetricCompute[g, Euclidean, "Christoffel"[1,-1,-1], CVSimplify -> Simplify];
AllComponentValues[ToBasis[Euclidean][epsilong[-a,e,f]],
Table[Signature[{i,j,k}],{i,3},{j,3},{k,3}]];
RuleToSet[ChristoffelCDPDEuclidean];
RuleToSet[g];
RuleToSet[epsilong];
(* Register the tensor quantities with the TensorTools package *)
DefTensor[El[-a],EuclideanM];
DefTensor[B[-a],EuclideanM];
(**************************************************************************************)
(* Groups *)
(**************************************************************************************)
(* NB This will give B the symmetries of a VECTOR, which is not correct *)
evolvedGroups = Map[CreateGroupFromTensor, ToBasis[Euclidean][{El[-a], B[-a]}]];
evaluatedGroups =
{{"constraints", {CEl, CB}},
{"endens",{rho}}};
declaredGroups = Join[evolvedGroups, evaluatedGroups];
declaredGroupNames = Map[First, declaredGroups];
groups = Join[declaredGroups];
(**************************************************************************************)
(* Initial data *)
(**************************************************************************************)
initialCalc =
{
Name -> "EM_initial",
Schedule -> {"at CCTK_INITIAL"},
Equations ->
{
El1 -> sigma*Cos[2 Pi (x + y)] ,
El2 -> - (1 - sigma)*Cos[2 Pi x] - sigma*Cos[2 Pi (x + y)],
El3 -> 0,
B1 -> 0,
B2 -> 0,
B3 -> (1 - sigma)*Cos[2 Pi x] + sigma*Cos[2 Pi (x + y)]
}
};
(**************************************************************************************)
(* Evolution equations *)
(**************************************************************************************)
evolCalc =
{
Name -> "EM_evol",
Schedule -> {"in MoL_CalcRHS"},
Where -> Interior,
Equations ->
{
dot[ToBasis[Euclidean][El[-a]]] -> ToBasis[Euclidean][(epsilong[-a,e,f] CD[-e][B[-f]])],
dot[ToBasis[Euclidean][ B[-a]]] -> ToBasis[Euclidean][-(epsilong[-a,e,f] CD[-e][El[-f]])]
}
};
(**************************************************************************************)
(* Constraint equations *)
(**************************************************************************************)
constraintsCalc =
{
Name -> "EM_constraints",
Where -> Interior,
Equations ->
{
CEl -> ToBasis[Euclidean][g[a,b]CD[-b][El[-a]]],
CB -> ToBasis[Euclidean][ g[a,b]CD[-b][B[-a]]]
}
};
(**************************************************************************************)
(* Energy equation *)
(**************************************************************************************)
energyCalc =
{
Name -> "EM_energy",
Equations ->
{
rho -> ToBasis[Euclidean][g[a,b] El[-a] El[-b]/2 + g[a,b] B[-a] B[-b]/2]
}
};
realParameters = {sigma};
(**************************************************************************************)
(* Construct the thorn *)
(**************************************************************************************)
calculations =
{
initialCalc,
evolCalc,
constraintsCalc,
energyCalc
};
CreateKrancThornTT[groups, "xTensor", "EM",
Calculations -> calculations,
DeclaredGroups -> declaredGroupNames,
PartialDerivatives -> derivatives,
RealParameters -> realParameters];
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