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 : namespace gh {
12 : namespace gauges {
13 : namespace DampedHarmonicGauge_detail {
14 : /*
15 : * Spatial weight function used in the damped harmonic gauge source
16 : * function.
17 : *
18 : * The spatial weight function is:
19 : * \f{align*}{
20 : * W(x^i) = \exp(- (r / \sigma_r)^2),
21 : * \f}
22 : *
23 : * where \f$r=\sqrt{x^i\delta_{ij}x^j}\f$ is the coordinate radius, and
24 : * \f$\sigma_r\f$ is the width of the Gaussian.
25 : *
26 : * This function can be written with an extra factor inside the exponent in
27 : * literature, e.g. \cite Deppe2018uye. We absorb that in \f$\sigma_r\f$.
28 : */
29 : template <typename DataType, size_t SpatialDim, typename Frame>
30 : void spatial_weight_function(gsl::not_null<Scalar<DataType>*> weight,
31 : const tnsr::I<DataType, SpatialDim, Frame>& coords,
32 : double sigma_r);
33 :
34 : /*
35 : * Spacetime derivatives of the spatial weight function that enters the
36 : * damped harmonic gauge source function.
37 : *
38 : * Compute the derivatives:
39 : * \f{align*}{
40 : * \partial_a W(x^i)= \partial_a \exp(- (r/\sigma_r)^2)
41 : * = (-2 * x^i / \sigma_r^2) * exp(-(r/\sigma_r)^2)
42 : * \f}
43 : *
44 : * where \f$r=\sqrt{x^i\delta_{ij}x^j}\f$ is the coordinate radius, and
45 : * \f$\sigma_r\f$ is the width of the Gaussian. Since the weight function is
46 : * spatial, the time derivative is always zero.
47 : */
48 : template <typename DataType, size_t SpatialDim, typename Frame>
49 : void spacetime_deriv_of_spatial_weight_function(
50 : gsl::not_null<tnsr::a<DataType, SpatialDim, Frame>*> d4_weight,
51 : const tnsr::I<DataType, SpatialDim, Frame>& coords, double sigma_r,
52 : const Scalar<DataType>& weight_function);
53 :
54 : /*
55 : * The log factor that appears in damped harmonic gauge source function.
56 : *
57 : * Calculates: \f$ logF = \mathrm{log}(g^p/N) \f$.
58 : */
59 : template <typename DataType>
60 : void log_factor_metric_lapse(gsl::not_null<Scalar<DataType>*> logfac,
61 : const Scalar<DataType>& lapse,
62 : const Scalar<DataType>& sqrt_det_spatial_metric,
63 : double exponent);
64 :
65 : template <typename DataType>
66 : Scalar<DataType> log_factor_metric_lapse(
67 : const Scalar<DataType>& lapse,
68 : const Scalar<DataType>& sqrt_det_spatial_metric, double exponent);
69 :
70 : /*
71 : * Spacetime derivatives of the log factor that appears in the
72 : * damped harmonic gauge source function.
73 : *
74 : * Computes the spacetime derivatives:
75 : * \f{align*}{
76 : * \partial_a logF = (p/g)\partial_a g - (1/N)\partial_a N
77 : * \f}
78 : */
79 : template <typename DataType, size_t SpatialDim, typename Frame>
80 : void spacetime_deriv_of_log_factor_metric_lapse(
81 : gsl::not_null<tnsr::a<DataType, SpatialDim, Frame>*> d4_logfac,
82 : const Scalar<DataType>& lapse,
83 : const tnsr::I<DataType, SpatialDim, Frame>& shift,
84 : const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
85 : const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,
86 : const Scalar<DataType>& sqrt_det_spatial_metric,
87 : const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric,
88 : const tnsr::aa<DataType, SpatialDim, Frame>& pi,
89 : const tnsr::iaa<DataType, SpatialDim, Frame>& phi, double exponent);
90 :
91 : template <typename DataType, size_t SpatialDim, typename Frame>
92 : tnsr::a<DataType, SpatialDim, Frame> spacetime_deriv_of_log_factor_metric_lapse(
93 : const Scalar<DataType>& lapse,
94 : const tnsr::I<DataType, SpatialDim, Frame>& shift,
95 : const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
96 : const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,
97 : const Scalar<DataType>& sqrt_det_spatial_metric,
98 : const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric,
99 : const tnsr::aa<DataType, SpatialDim, Frame>& pi,
100 : const tnsr::iaa<DataType, SpatialDim, Frame>& phi, double exponent);
101 :
102 : /*
103 : * Spacetime derivatives of the log factor (that appears in
104 : * damped harmonic gauge source function), raised to an exponent.
105 : *
106 : * Computes the spacetime derivatives:
107 : * \f{align*}{
108 : * \partial_a (logF)^q = q (logF)^{q-1} \partial_a (logF)
109 : * \f}
110 : */
111 : template <typename DataType, size_t SpatialDim, typename Frame>
112 : void spacetime_deriv_of_power_log_factor_metric_lapse(
113 : gsl::not_null<tnsr::a<DataType, SpatialDim, Frame>*> d4_powlogfac,
114 : const Scalar<DataType>& lapse,
115 : const tnsr::I<DataType, SpatialDim, Frame>& shift,
116 : const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
117 : const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,
118 : const Scalar<DataType>& sqrt_det_spatial_metric,
119 : const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric,
120 : const tnsr::aa<DataType, SpatialDim, Frame>& pi,
121 : const tnsr::iaa<DataType, SpatialDim, Frame>& phi, double g_exponent,
122 : int exponent);
123 :
124 : template <typename DataType, size_t SpatialDim, typename Frame>
125 : tnsr::a<DataType, SpatialDim, Frame>
126 : spacetime_deriv_of_power_log_factor_metric_lapse(
127 : const Scalar<DataType>& lapse,
128 : const tnsr::I<DataType, SpatialDim, Frame>& shift,
129 : const tnsr::A<DataType, SpatialDim, Frame>& spacetime_unit_normal,
130 : const tnsr::II<DataType, SpatialDim, Frame>& inverse_spatial_metric,
131 : const Scalar<DataType>& sqrt_det_spatial_metric,
132 : const tnsr::ii<DataType, SpatialDim, Frame>& dt_spatial_metric,
133 : const tnsr::aa<DataType, SpatialDim, Frame>& pi,
134 : const tnsr::iaa<DataType, SpatialDim, Frame>& phi, double g_exponent,
135 : int exponent);
136 :
137 : } // namespace DampedHarmonicGauge_detail
138 : } // namespace gauges
139 : } // namespace gh
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