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Generalize DerivChristoffel in the CCZ4 system to allow more tensor symmetry types #6600

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nilsdeppe merged 1 commit into from
Apr 29, 2025
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Generalize DerivChristoffel in the CCZ4 system to allow more tensor symmetry types #6600

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7 changes: 7 additions & 0 deletions src/DataStructures/Tensor/TypeAliases.hpp
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Expand Up @@ -423,6 +423,13 @@ using iJkk = Tensor<DataType, tmpl::integral_list<std::int32_t, 3, 2, 1, 1>,
SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;

template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
using iijj = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
SpatialIndex<SpatialDim, UpLo::Lo, Fr>>>;

template <typename DataType, size_t SpatialDim, typename Fr = Frame::Inertial>
using iiJJ = Tensor<DataType, tmpl::integral_list<std::int32_t, 2, 2, 1, 1>,
index_list<SpatialIndex<SpatialDim, UpLo::Lo, Fr>,
Expand Down
130 changes: 78 additions & 52 deletions src/Evolution/Systems/Ccz4/DerivChristoffel.cpp
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Expand Up @@ -4,53 +4,69 @@
#include "Evolution/Systems/Ccz4/DerivChristoffel.hpp"

#include <cstddef>
#include <type_traits>

#include "DataStructures/DataVector.hpp"
#include "DataStructures/Tensor/Tensor.hpp"
#include "Utilities/GenerateInstantiations.hpp"
#include "Utilities/Gsl.hpp"

namespace Ccz4 {
template <typename DataType, size_t Dim, typename Frame>
template <typename DataType, size_t Dim, typename Frame, typename TensorType>
void deriv_conformal_christoffel_second_kind(
const gsl::not_null<tnsr::iJkk<DataType, Dim, Frame>*> result,
const tnsr::II<DataType, Dim, Frame>& inverse_conformal_spatial_metric,
const tnsr::ijj<DataType, Dim, Frame>& field_d,
const tnsr::ijkk<DataType, Dim, Frame>& d_field_d,
const tnsr::ijj<DataType, Dim, Frame>& field_d, const TensorType& d_field_d,
const tnsr::iJJ<DataType, Dim, Frame>& field_d_up) {
for (size_t i = 0; i < Dim; ++i) {
for (size_t j = i; j < Dim; ++j) {
for (size_t k = 0; k < Dim; ++k) {
for (size_t m = 0; m < Dim; ++m) {
(*result).get(k, m, i, j) =
-2.0 * field_d_up.get(k, m, 0) *
(field_d.get(i, j, 0) + field_d.get(j, i, 0) -
field_d.get(0, i, j)) +
0.5 * inverse_conformal_spatial_metric.get(m, 0) *
(d_field_d.get(k, i, j, 0) + d_field_d.get(i, k, j, 0) +
d_field_d.get(k, j, i, 0) + d_field_d.get(j, k, i, 0) -
d_field_d.get(k, 0, i, j) - d_field_d.get(0, k, i, j));
for (size_t l = 1; l < Dim; ++l) {
(*result).get(k, m, i, j) +=
-2.0 * field_d_up.get(k, m, l) *
(field_d.get(i, j, l) + field_d.get(j, i, l) -
field_d.get(l, i, j)) +
0.5 * inverse_conformal_spatial_metric.get(m, l) *
(d_field_d.get(k, i, j, l) + d_field_d.get(i, k, j, l) +
d_field_d.get(k, j, i, l) + d_field_d.get(j, k, i, l) -
d_field_d.get(k, l, i, j) - d_field_d.get(l, k, i, j));
// We keep this for loop specialization for faster speed when no symmetry
// of d_field_d is present.
if constexpr (std::is_same_v<TensorType, tnsr::ijkk<DataType, Dim, Frame>>) {
for (size_t i = 0; i < Dim; ++i) {
for (size_t j = i; j < Dim; ++j) {
for (size_t k = 0; k < Dim; ++k) {
for (size_t m = 0; m < Dim; ++m) {
(*result).get(k, m, i, j) =
-2.0 * field_d_up.get(k, m, 0) *
(field_d.get(i, j, 0) + field_d.get(j, i, 0) -
field_d.get(0, i, j)) +
0.5 * inverse_conformal_spatial_metric.get(m, 0) *
(d_field_d.get(k, i, j, 0) + d_field_d.get(i, k, j, 0) +
d_field_d.get(k, j, i, 0) + d_field_d.get(j, k, i, 0) -
d_field_d.get(k, 0, i, j) - d_field_d.get(0, k, i, j));
for (size_t l = 1; l < Dim; ++l) {
(*result).get(k, m, i, j) +=
-2.0 * field_d_up.get(k, m, l) *
(field_d.get(i, j, l) + field_d.get(j, i, l) -
field_d.get(l, i, j)) +
0.5 * inverse_conformal_spatial_metric.get(m, l) *
(d_field_d.get(k, i, j, l) + d_field_d.get(i, k, j, l) +
d_field_d.get(k, j, i, l) + d_field_d.get(j, k, i, l) -
d_field_d.get(k, l, i, j) - d_field_d.get(l, k, i, j));
}
}
}
}
}
} else {
::tenex::evaluate<ti::k, ti::M, ti::i, ti::j>(
result,
-2.0 * field_d_up(ti::k, ti::M, ti::L) *
(field_d(ti::i, ti::j, ti::l) + field_d(ti::j, ti::i, ti::l) -
field_d(ti::l, ti::i, ti::j)) +
inverse_conformal_spatial_metric(ti::M, ti::L) * 0.5 *
(d_field_d(ti::k, ti::i, ti::j, ti::l) +
d_field_d(ti::i, ti::k, ti::j, ti::l) +
d_field_d(ti::k, ti::j, ti::i, ti::l) +
d_field_d(ti::j, ti::k, ti::i, ti::l) -
d_field_d(ti::k, ti::l, ti::i, ti::j) -
d_field_d(ti::l, ti::k, ti::i, ti::j)));
}
}

template <typename DataType, size_t Dim, typename Frame>
template <typename DataType, size_t Dim, typename Frame, typename TensorType>
tnsr::iJkk<DataType, Dim, Frame> deriv_conformal_christoffel_second_kind(
const tnsr::II<DataType, Dim, Frame>& inverse_conformal_spatial_metric,
const tnsr::ijj<DataType, Dim, Frame>& field_d,
const tnsr::ijkk<DataType, Dim, Frame>& d_field_d,
const tnsr::ijj<DataType, Dim, Frame>& field_d, const TensorType& d_field_d,
const tnsr::iJJ<DataType, Dim, Frame>& field_d_up) {
tnsr::iJkk<DataType, Dim, Frame> result{};
deriv_conformal_christoffel_second_kind(make_not_null(&result),
Expand Down Expand Up @@ -94,47 +110,57 @@ deriv_contracted_conformal_christoffel_second_kind(
#define DIM(data) BOOST_PP_TUPLE_ELEM(0, data)
#define FRAME(data) BOOST_PP_TUPLE_ELEM(1, data)
#define DTYPE(data) BOOST_PP_TUPLE_ELEM(2, data)
#define TTYPE(data) BOOST_PP_TUPLE_ELEM(3, data)

#define INSTANTIATE(_, data) \
#define INSTANTIATE_CONFORMAL_CHRISTOFFEL(_, data) \
template void Ccz4::deriv_conformal_christoffel_second_kind( \
const gsl::not_null<tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)>*> \
result, \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::ijj<DTYPE(data), DIM(data), FRAME(data)>& field_d, \
const tnsr::ijkk<DTYPE(data), DIM(data), FRAME(data)>& d_field_d, \
const TTYPE(data) < DTYPE(data), DIM(data), FRAME(data) > &d_field_d, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up); \
template tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)> \
Ccz4::deriv_conformal_christoffel_second_kind( \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::ijj<DTYPE(data), DIM(data), FRAME(data)>& field_d, \
const tnsr::ijkk<DTYPE(data), DIM(data), FRAME(data)>& d_field_d, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up); \
template void Ccz4::deriv_contracted_conformal_christoffel_second_kind( \
const gsl::not_null<tnsr::iJ<DTYPE(data), DIM(data), FRAME(data)>*> \
result, \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up, \
const tnsr::Ijj<DTYPE(data), DIM(data), FRAME(data)>& \
conformal_christoffel_second_kind, \
const tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)>& \
d_conformal_christoffel_second_kind); \
template tnsr::iJ<DTYPE(data), DIM(data), FRAME(data)> \
Ccz4::deriv_contracted_conformal_christoffel_second_kind( \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up, \
const tnsr::Ijj<DTYPE(data), DIM(data), FRAME(data)>& \
conformal_christoffel_second_kind, \
const tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)>& \
const TTYPE(data) < DTYPE(data), DIM(data), FRAME(data) > &d_field_d, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up);

GENERATE_INSTANTIATIONS(INSTANTIATE_CONFORMAL_CHRISTOFFEL, (1, 2, 3),
(Frame::Grid, Frame::Inertial), (double, DataVector),
(tnsr::iijj, tnsr::ijkk))

#undef INSTANTIATE_CONFORMAL_CHRISTOFFEL
#undef TTYPE

#define INSTANTIATE_CONTRACTED_CHRISTOFFEL(_, data) \
template void Ccz4::deriv_contracted_conformal_christoffel_second_kind( \
const gsl::not_null<tnsr::iJ<DTYPE(data), DIM(data), FRAME(data)>*> \
result, \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up, \
const tnsr::Ijj<DTYPE(data), DIM(data), FRAME(data)>& \
conformal_christoffel_second_kind, \
const tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)>& \
d_conformal_christoffel_second_kind); \
template tnsr::iJ<DTYPE(data), DIM(data), FRAME(data)> \
Ccz4::deriv_contracted_conformal_christoffel_second_kind( \
const tnsr::II<DTYPE(data), DIM(data), FRAME(data)>& \
inverse_conformal_spatial_metric, \
const tnsr::iJJ<DTYPE(data), DIM(data), FRAME(data)>& field_d_up, \
const tnsr::Ijj<DTYPE(data), DIM(data), FRAME(data)>& \
conformal_christoffel_second_kind, \
const tnsr::iJkk<DTYPE(data), DIM(data), FRAME(data)>& \
d_conformal_christoffel_second_kind);

GENERATE_INSTANTIATIONS(INSTANTIATE, (1, 2, 3), (Frame::Grid, Frame::Inertial),
(double, DataVector))
GENERATE_INSTANTIATIONS(INSTANTIATE_CONTRACTED_CHRISTOFFEL, (1, 2, 3),
(Frame::Grid, Frame::Inertial), (double, DataVector))

#undef INSTANTIATE
#undef INSTANTIATE_CONTRACTED_CHRISTOFFEL
#undef DTYPE
#undef FRAME
#undef DIM
16 changes: 10 additions & 6 deletions src/Evolution/Systems/Ccz4/DerivChristoffel.hpp
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Expand Up @@ -26,21 +26,25 @@ namespace Ccz4 {
* `Ccz4::Tags::InverseConformalMetric`, the CCZ4 auxiliary variable defined by
* `Ccz4::Tags::FieldD`, its spatial derivative, and the CCZ4 identity defined
* by `Ccz4::Tags::FieldDUp`.
* \note In second-order Ccz4, we impose symmetry of index k and l
* in \f$ \partial_l D_{kij}=\frac{1}{2}\partial_l \partial_k
* \tilde{\gamma}_{ij} \f$, because partial derivatives commute and to use
* `second_partial_derivatives()`. \f$ D_{kij} \f$ is evolved in
* the first-order system so no such symmetry is imposed.
*/
template <typename DataType, size_t Dim, typename Frame>
template <typename DataType, size_t Dim, typename Frame, typename TensorType>
void deriv_conformal_christoffel_second_kind(
const gsl::not_null<tnsr::iJkk<DataType, Dim, Frame>*> result,
const tnsr::II<DataType, Dim, Frame>& inverse_conformal_spatial_metric,
const tnsr::ijj<DataType, Dim, Frame>& field_d,
const tnsr::ijkk<DataType, Dim, Frame>& d_field_d,
const tnsr::ijj<DataType, Dim, Frame>& field_d, const TensorType& d_field_d,
const tnsr::iJJ<DataType, Dim, Frame>& field_d_up);

template <typename DataType, size_t Dim, typename Frame>
template <typename DataType, size_t Dim, typename Frame, typename TensorType>
tnsr::iJkk<DataType, Dim, Frame> deriv_conformal_christoffel_second_kind(
const tnsr::II<DataType, Dim, Frame>& inverse_conformal_spatial_metric,
const tnsr::ijj<DataType, Dim, Frame>& field_d,
const tnsr::ijkk<DataType, Dim, Frame>& d_field_d,
const tnsr::ijj<DataType, Dim, Frame>& field_d, const TensorType& d_field_d,
const tnsr::iJJ<DataType, Dim, Frame>& field_d_up);

/// @}

/// @{
Expand Down
10 changes: 10 additions & 0 deletions tests/Unit/Evolution/Systems/Ccz4/Test_DerivChristoffel.cpp
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Expand Up @@ -27,6 +27,16 @@ void test_compute_deriv_conformal_christoffel_second_kind(
Frame::Inertial>),
"DerivChristoffel", "deriv_conformal_christoffel_second_kind",
{{{-1., 1.}}}, used_for_size);
pypp::check_with_random_values<1>(
static_cast<tnsr::iJkk<DataType, Dim, Frame::Inertial> (*)(
const tnsr::II<DataType, Dim, Frame::Inertial>&,
const tnsr::ijj<DataType, Dim, Frame::Inertial>&,
const tnsr::iijj<DataType, Dim, Frame::Inertial>&,
const tnsr::iJJ<DataType, Dim, Frame::Inertial>&)>(
&Ccz4::deriv_conformal_christoffel_second_kind<DataType, Dim,
Frame::Inertial>),
"DerivChristoffel", "deriv_conformal_christoffel_second_kind",
{{{-1., 1.}}}, used_for_size);
}

template <size_t Dim, typename DataType>
Expand Down
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