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<< "KrancThorn.m";
groups = {{"phi_g", {phi}}, {"pi_g", {pi}}};
derivatives =
{
PDstandard2nd[i_] -> StandardCenteredDifferenceOperator[1,1,i],
PDstandard2nd[i_, i_] -> StandardCenteredDifferenceOperator[2,1,i]
};
PD = PDstandard2nd;
initialSineCalc =
{
Name -> "initial_sine",
Schedule -> {"AT INITIAL"},
Equations ->
{
phi -> Sin[2 Pi (x - t)],
pi -> -2 Pi Cos[2 Pi (x - t)]
}
};
evolveCalc =
{
Name -> "calc_rhs",
Schedule -> {"at EVOL"},
Where -> Interior,
Equations ->
{
dot[phi] -> pi,
dot[pi] -> Euc[ui,uj] PD[phi,li,lj]
}
};
integrateCalc =
{
Name -> "rk1",
Schedule -> {"at EVOL after calc_rhs"},
Where -> Interior,
Equations ->
{
phi -> phi + dt dot[phi]
pi -> pi + dt dot[pi]
}
};
CreateKrancThornTT[groups, ".",
"SimpleWaveCaKernel",
Calculations -> {initialSineCalc, evolveCalc, integrateCalc},
PartialDerivatives -> derivatives,
UseCaKernel -> True,
DeclaredGroups -> {"phi_g","pi_g"}];
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