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Solve for psi-1 in XCTS system #5684

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merged 5 commits into from
Jan 12, 2024
Merged

Solve for psi-1 in XCTS system #5684

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49158a7
Add constant to Lorentzian solution
nilsvu Dec 11, 2023
003a61e
Make GetFundamentalType work with Blaze expressions
nilsvu Nov 28, 2023
e13f284
Solve for psi-1 in XCTS system
nilsvu Dec 11, 2023
98f2a02
Solve for BBH ID at large outer radius
nilsvu Dec 20, 2023
ccd8781
Fix a typo in docs
nilsvu Jan 6, 2024
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2 changes: 1 addition & 1 deletion src/Elliptic/DiscontinuousGalerkin/DgOperator.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -80,7 +80,7 @@
* u^* &= \frac{1}{2} \left(u^\mathrm{int} + u^\mathrm{ext}\right) \\
* (n_i F^i)^* &= \frac{1}{2} n_i \left(
* F^i_\mathrm{int} + F^i_\mathrm{ext} \right)
* - \sigma n_i F^i(n_j (u^\mathrm{int} - u^\mathrm{ext})) \right)
* - \sigma n_i F^i(n_j (u^\mathrm{int} - u^\mathrm{ext}))
* \f}
*
* Note that \f$n_i\f$ denotes the face normal on the "interior" side of the
Expand Down
4 changes: 3 additions & 1 deletion src/Elliptic/Executables/Xcts/SolveXcts.hpp
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Expand Up @@ -62,7 +62,9 @@ struct Metavariables {
using analytic_solution_fields = tmpl::append<typename system::primal_fields,
typename system::primal_fluxes>;
using spacetime_quantities_compute = Xcts::Tags::SpacetimeQuantitiesCompute<
tmpl::list<gr::Tags::HamiltonianConstraint<DataVector>,
tmpl::list<Xcts::Tags::ConformalFactor<DataVector>,
Xcts::Tags::LapseTimesConformalFactor<DataVector>,
gr::Tags::HamiltonianConstraint<DataVector>,
gr::Tags::MomentumConstraint<DataVector, 3>,
gr::Tags::SpatialMetric<DataVector, 3>,
gr::Tags::Lapse<DataVector>, gr::Tags::Shift<DataVector, 3>,
Expand Down
95 changes: 53 additions & 42 deletions src/Elliptic/Systems/Xcts/BoundaryConditions/ApparentHorizon.cpp
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Expand Up @@ -190,8 +190,9 @@ void negative_expansion_quantities(

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[optional, random line] there are a lot of divisions by the conformal factor. I'm not sure if it matters because this is a BC, but it may be possible to factor those out and do only one. Probably doesn't matter, though.

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Haven't profiled this recently, but I'll keep this in mind when doing a round of optimizations 👍 Not much use to do this blindly I think.

template <Xcts::Geometry ConformalGeometry>
void apparent_horizon_impl(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
lapse_times_conformal_factor_minus_one,
const gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
const gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
const gsl::not_null<Scalar<DataVector>*>
Expand Down Expand Up @@ -259,12 +260,13 @@ void apparent_horizon_impl(
// Shift
{
if (solution_for_negative_expansion.has_value()) {
get(beta_orthogonal) /= square(get(*conformal_factor));
get(beta_orthogonal) /= square(get(*conformal_factor_minus_one) + 1.);
} else {
get(beta_orthogonal) = 0.;
}
get(beta_orthogonal) +=
get(*lapse_times_conformal_factor) / cube(get(*conformal_factor));
(get(*lapse_times_conformal_factor_minus_one) + 1.) /
cube(get(*conformal_factor_minus_one) + 1.);
for (size_t i = 0; i < 3; ++i) {
shift_excess->get(i) = -get(beta_orthogonal) * face_normal_raised.get(i) -
shift_background.get(i);
Expand Down Expand Up @@ -292,10 +294,12 @@ void apparent_horizon_impl(
}
// At this point we're done with `face_normal_raised`, so we can re-purpose
// the memory buffer.
get(*n_dot_conformal_factor_gradient) *= -0.25 * get(*conformal_factor);
get(*n_dot_conformal_factor_gradient) *=
-0.25 * (get(*conformal_factor_minus_one) + 1.);
if (solution_for_negative_expansion.has_value()) {
get(*n_dot_conformal_factor_gradient) -=
0.25 * cube(get(*conformal_factor)) * get(expansion_of_solution);
0.25 * cube(get(*conformal_factor_minus_one) + 1.) *
get(expansion_of_solution);
}
{
tnsr::I<DataVector, 3>& n_dot_longitudinal_shift =
Expand All @@ -311,21 +315,23 @@ void apparent_horizon_impl(
normal_dot_flux(make_not_null(&nn_dot_longitudinal_shift), face_normal,
n_dot_longitudinal_shift);
get(*n_dot_conformal_factor_gradient) +=
-get(extrinsic_curvature_trace) * cube(get(*conformal_factor)) / 6. +
pow<4>(get(*conformal_factor)) / 8. /
get(*lapse_times_conformal_factor) * get(nn_dot_longitudinal_shift);
-get(extrinsic_curvature_trace) *
cube(get(*conformal_factor_minus_one) + 1.) / 6. +
pow<4>(get(*conformal_factor_minus_one) + 1.) / 8. /
(get(*lapse_times_conformal_factor_minus_one) + 1.) *
get(nn_dot_longitudinal_shift);
}

// Lapse
if (solution_for_lapse.has_value()) {
*lapse_times_conformal_factor = call_with_dynamic_type<
*lapse_times_conformal_factor_minus_one = call_with_dynamic_type<
Scalar<DataVector>, Xcts::Solutions::all_analytic_solutions>(
solution_for_lapse.value().get(),
[&x](const auto* const local_solution) {
return get<Xcts::Tags::LapseTimesConformalFactor<DataVector>>(
return get<Xcts::Tags::LapseTimesConformalFactorMinusOne<DataVector>>(
local_solution->variables(
x, tmpl::list<
Xcts::Tags::LapseTimesConformalFactor<DataVector>>{}));
x, tmpl::list<Xcts::Tags::LapseTimesConformalFactorMinusOne<
DataVector>>{}));
});
} else {
get(*n_dot_lapse_times_conformal_factor_gradient) = 0.;
Expand Down Expand Up @@ -357,8 +363,8 @@ void linearized_apparent_horizon_impl(
const tnsr::I<DataVector, 3>& x_offcenter,
const Scalar<DataVector>& extrinsic_curvature_trace,
const tnsr::II<DataVector, 3>& longitudinal_shift_background,
const Scalar<DataVector>& conformal_factor,
const Scalar<DataVector>& lapse_times_conformal_factor,
const Scalar<DataVector>& conformal_factor_minus_one,
const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
const tnsr::I<DataVector, 3>& n_dot_longitudinal_shift_excess,
[[maybe_unused]] const std::optional<
std::reference_wrapper<const tnsr::II<DataVector, 3>>>
Expand Down Expand Up @@ -404,14 +410,16 @@ void linearized_apparent_horizon_impl(
{
if (solution_for_negative_expansion.has_value()) {
get(beta_orthogonal_correction) *=
-2. * get(*conformal_factor_correction) / cube(get(conformal_factor));
-2. * get(*conformal_factor_correction) /
cube(get(conformal_factor_minus_one) + 1.);
} else {
get(beta_orthogonal_correction) = 0.;
}
get(beta_orthogonal_correction) +=
get(*lapse_times_conformal_factor_correction) /
cube(get(conformal_factor)) -
3. * get(lapse_times_conformal_factor) / pow<4>(get(conformal_factor)) *
cube(get(conformal_factor_minus_one) + 1.) -
3. * (get(lapse_times_conformal_factor_minus_one) + 1.) /
pow<4>(get(conformal_factor_minus_one) + 1.) *
get(*conformal_factor_correction);
for (size_t i = 0; i < 3; ++i) {
shift_correction->get(i) =
Expand Down Expand Up @@ -440,8 +448,8 @@ void linearized_apparent_horizon_impl(
-0.25 * get(*conformal_factor_correction);
if (solution_for_negative_expansion.has_value()) {
get(*n_dot_conformal_factor_gradient_correction) -=
0.75 * square(get(conformal_factor)) * get(expansion_of_solution) *
get(*conformal_factor_correction);
0.75 * square(get(conformal_factor_minus_one) + 1.) *
get(expansion_of_solution) * get(*conformal_factor_correction);
}
{
tnsr::I<DataVector, 3>& n_dot_longitudinal_shift =
Expand All @@ -456,13 +464,14 @@ void linearized_apparent_horizon_impl(
normal_dot_flux(make_not_null(&nn_dot_longitudinal_shift), face_normal,
n_dot_longitudinal_shift);
get(*n_dot_conformal_factor_gradient_correction) +=
-0.5 * get(extrinsic_curvature_trace) * square(get(conformal_factor)) *
-0.5 * get(extrinsic_curvature_trace) *
square(get(conformal_factor_minus_one) + 1.) *
get(*conformal_factor_correction) +
0.5 * pow<3>(get(conformal_factor)) /
get(lapse_times_conformal_factor) * get(nn_dot_longitudinal_shift) *
get(*conformal_factor_correction) -
0.125 * pow<4>(get(conformal_factor)) /
square(get(lapse_times_conformal_factor)) *
0.5 * pow<3>(get(conformal_factor_minus_one) + 1.) /
(get(lapse_times_conformal_factor_minus_one) + 1.) *
get(nn_dot_longitudinal_shift) * get(*conformal_factor_correction) -
0.125 * pow<4>(get(conformal_factor_minus_one) + 1.) /
square(get(lapse_times_conformal_factor_minus_one) + 1.) *
get(nn_dot_longitudinal_shift) *
get(*lapse_times_conformal_factor_correction);
}
Expand All @@ -472,8 +481,8 @@ void linearized_apparent_horizon_impl(
normal_dot_flux(make_not_null(&nn_dot_longitudinal_shift_correction),
face_normal, *n_dot_longitudinal_shift_correction);
get(*n_dot_conformal_factor_gradient_correction) +=
0.125 * pow<4>(get(conformal_factor)) /
get(lapse_times_conformal_factor) *
0.125 * pow<4>(get(conformal_factor_minus_one) + 1.) /
(get(lapse_times_conformal_factor_minus_one) + 1.) *
get(nn_dot_longitudinal_shift_correction);
}

Expand All @@ -488,8 +497,9 @@ void linearized_apparent_horizon_impl(

template <Xcts::Geometry ConformalGeometry>
void ApparentHorizon<ConformalGeometry>::apply(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
lapse_times_conformal_factor_minus_one,
const gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
const gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
const gsl::not_null<Scalar<DataVector>*>
Expand All @@ -504,8 +514,8 @@ void ApparentHorizon<ConformalGeometry>::apply(
const tnsr::I<DataVector, 3>& shift_background,
const tnsr::II<DataVector, 3>& longitudinal_shift_background) const {
apparent_horizon_impl<ConformalGeometry>(
conformal_factor, lapse_times_conformal_factor, shift_excess,
n_dot_conformal_factor_gradient,
conformal_factor_minus_one, lapse_times_conformal_factor_minus_one,
shift_excess, n_dot_conformal_factor_gradient,
n_dot_lapse_times_conformal_factor_gradient,
n_dot_longitudinal_shift_excess, center_, rotation_, solution_for_lapse_,
solution_for_negative_expansion_, face_normal,
Expand All @@ -516,8 +526,9 @@ void ApparentHorizon<ConformalGeometry>::apply(

template <Xcts::Geometry ConformalGeometry>
void ApparentHorizon<ConformalGeometry>::apply(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
lapse_times_conformal_factor_minus_one,
const gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
const gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
const gsl::not_null<Scalar<DataVector>*>
Expand All @@ -534,8 +545,8 @@ void ApparentHorizon<ConformalGeometry>::apply(
const tnsr::II<DataVector, 3>& inv_conformal_metric,
const tnsr::Ijj<DataVector, 3>& conformal_christoffel_second_kind) const {
apparent_horizon_impl<ConformalGeometry>(
conformal_factor, lapse_times_conformal_factor, shift_excess,
n_dot_conformal_factor_gradient,
conformal_factor_minus_one, lapse_times_conformal_factor_minus_one,
shift_excess, n_dot_conformal_factor_gradient,
n_dot_lapse_times_conformal_factor_gradient,
n_dot_longitudinal_shift_excess, center_, rotation_, solution_for_lapse_,
solution_for_negative_expansion_, face_normal,
Expand Down Expand Up @@ -563,8 +574,8 @@ void ApparentHorizon<ConformalGeometry>::apply_linearized(
const tnsr::I<DataVector, 3>& x,
const Scalar<DataVector>& extrinsic_curvature_trace,
const tnsr::II<DataVector, 3>& longitudinal_shift_background,
const Scalar<DataVector>& conformal_factor,
const Scalar<DataVector>& lapse_times_conformal_factor,
const Scalar<DataVector>& conformal_factor_minus_one,
const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
const tnsr::I<DataVector, 3>& n_dot_longitudinal_shift_excess) const {
linearized_apparent_horizon_impl<ConformalGeometry>(
conformal_factor_correction, lapse_times_conformal_factor_correction,
Expand All @@ -574,7 +585,7 @@ void ApparentHorizon<ConformalGeometry>::apply_linearized(
solution_for_negative_expansion_, face_normal,
deriv_unnormalized_face_normal, face_normal_magnitude, x,
extrinsic_curvature_trace, longitudinal_shift_background,
conformal_factor, lapse_times_conformal_factor,
conformal_factor_minus_one, lapse_times_conformal_factor_minus_one,
n_dot_longitudinal_shift_excess, std::nullopt, std::nullopt);
}

Expand All @@ -596,8 +607,8 @@ void ApparentHorizon<ConformalGeometry>::apply_linearized(
const tnsr::I<DataVector, 3>& x,
const Scalar<DataVector>& extrinsic_curvature_trace,
const tnsr::II<DataVector, 3>& longitudinal_shift_background,
const Scalar<DataVector>& conformal_factor,
const Scalar<DataVector>& lapse_times_conformal_factor,
const Scalar<DataVector>& conformal_factor_minus_one,
const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
const tnsr::I<DataVector, 3>& n_dot_longitudinal_shift_excess,
const tnsr::II<DataVector, 3>& inv_conformal_metric,
const tnsr::Ijj<DataVector, 3>& conformal_christoffel_second_kind) const {
Expand All @@ -609,7 +620,7 @@ void ApparentHorizon<ConformalGeometry>::apply_linearized(
solution_for_negative_expansion_, face_normal,
deriv_unnormalized_face_normal, face_normal_magnitude, x,
extrinsic_curvature_trace, longitudinal_shift_background,
conformal_factor, lapse_times_conformal_factor,
conformal_factor_minus_one, lapse_times_conformal_factor_minus_one,
n_dot_longitudinal_shift_excess, inv_conformal_metric,
conformal_christoffel_second_kind);
}
Expand Down
20 changes: 10 additions & 10 deletions src/Elliptic/Systems/Xcts/BoundaryConditions/ApparentHorizon.hpp
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Expand Up @@ -231,8 +231,8 @@ class ApparentHorizon
using volume_tags = tmpl::list<>;

void apply(
gsl::not_null<Scalar<DataVector>*> conformal_factor,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor_minus_one,
gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
gsl::not_null<Scalar<DataVector>*>
Expand All @@ -247,8 +247,8 @@ class ApparentHorizon
const tnsr::II<DataVector, 3>& longitudinal_shift_background) const;

void apply(
gsl::not_null<Scalar<DataVector>*> conformal_factor,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor_minus_one,
gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
gsl::not_null<Scalar<DataVector>*>
Expand All @@ -275,8 +275,8 @@ class ApparentHorizon
gr::Tags::TraceExtrinsicCurvature<DataVector>,
Tags::LongitudinalShiftBackgroundMinusDtConformalMetric<DataVector, 3,
Frame::Inertial>,
Tags::ConformalFactor<DataVector>,
Tags::LapseTimesConformalFactor<DataVector>,
Tags::ConformalFactorMinusOne<DataVector>,
Tags::LapseTimesConformalFactorMinusOne<DataVector>,
::Tags::NormalDotFlux<Tags::ShiftExcess<DataVector, 3, Frame::Inertial>>,
tmpl::conditional_t<ConformalGeometry == Xcts::Geometry::Curved,
tmpl::list<Tags::InverseConformalMetric<
Expand All @@ -303,8 +303,8 @@ class ApparentHorizon
const tnsr::I<DataVector, 3>& x,
const Scalar<DataVector>& extrinsic_curvature_trace,
const tnsr::II<DataVector, 3>& longitudinal_shift_background,
const Scalar<DataVector>& conformal_factor,
const Scalar<DataVector>& lapse_times_conformal_factor,
const Scalar<DataVector>& conformal_factor_minus_one,
const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
const tnsr::I<DataVector, 3>& n_dot_longitudinal_shift_excess) const;

void apply_linearized(
Expand All @@ -324,8 +324,8 @@ class ApparentHorizon
const tnsr::I<DataVector, 3>& x,
const Scalar<DataVector>& extrinsic_curvature_trace,
const tnsr::II<DataVector, 3>& longitudinal_shift_background,
const Scalar<DataVector>& conformal_factor,
const Scalar<DataVector>& lapse_times_conformal_factor,
const Scalar<DataVector>& conformal_factor_minus_one,
const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
const tnsr::I<DataVector, 3>& n_dot_longitudinal_shift_excess,
const tnsr::II<DataVector, 3>& inv_conformal_metric,
const tnsr::Ijj<DataVector, 3>& conformal_christoffel_second_kind) const;
Expand Down
22 changes: 12 additions & 10 deletions src/Elliptic/Systems/Xcts/BoundaryConditions/Flatness.cpp
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Expand Up @@ -15,37 +15,39 @@ namespace Xcts::BoundaryConditions {

template <>
void Flatness<Xcts::Equations::Hamiltonian>::apply(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
/*n_dot_conformal_factor_gradient*/) {
get(*conformal_factor) = 1.;
get(*conformal_factor_minus_one) = 0.;
}

template <>
void Flatness<Xcts::Equations::HamiltonianAndLapse>::apply(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
lapse_times_conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
/*n_dot_conformal_factor_gradient*/,
const gsl::not_null<Scalar<DataVector>*>
/*n_dot_lapse_times_conformal_factor_gradient*/) {
get(*conformal_factor) = 1.;
get(*lapse_times_conformal_factor) = 1.;
get(*conformal_factor_minus_one) = 0.;
get(*lapse_times_conformal_factor_minus_one) = 0.;
}

template <>
void Flatness<Xcts::Equations::HamiltonianLapseAndShift>::apply(
const gsl::not_null<Scalar<DataVector>*> conformal_factor,
const gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
const gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
const gsl::not_null<Scalar<DataVector>*>
lapse_times_conformal_factor_minus_one,
const gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
const gsl::not_null<Scalar<DataVector>*>
/*n_dot_conformal_factor_gradient*/,
const gsl::not_null<Scalar<DataVector>*>
/*n_dot_lapse_times_conformal_factor_gradient*/,
const gsl::not_null<tnsr::I<DataVector, 3>*>
/*n_dot_longitudinal_shift_excess*/) {
get(*conformal_factor) = 1.;
get(*lapse_times_conformal_factor) = 1.;
get(*conformal_factor_minus_one) = 0.;
get(*lapse_times_conformal_factor_minus_one) = 0.;
std::fill(shift_excess->begin(), shift_excess->end(), 0.);
}

Expand Down
10 changes: 5 additions & 5 deletions src/Elliptic/Systems/Xcts/BoundaryConditions/Flatness.hpp
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Expand Up @@ -83,19 +83,19 @@ class Flatness : public elliptic::BoundaryConditions::BoundaryCondition<3> {
using volume_tags = tmpl::list<>;

static void apply(
gsl::not_null<Scalar<DataVector>*> conformal_factor,
gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient);

static void apply(
gsl::not_null<Scalar<DataVector>*> conformal_factor,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
gsl::not_null<Scalar<DataVector>*>
n_dot_lapse_times_conformal_factor_gradient);

static void apply(
gsl::not_null<Scalar<DataVector>*> conformal_factor,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor,
gsl::not_null<Scalar<DataVector>*> conformal_factor_minus_one,
gsl::not_null<Scalar<DataVector>*> lapse_times_conformal_factor_minus_one,
gsl::not_null<tnsr::I<DataVector, 3>*> shift_excess,
gsl::not_null<Scalar<DataVector>*> n_dot_conformal_factor_gradient,
gsl::not_null<Scalar<DataVector>*>
Expand Down
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