Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cstddef>
7 :
8 : #include "DataStructures/Tensor/TypeAliases.hpp"
9 : #include "Utilities/Gsl.hpp"
10 :
11 : /// \cond
12 : class DataVector;
13 : /// \endcond
14 :
15 : namespace Xcts {
16 : namespace detail {
17 : // Tensor-contraction helper functions that should be replaced by tensor
18 : // expressions once those work
19 : void fully_contract_flat_cartesian(gsl::not_null<Scalar<DataVector>*> result,
20 : const tnsr::II<DataVector, 3>& tensor1,
21 : const tnsr::II<DataVector, 3>& tensor2);
22 : void fully_contract(gsl::not_null<Scalar<DataVector>*> result,
23 : gsl::not_null<DataVector*> buffer1,
24 : gsl::not_null<DataVector*> buffer2,
25 : const tnsr::II<DataVector, 3>& tensor1,
26 : const tnsr::II<DataVector, 3>& tensor2,
27 : const tnsr::ii<DataVector, 3>& metric);
28 : } // namespace detail
29 :
30 : /*!
31 : * \brief Add the nonlinear source to the Hamiltonian constraint on a flat
32 : * conformal background in Cartesian coordinates and with
33 : * \f$\bar{u}_{ij}=0=\beta^i\f$.
34 : *
35 : * Adds \f$\frac{1}{12}\psi^5 K^2 - 2\pi\psi^{5-n}\bar{\rho}\f$ where \f$n\f$ is
36 : * the `ConformalMatterScale` and \f$\bar{\rho}=\psi^n\rho\f$ is the
37 : * conformally-scaled energy density. Additional sources can be added with
38 : * `add_distortion_hamiltonian_sources` and
39 : * `add_curved_hamiltonian_or_lapse_sources`.
40 : *
41 : * \see Xcts
42 : */
43 : template <int ConformalMatterScale>
44 1 : void add_hamiltonian_sources(
45 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
46 : const Scalar<DataVector>& conformal_energy_density,
47 : const Scalar<DataVector>& extrinsic_curvature_trace,
48 : const Scalar<DataVector>& conformal_factor_minus_one);
49 :
50 : /// The linearization of `add_hamiltonian_sources`
51 : template <int ConformalMatterScale>
52 1 : void add_linearized_hamiltonian_sources(
53 : gsl::not_null<Scalar<DataVector>*> linearized_hamiltonian_constraint,
54 : const Scalar<DataVector>& conformal_energy_density,
55 : const Scalar<DataVector>& extrinsic_curvature_trace,
56 : const Scalar<DataVector>& conformal_factor_minus_one,
57 : const Scalar<DataVector>& conformal_factor_correction);
58 :
59 : /*!
60 : * \brief Add the "distortion" source term to the Hamiltonian constraint.
61 : *
62 : * Adds \f$-\frac{1}{8}\psi^{-7}\bar{A}^{ij}\bar{A}_{ij}\f$.
63 : *
64 : * \see Xcts
65 : * \see Xcts::Tags::LongitudinalShiftMinusDtConformalMetricOverLapseSquare
66 : */
67 1 : void add_distortion_hamiltonian_sources(
68 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
69 : const Scalar<DataVector>&
70 : longitudinal_shift_minus_dt_conformal_metric_over_lapse_square,
71 : const Scalar<DataVector>& conformal_factor_minus_one);
72 :
73 : /*!
74 : * \brief The linearization of `add_distortion_hamiltonian_sources`
75 : *
76 : * Note that this linearization is only w.r.t. \f$\psi\f$.
77 : */
78 1 : void add_linearized_distortion_hamiltonian_sources(
79 : gsl::not_null<Scalar<DataVector>*> linearized_hamiltonian_constraint,
80 : const Scalar<DataVector>&
81 : longitudinal_shift_minus_dt_conformal_metric_over_lapse_square,
82 : const Scalar<DataVector>& conformal_factor_minus_one,
83 : const Scalar<DataVector>& conformal_factor_correction);
84 :
85 : /*!
86 : * \brief Add the contributions from a curved background geometry to the
87 : * Hamiltonian constraint or lapse equation
88 : *
89 : * Adds \f$\frac{1}{8}\psi\bar{R}\f$. This term appears both in the Hamiltonian
90 : * constraint and the lapse equation (where in the latter \f$\psi\f$ is replaced
91 : * by \f$\alpha\psi\f$).
92 : *
93 : * This term is linear.
94 : *
95 : * \see Xcts
96 : */
97 1 : void add_curved_hamiltonian_or_lapse_sources(
98 : gsl::not_null<Scalar<DataVector>*> hamiltonian_or_lapse_equation,
99 : const Scalar<DataVector>& conformal_ricci_scalar,
100 : const Scalar<DataVector>& field, double add_constant = 0.);
101 :
102 : /*!
103 : * \brief Add the nonlinear source to the lapse equation on a flat conformal
104 : * background in Cartesian coordinates and with \f$\bar{u}_{ij}=0=\beta^i\f$.
105 : *
106 : * Adds \f$(\alpha\psi)\left(\frac{5}{12}\psi^4 K^2 + 2\pi\psi^{4-n}
107 : * \left(\bar{\rho} + 2\bar{S}\right)\right) + \psi^5
108 : * \left(\beta^i\partial_i K - \partial_t K\right)\f$ where \f$n\f$ is the
109 : * `ConformalMatterScale` and matter quantities are conformally-scaled.
110 : * Additional sources can be added with
111 : * `add_distortion_hamiltonian_and_lapse_sources` and
112 : * `add_curved_hamiltonian_or_lapse_sources`.
113 : *
114 : * \see Xcts
115 : */
116 : template <int ConformalMatterScale>
117 1 : void add_lapse_sources(
118 : gsl::not_null<Scalar<DataVector>*> lapse_equation,
119 : const Scalar<DataVector>& conformal_energy_density,
120 : const Scalar<DataVector>& conformal_stress_trace,
121 : const Scalar<DataVector>& extrinsic_curvature_trace,
122 : const Scalar<DataVector>& dt_extrinsic_curvature_trace,
123 : const Scalar<DataVector>& shift_dot_deriv_extrinsic_curvature_trace,
124 : const Scalar<DataVector>& conformal_factor_minus_one,
125 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one);
126 :
127 : /*!
128 : * \brief The linearization of `add_lapse_sources`
129 : *
130 : * Note that this linearization is only w.r.t. \f$\psi\f$ and \f$\alpha\psi\f$.
131 : * The linearization w.r.t. \f$\beta^i\f$ is added in
132 : * `add_curved_linearized_momentum_sources` or
133 : * `add_flat_cartesian_linearized_momentum_sources`.
134 : */
135 : template <int ConformalMatterScale>
136 1 : void add_linearized_lapse_sources(
137 : gsl::not_null<Scalar<DataVector>*> linearized_lapse_equation,
138 : const Scalar<DataVector>& conformal_energy_density,
139 : const Scalar<DataVector>& conformal_stress_trace,
140 : const Scalar<DataVector>& extrinsic_curvature_trace,
141 : const Scalar<DataVector>& dt_extrinsic_curvature_trace,
142 : const Scalar<DataVector>& shift_dot_deriv_extrinsic_curvature_trace,
143 : const Scalar<DataVector>& conformal_factor_minus_one,
144 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
145 : const Scalar<DataVector>& conformal_factor_correction,
146 : const Scalar<DataVector>& lapse_times_conformal_factor_correction);
147 :
148 : /*!
149 : * \brief Add the "distortion" source term to the Hamiltonian constraint and the
150 : * lapse equation.
151 : *
152 : * Adds \f$-\frac{1}{8}\psi^{-7}\bar{A}^{ij}\bar{A}_{ij}\f$ to the Hamiltonian
153 : * constraint and \f$\frac{7}{8}\alpha\psi^{-7}\bar{A}^{ij}\bar{A}_{ij}\f$ to
154 : * the lapse equation.
155 : *
156 : * \see Xcts
157 : * \see Xcts::Tags::LongitudinalShiftMinusDtConformalMetricSquare
158 : */
159 1 : void add_distortion_hamiltonian_and_lapse_sources(
160 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
161 : gsl::not_null<Scalar<DataVector>*> lapse_equation,
162 : const Scalar<DataVector>&
163 : longitudinal_shift_minus_dt_conformal_metric_square,
164 : const Scalar<DataVector>& conformal_factor_minus_one,
165 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one);
166 :
167 : /*!
168 : * \brief The linearization of `add_distortion_hamiltonian_and_lapse_sources`
169 : *
170 : * Note that this linearization is only w.r.t. \f$\psi\f$ and \f$\alpha\psi\f$.
171 : */
172 1 : void add_linearized_distortion_hamiltonian_and_lapse_sources(
173 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
174 : gsl::not_null<Scalar<DataVector>*> lapse_equation,
175 : const Scalar<DataVector>&
176 : longitudinal_shift_minus_dt_conformal_metric_square,
177 : const Scalar<DataVector>& conformal_factor_minus_one,
178 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
179 : const Scalar<DataVector>& conformal_factor_correction,
180 : const Scalar<DataVector>& lapse_times_conformal_factor_correction);
181 :
182 : /*!
183 : * \brief Add the nonlinear source to the momentum constraint and add the
184 : * "distortion" source term to the Hamiltonian constraint and lapse equation.
185 : *
186 : * Adds \f$\left((\bar{L}\beta)^{ij} - \bar{u}^{ij}\right)
187 : * \left(\frac{\partial_j (\alpha\psi)}{\alpha\psi}
188 : * - 7 \frac{\partial_j \psi}{\psi}\right)
189 : * + \partial_j\bar{u}^{ij}
190 : * + \frac{4}{3}\frac{\alpha\psi}{\psi}\bar{\gamma}^{ij}\partial_j K
191 : * + 16\pi\left(\alpha\psi\right)\psi^{3-n} \bar{S}^i\f$ to the momentum
192 : * constraint, where \f$n\f$ is the `ConformalMatterScale` and
193 : * \f$\bar{S}^i=\psi^n S^i\f$ is the conformally-scaled momentum density.
194 : *
195 : * Note that the \f$\partial_j\bar{u}^{ij}\f$ term is not the full covariant
196 : * divergence, but only the partial-derivatives part of it. The curved
197 : * contribution to this term can be added together with the curved contribution
198 : * to the flux divergence of the dynamic shift variable with the
199 : * `Elasticity::add_curved_sources` function.
200 : *
201 : * Also adds \f$-\frac{1}{8}\psi^{-7}\bar{A}^{ij}\bar{A}_{ij}\f$ to the
202 : * Hamiltonian constraint and
203 : * \f$\frac{7}{8}\alpha\psi^{-7}\bar{A}^{ij}\bar{A}_{ij}\f$ to the lapse
204 : * equation.
205 : *
206 : * \see Xcts
207 : */
208 : /// @{
209 : template <int ConformalMatterScale>
210 1 : void add_curved_momentum_sources(
211 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
212 : gsl::not_null<Scalar<DataVector>*> lapse_equation,
213 : gsl::not_null<tnsr::I<DataVector, 3>*> momentum_constraint,
214 : const tnsr::I<DataVector, 3>& conformal_momentum_density,
215 : const tnsr::i<DataVector, 3>& extrinsic_curvature_trace_gradient,
216 : const tnsr::ii<DataVector, 3>& conformal_metric,
217 : const tnsr::II<DataVector, 3>& inv_conformal_metric,
218 : const tnsr::I<DataVector, 3>& minus_div_dt_conformal_metric,
219 : const Scalar<DataVector>& conformal_factor_minus_one,
220 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
221 : const tnsr::I<DataVector, 3>& conformal_factor_flux,
222 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux,
223 : const tnsr::II<DataVector, 3>&
224 : longitudinal_shift_minus_dt_conformal_metric);
225 :
226 : template <int ConformalMatterScale>
227 1 : void add_flat_cartesian_momentum_sources(
228 : gsl::not_null<Scalar<DataVector>*> hamiltonian_constraint,
229 : gsl::not_null<Scalar<DataVector>*> lapse_equation,
230 : gsl::not_null<tnsr::I<DataVector, 3>*> momentum_constraint,
231 : const tnsr::I<DataVector, 3>& conformal_momentum_density,
232 : const tnsr::i<DataVector, 3>& extrinsic_curvature_trace_gradient,
233 : const tnsr::I<DataVector, 3>& minus_div_dt_conformal_metric,
234 : const Scalar<DataVector>& conformal_factor_minus_one,
235 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
236 : const tnsr::I<DataVector, 3>& conformal_factor_flux,
237 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux,
238 : const tnsr::II<DataVector, 3>&
239 : longitudinal_shift_minus_dt_conformal_metric);
240 : /// @}
241 :
242 : /// The linearization of `add_curved_momentum_sources`
243 : template <int ConformalMatterScale>
244 1 : void add_curved_linearized_momentum_sources(
245 : gsl::not_null<Scalar<DataVector>*> linearized_hamiltonian_constraint,
246 : gsl::not_null<Scalar<DataVector>*> linearized_lapse_equation,
247 : gsl::not_null<tnsr::I<DataVector, 3>*> linearized_momentum_constraint,
248 : const tnsr::I<DataVector, 3>& conformal_momentum_density,
249 : const tnsr::i<DataVector, 3>& extrinsic_curvature_trace_gradient,
250 : const tnsr::ii<DataVector, 3>& conformal_metric,
251 : const tnsr::II<DataVector, 3>& inv_conformal_metric,
252 : const Scalar<DataVector>& conformal_factor_minus_one,
253 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
254 : const tnsr::I<DataVector, 3>& conformal_factor_flux,
255 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux,
256 : const tnsr::II<DataVector, 3>& longitudinal_shift_minus_dt_conformal_metric,
257 : const Scalar<DataVector>& conformal_factor_correction,
258 : const Scalar<DataVector>& lapse_times_conformal_factor_correction,
259 : const tnsr::I<DataVector, 3>& shift_correction,
260 : const tnsr::I<DataVector, 3>& conformal_factor_flux_correction,
261 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux_correction,
262 : const tnsr::II<DataVector, 3>& longitudinal_shift_correction);
263 :
264 : /// The linearization of `add_flat_cartesian_momentum_sources`
265 : template <int ConformalMatterScale>
266 1 : void add_flat_cartesian_linearized_momentum_sources(
267 : gsl::not_null<Scalar<DataVector>*> linearized_hamiltonian_constraint,
268 : gsl::not_null<Scalar<DataVector>*> linearized_lapse_equation,
269 : gsl::not_null<tnsr::I<DataVector, 3>*> linearized_momentum_constraint,
270 : const tnsr::I<DataVector, 3>& conformal_momentum_density,
271 : const tnsr::i<DataVector, 3>& extrinsic_curvature_trace_gradient,
272 : const Scalar<DataVector>& conformal_factor_minus_one,
273 : const Scalar<DataVector>& lapse_times_conformal_factor_minus_one,
274 : const tnsr::I<DataVector, 3>& conformal_factor_flux,
275 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux,
276 : const tnsr::II<DataVector, 3>& longitudinal_shift_minus_dt_conformal_metric,
277 : const Scalar<DataVector>& conformal_factor_correction,
278 : const Scalar<DataVector>& lapse_times_conformal_factor_correction,
279 : const tnsr::I<DataVector, 3>& shift_correction,
280 : const tnsr::I<DataVector, 3>& conformal_factor_flux_correction,
281 : const tnsr::I<DataVector, 3>& lapse_times_conformal_factor_flux_correction,
282 : const tnsr::II<DataVector, 3>& longitudinal_shift_correction);
283 : } // namespace Xcts
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