SpECTRE
v2024.12.16
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Items related to evolving the first-order CCZ4 system. More...
Namespaces | |
namespace | OptionTags |
Input option tags for the CCZ4 evolution system. | |
namespace | Tags |
Tags for the CCZ4 formulation of Einstein equations. | |
Classes | |
struct | TimeDerivative |
Compute the RHS of the first order CCZ4 formulation of Einstein's equations [63]. More... | |
Enumerations | |
enum class | EvolveShift : bool { False = false , True = true } |
Indicates whether or not to evolve the shift in a system evolved using first order CCZ4 [63]. More... | |
enum class | SlicingConditionType : char { Harmonic , Log } |
Indicates which slicing condition to use in a system evolved using first order CCZ4 [63]. More... | |
Functions | |
template<typename DataType , size_t Dim, typename Frame > | |
void | a_tilde (const gsl::not_null< tnsr::ii< DataType, Dim, Frame > * > result, const gsl::not_null< Scalar< DataType > * > buffer, const Scalar< DataType > &conformal_factor_squared, const tnsr::ii< DataType, Dim, Frame > &spatial_metric, const tnsr::ii< DataType, Dim, Frame > &extrinsic_curvature, const Scalar< DataType > &trace_extrinsic_curvature) |
Computes the trace-free part of the extrinsic curvature. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::ii< DataType, Dim, Frame > | a_tilde (const Scalar< DataType > &conformal_factor_squared, const tnsr::ii< DataType, Dim, Frame > &spatial_metric, const tnsr::ii< DataType, Dim, Frame > &extrinsic_curvature, const Scalar< DataType > &trace_extrinsic_curvature) |
Computes the trace-free part of the extrinsic curvature. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | conformal_christoffel_second_kind (const gsl::not_null< tnsr::Ijj< DataType, Dim, Frame > * > result, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &field_d) |
Computes the conformal spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::Ijj< DataType, Dim, Frame > | conformal_christoffel_second_kind (const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &field_d) |
Computes the conformal spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | christoffel_second_kind (const gsl::not_null< tnsr::Ijj< DataType, Dim, Frame > * > result, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::i< DataType, Dim, Frame > &field_p, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind) |
Computes the spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::Ijj< DataType, Dim, Frame > | christoffel_second_kind (const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::i< DataType, Dim, Frame > &field_p, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind) |
Computes the spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | contracted_conformal_christoffel_second_kind (const gsl::not_null< tnsr::I< DataType, Dim, Frame > * > result, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind) |
Computes the contraction of the conformal spatial Christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::I< DataType, Dim, Frame > | contracted_conformal_christoffel_second_kind (const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind) |
Computes the contraction of the conformal spatial Christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
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_up) |
Computes the spatial derivative of the conformal spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
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_up) |
Computes the spatial derivative of the conformal spatial christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | deriv_contracted_conformal_christoffel_second_kind (const gsl::not_null< tnsr::iJ< DataType, Dim, Frame > * > result, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::iJJ< DataType, Dim, Frame > &field_d_up, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind, const tnsr::iJkk< DataType, Dim, Frame > &d_conformal_christoffel_second_kind) |
Computes the spatial derivative of the contraction of the conformal spatial Christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::iJ< DataType, Dim, Frame > | deriv_contracted_conformal_christoffel_second_kind (const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::iJJ< DataType, Dim, Frame > &field_d_up, const tnsr::Ijj< DataType, Dim, Frame > &conformal_christoffel_second_kind, const tnsr::iJkk< DataType, Dim, Frame > &d_conformal_christoffel_second_kind) |
Computes the spatial derivative of the contraction of the conformal spatial Christoffel symbols of the second kind. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | grad_grad_lapse (const gsl::not_null< tnsr::ij< DataType, Dim, Frame > * > result, const Scalar< DataType > &lapse, const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::i< DataType, Dim, Frame > &field_a, const tnsr::ij< DataType, Dim, Frame > &d_field_a) |
Computes the gradient of the gradient of the lapse. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::ij< DataType, Dim, Frame > | grad_grad_lapse (const Scalar< DataType > &lapse, const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::i< DataType, Dim, Frame > &field_a, const tnsr::ij< DataType, Dim, Frame > &d_field_a) |
Computes the gradient of the gradient of the lapse. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | divergence_lapse (const gsl::not_null< Scalar< DataType > * > result, const Scalar< DataType > &conformal_factor_squared, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_metric, const tnsr::ij< DataType, Dim, Frame > &grad_grad_lapse) |
Computes the divergence of the lapse. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
Scalar< DataType > | divergence_lapse (const Scalar< DataType > &conformal_factor_squared, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_metric, const tnsr::ij< DataType, Dim, Frame > &grad_grad_lapse) |
Computes the divergence of the lapse. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | grad_spatial_z4_constraint (const gsl::not_null< tnsr::ij< DataType, Dim, Frame > * > result, const tnsr::i< DataType, Dim, Frame > &spatial_z4_constraint, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::ijj< DataType, Dim, Frame > &field_d, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel, const tnsr::iJ< DataType, Dim, Frame > &d_gamma_hat_minus_contracted_conformal_christoffel) |
Computes the gradient of the spatial part of the Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::ij< DataType, Dim, Frame > | grad_spatial_z4_constraint (const tnsr::i< DataType, Dim, Frame > &spatial_z4_constraint, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::ijj< DataType, Dim, Frame > &field_d, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel, const tnsr::iJ< DataType, Dim, Frame > &d_gamma_hat_minus_contracted_conformal_christoffel) |
Computes the gradient of the spatial part of the Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | spatial_ricci_tensor (const gsl::not_null< tnsr::ii< DataType, Dim, Frame > * > result, const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::i< DataType, Dim, Frame > &contracted_christoffel_second_kind, const tnsr::ij< DataType, Dim, Frame > &contracted_d_conformal_christoffel_difference, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &field_d, const tnsr::iJJ< DataType, Dim, Frame > &field_d_up, const tnsr::I< DataType, Dim, Frame > &contracted_field_d_up, const tnsr::i< DataType, Dim, Frame > &field_p, const tnsr::ij< DataType, Dim, Frame > &d_field_p) |
Computes the spatial Ricci tensor. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::ii< DataType, Dim, Frame > | spatial_ricci_tensor (const tnsr::Ijj< DataType, Dim, Frame > &christoffel_second_kind, const tnsr::i< DataType, Dim, Frame > &contracted_christoffel_second_kind, const tnsr::ij< DataType, Dim, Frame > &contracted_d_conformal_christoffel_difference, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &field_d, const tnsr::iJJ< DataType, Dim, Frame > &field_d_up, const tnsr::I< DataType, Dim, Frame > &contracted_field_d_up, const tnsr::i< DataType, Dim, Frame > &field_p, const tnsr::ij< DataType, Dim, Frame > &d_field_p) |
Computes the spatial Ricci tensor. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | ricci_scalar_plus_divergence_z4_constraint (const gsl::not_null< Scalar< DataType > * > result, const Scalar< DataType > &conformal_factor_squared, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ii< DataType, Dim, Frame > &spatial_ricci_tensor, const tnsr::ij< DataType, Dim, Frame > &grad_spatial_z4_constraint) |
Computes the sum of the Ricci scalar and twice the divergence of the upper spatial Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
Scalar< DataType > | ricci_scalar_plus_divergence_z4_constraint (const Scalar< DataType > &conformal_factor_squared, const tnsr::II< DataType, Dim, Frame > &inverse_conformal_spatial_metric, const tnsr::ii< DataType, Dim, Frame > &spatial_ricci_tensor, const tnsr::ij< DataType, Dim, Frame > &grad_spatial_z4_constraint) |
Computes the sum of the Ricci scalar and twice the divergence of the upper spatial Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | spatial_z4_constraint (const gsl::not_null< tnsr::i< DataType, Dim, Frame > * > result, const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel) |
Computes the spatial part of the Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::i< DataType, Dim, Frame > | spatial_z4_constraint (const tnsr::ii< DataType, Dim, Frame > &conformal_spatial_metric, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel) |
Computes the spatial part of the Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
void | upper_spatial_z4_constraint (const gsl::not_null< tnsr::I< DataType, Dim, Frame > * > result, const Scalar< DataType > &half_conformal_factor_squared, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel) |
Computes the spatial part of the upper Z4 constraint. More... | |
template<typename DataType , size_t Dim, typename Frame > | |
tnsr::I< DataType, Dim, Frame > | upper_spatial_z4_constraint (const Scalar< DataType > &half_conformal_factor_squared, const tnsr::I< DataType, Dim, Frame > &gamma_hat_minus_contracted_conformal_christoffel) |
Computes the spatial part of the upper Z4 constraint. More... | |
Items related to evolving the first-order CCZ4 system.
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strong |
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strong |
void Ccz4::a_tilde | ( | const gsl::not_null< tnsr::ii< DataType, Dim, Frame > * > | result, |
const gsl::not_null< Scalar< DataType > * > | buffer, | ||
const Scalar< DataType > & | conformal_factor_squared, | ||
const tnsr::ii< DataType, Dim, Frame > & | spatial_metric, | ||
const tnsr::ii< DataType, Dim, Frame > & | extrinsic_curvature, | ||
const Scalar< DataType > & | trace_extrinsic_curvature | ||
) |
Computes the trace-free part of the extrinsic curvature.
Computes the trace-free part as:
where Ccz4::Tags::ConformalFactorSquared
, gr::Tags::SpatialMetric
, gr::Tags::ExtrinsicCurvature
, and gr::Tags::TraceExtrinsicCurvature
.
tnsr::ii< DataType, Dim, Frame > Ccz4::a_tilde | ( | const Scalar< DataType > & | conformal_factor_squared, |
const tnsr::ii< DataType, Dim, Frame > & | spatial_metric, | ||
const tnsr::ii< DataType, Dim, Frame > & | extrinsic_curvature, | ||
const Scalar< DataType > & | trace_extrinsic_curvature | ||
) |
Computes the trace-free part of the extrinsic curvature.
Computes the trace-free part as:
where Ccz4::Tags::ConformalFactorSquared
, gr::Tags::SpatialMetric
, gr::Tags::ExtrinsicCurvature
, and gr::Tags::TraceExtrinsicCurvature
.
void Ccz4::christoffel_second_kind | ( | const gsl::not_null< tnsr::Ijj< DataType, Dim, Frame > * > | result, |
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::i< DataType, Dim, Frame > & | field_p, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind | ||
) |
Computes the spatial christoffel symbols of the second kind.
Computes the christoffel symbols as:
where Ccz4::Tags::ConformalMetric
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::ConformalChristoffelSecondKind
, and Ccz4::Tags::FieldP
, respectively.
tnsr::Ijj< DataType, Dim, Frame > Ccz4::christoffel_second_kind | ( | const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, |
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::i< DataType, Dim, Frame > & | field_p, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind | ||
) |
Computes the spatial christoffel symbols of the second kind.
Computes the christoffel symbols as:
where Ccz4::Tags::ConformalMetric
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::ConformalChristoffelSecondKind
, and Ccz4::Tags::FieldP
, respectively.
void Ccz4::conformal_christoffel_second_kind | ( | const gsl::not_null< tnsr::Ijj< DataType, Dim, Frame > * > | result, |
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::ijj< DataType, Dim, Frame > & | field_d | ||
) |
Computes the conformal spatial christoffel symbols of the second kind.
Computes the christoffel symbols as:
where Ccz4::Tags::InverseConformalMetric
and Ccz4::Tags::FieldD
, respectively.
tnsr::Ijj< DataType, Dim, Frame > Ccz4::conformal_christoffel_second_kind | ( | const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, |
const tnsr::ijj< DataType, Dim, Frame > & | field_d | ||
) |
Computes the conformal spatial christoffel symbols of the second kind.
Computes the christoffel symbols as:
where Ccz4::Tags::InverseConformalMetric
and Ccz4::Tags::FieldD
, respectively.
void Ccz4::contracted_conformal_christoffel_second_kind | ( | const gsl::not_null< tnsr::I< DataType, Dim, Frame > * > | result, |
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind | ||
) |
Computes the contraction of the conformal spatial Christoffel symbols of the second kind.
Computes the contraction as:
where Ccz4::Tags::InverseConformalMetric
and Ccz4::Tags::ConformalChristoffelSecondKind
.
tnsr::I< DataType, Dim, Frame > Ccz4::contracted_conformal_christoffel_second_kind | ( | const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, |
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind | ||
) |
Computes the contraction of the conformal spatial Christoffel symbols of the second kind.
Computes the contraction as:
where Ccz4::Tags::InverseConformalMetric
and Ccz4::Tags::ConformalChristoffelSecondKind
.
void Ccz4::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_up | ||
) |
Computes the spatial derivative of the conformal spatial christoffel symbols of the second kind.
Computes the derivative as:
where Ccz4::Tags::InverseConformalMetric
, the CCZ4 auxiliary variable defined by Ccz4::Tags::FieldD
, its spatial derivative, and the CCZ4 identity defined by Ccz4::Tags::FieldDUp
.
tnsr::iJkk< DataType, Dim, Frame > Ccz4::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_up | ||
) |
Computes the spatial derivative of the conformal spatial christoffel symbols of the second kind.
Computes the derivative as:
where Ccz4::Tags::InverseConformalMetric
, the CCZ4 auxiliary variable defined by Ccz4::Tags::FieldD
, its spatial derivative, and the CCZ4 identity defined by Ccz4::Tags::FieldDUp
.
void Ccz4::deriv_contracted_conformal_christoffel_second_kind | ( | const gsl::not_null< tnsr::iJ< DataType, Dim, Frame > * > | result, |
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::iJJ< DataType, Dim, Frame > & | field_d_up, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind, | ||
const tnsr::iJkk< DataType, Dim, Frame > & | d_conformal_christoffel_second_kind | ||
) |
Computes the spatial derivative of the contraction of the conformal spatial Christoffel symbols of the second kind.
Computes the derivative as:
where Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::FieldDUp
, Ccz4::Tags::ConformalChristoffelSecondKind
, and Ccz4::Tags::DerivConformalChristoffelSecondKind
.
tnsr::iJ< DataType, Dim, Frame > Ccz4::deriv_contracted_conformal_christoffel_second_kind | ( | const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, |
const tnsr::iJJ< DataType, Dim, Frame > & | field_d_up, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | conformal_christoffel_second_kind, | ||
const tnsr::iJkk< DataType, Dim, Frame > & | d_conformal_christoffel_second_kind | ||
) |
Computes the spatial derivative of the contraction of the conformal spatial Christoffel symbols of the second kind.
Computes the derivative as:
where Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::FieldDUp
, Ccz4::Tags::ConformalChristoffelSecondKind
, and Ccz4::Tags::DerivConformalChristoffelSecondKind
.
void Ccz4::grad_grad_lapse | ( | const gsl::not_null< tnsr::ij< DataType, Dim, Frame > * > | result, |
const Scalar< DataType > & | lapse, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, | ||
const tnsr::i< DataType, Dim, Frame > & | field_a, | ||
const tnsr::ij< DataType, Dim, Frame > & | d_field_a | ||
) |
Computes the gradient of the gradient of the lapse.
Computes the gradient of the gradient as:
where Ccz4::Tags::FieldA
, and its spatial derivative, respectively.
tnsr::ij< DataType, Dim, Frame > Ccz4::grad_grad_lapse | ( | const Scalar< DataType > & | lapse, |
const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, | ||
const tnsr::i< DataType, Dim, Frame > & | field_a, | ||
const tnsr::ij< DataType, Dim, Frame > & | d_field_a | ||
) |
Computes the gradient of the gradient of the lapse.
Computes the gradient of the gradient as:
where Ccz4::Tags::FieldA
, and its spatial derivative, respectively.
void Ccz4::grad_spatial_z4_constraint | ( | const gsl::not_null< tnsr::ij< DataType, Dim, Frame > * > | result, |
const tnsr::i< DataType, Dim, Frame > & | spatial_z4_constraint, | ||
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, | ||
const tnsr::ijj< DataType, Dim, Frame > & | field_d, | ||
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel, | ||
const tnsr::iJ< DataType, Dim, Frame > & | d_gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the gradient of the spatial part of the Z4 constraint.
Computes the gradient as:
where Ccz4::Tags::SpatialZ4Constraint
, Ccz4::Tags::ConformalMetric
, Ccz4::Tags::ChristoffelSecondKind
, Ccz4::Tags::FieldD
, Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
, and
tnsr::ij< DataType, Dim, Frame > Ccz4::grad_spatial_z4_constraint | ( | const tnsr::i< DataType, Dim, Frame > & | spatial_z4_constraint, |
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, | ||
const tnsr::ijj< DataType, Dim, Frame > & | field_d, | ||
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel, | ||
const tnsr::iJ< DataType, Dim, Frame > & | d_gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the gradient of the spatial part of the Z4 constraint.
Computes the gradient as:
where Ccz4::Tags::SpatialZ4Constraint
, Ccz4::Tags::ConformalMetric
, Ccz4::Tags::ChristoffelSecondKind
, Ccz4::Tags::FieldD
, Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
, and
void Ccz4::ricci_scalar_plus_divergence_z4_constraint | ( | const gsl::not_null< Scalar< DataType > * > | result, |
const Scalar< DataType > & | conformal_factor_squared, | ||
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::ii< DataType, Dim, Frame > & | spatial_ricci_tensor, | ||
const tnsr::ij< DataType, Dim, Frame > & | grad_spatial_z4_constraint | ||
) |
Computes the sum of the Ricci scalar and twice the divergence of the upper spatial Z4 constraint.
Computes the expression as:
where Ccz4::Tags::Z4ConstraintUp
, Ccz4::Tags::ConformalFactorSquared
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::Ricci
, and Ccz4::Tags::GradZ4Constraint
.
Scalar< DataType > Ccz4::ricci_scalar_plus_divergence_z4_constraint | ( | const Scalar< DataType > & | conformal_factor_squared, |
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::ii< DataType, Dim, Frame > & | spatial_ricci_tensor, | ||
const tnsr::ij< DataType, Dim, Frame > & | grad_spatial_z4_constraint | ||
) |
Computes the sum of the Ricci scalar and twice the divergence of the upper spatial Z4 constraint.
Computes the expression as:
where Ccz4::Tags::Z4ConstraintUp
, Ccz4::Tags::ConformalFactorSquared
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::Ricci
, and Ccz4::Tags::GradZ4Constraint
.
void Ccz4::spatial_ricci_tensor | ( | const gsl::not_null< tnsr::ii< DataType, Dim, Frame > * > | result, |
const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, | ||
const tnsr::i< DataType, Dim, Frame > & | contracted_christoffel_second_kind, | ||
const tnsr::ij< DataType, Dim, Frame > & | contracted_d_conformal_christoffel_difference, | ||
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::ijj< DataType, Dim, Frame > & | field_d, | ||
const tnsr::iJJ< DataType, Dim, Frame > & | field_d_up, | ||
const tnsr::I< DataType, Dim, Frame > & | contracted_field_d_up, | ||
const tnsr::i< DataType, Dim, Frame > & | field_p, | ||
const tnsr::ij< DataType, Dim, Frame > & | d_field_p | ||
) |
Computes the spatial Ricci tensor.
Computes the spatial Ricci tensor as:
where
Ccz4::Tags::ChristoffelSecondKind
, Ccz4::Tags::DerivConformalChristoffelSecondKind
, Ccz4::Tags::ConformalMetric
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::FieldD
, Ccz4::Tags::FieldDUp
, Ccz4::Tags::FieldP
, and
After substituting in the full expressions for
The argument contracted_christoffel_second_kind
corresponds to the contracted_d_conformal_christoffel_difference
corresponds to the contracted_field_d_up
corresponds to the
tnsr::ii< DataType, Dim, Frame > Ccz4::spatial_ricci_tensor | ( | const tnsr::Ijj< DataType, Dim, Frame > & | christoffel_second_kind, |
const tnsr::i< DataType, Dim, Frame > & | contracted_christoffel_second_kind, | ||
const tnsr::ij< DataType, Dim, Frame > & | contracted_d_conformal_christoffel_difference, | ||
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::II< DataType, Dim, Frame > & | inverse_conformal_spatial_metric, | ||
const tnsr::ijj< DataType, Dim, Frame > & | field_d, | ||
const tnsr::iJJ< DataType, Dim, Frame > & | field_d_up, | ||
const tnsr::I< DataType, Dim, Frame > & | contracted_field_d_up, | ||
const tnsr::i< DataType, Dim, Frame > & | field_p, | ||
const tnsr::ij< DataType, Dim, Frame > & | d_field_p | ||
) |
Computes the spatial Ricci tensor.
Computes the spatial Ricci tensor as:
where
Ccz4::Tags::ChristoffelSecondKind
, Ccz4::Tags::DerivConformalChristoffelSecondKind
, Ccz4::Tags::ConformalMetric
, Ccz4::Tags::InverseConformalMetric
, Ccz4::Tags::FieldD
, Ccz4::Tags::FieldDUp
, Ccz4::Tags::FieldP
, and
After substituting in the full expressions for
The argument contracted_christoffel_second_kind
corresponds to the contracted_d_conformal_christoffel_difference
corresponds to the contracted_field_d_up
corresponds to the
void Ccz4::spatial_z4_constraint | ( | const gsl::not_null< tnsr::i< DataType, Dim, Frame > * > | result, |
const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, | ||
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the spatial part of the Z4 constraint.
Computes the constraint as:
where Ccz4::Tags::ConformalMetric
and Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
.
tnsr::i< DataType, Dim, Frame > Ccz4::spatial_z4_constraint | ( | const tnsr::ii< DataType, Dim, Frame > & | conformal_spatial_metric, |
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the spatial part of the Z4 constraint.
Computes the constraint as:
where Ccz4::Tags::ConformalMetric
and Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
.
void Ccz4::upper_spatial_z4_constraint | ( | const gsl::not_null< tnsr::I< DataType, Dim, Frame > * > | result, |
const Scalar< DataType > & | half_conformal_factor_squared, | ||
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the spatial part of the upper Z4 constraint.
Computes the constraint as:
where Ccz4::Tags::ConformalFactorSquared
and Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
.
tnsr::I< DataType, Dim, Frame > Ccz4::upper_spatial_z4_constraint | ( | const Scalar< DataType > & | half_conformal_factor_squared, |
const tnsr::I< DataType, Dim, Frame > & | gamma_hat_minus_contracted_conformal_christoffel | ||
) |
Computes the spatial part of the upper Z4 constraint.
Computes the constraint as:
where Ccz4::Tags::ConformalFactorSquared
and Ccz4::Tags::GammaHatMinusContractedConformalChristoffel
.