Compute KleinGordon Cce sources

src/Evolution/Systems/Cce/CMakeLists.txt

@@ -12,6 +12,7 @@ spectre_target_sources(
   BoundaryData.cpp
   Equations.cpp
   GaugeTransformBoundaryData.cpp
+  KleinGordonSource.cpp
   LinearOperators.cpp
   LinearSolve.cpp
   NewmanPenrose.cpp
@@ -47,6 +48,7 @@ spectre_target_headers(
   SpecBoundaryData.hpp
   SwshDerivatives.hpp
   System.hpp
+  KleinGordonSource.hpp
   KleinGordonSystem.hpp
   Tags.hpp
   WorldtubeBufferUpdater.hpp

src/Evolution/Systems/Cce/Components/KleinGordonCharacteristicEvolution.hpp

@@ -9,6 +9,7 @@
 #include "Evolution/Systems/Cce/Actions/InitializeKleinGordonVariables.hpp"
 #include "Evolution/Systems/Cce/Actions/PrecomputeKleinGordonSourceVariables.hpp"
 #include "Evolution/Systems/Cce/Components/CharacteristicEvolution.hpp"
+#include "Evolution/Systems/Cce/KleinGordonSource.hpp"
 #include "Evolution/Systems/Cce/KleinGordonSystem.hpp"
 #include "Parallel/GlobalCache.hpp"
 #include "Parallel/Local.hpp"
@@ -89,6 +90,10 @@ struct KleinGordonCharacteristicEvolution
                           Actions::CalculatePsi0AndDerivAtInnerBoundary,
                           tmpl::list<>>,
       Actions::PrecomputeKleinGordonSourceVariables,
+      tmpl::transform<
+          bondi_hypersurface_step_tags,
+          tmpl::bind<::Actions::MutateApply,
+                     tmpl::bind<ComputeKleinGordonSource, tmpl::_1>>>,
       tmpl::transform<bondi_hypersurface_step_tags,
                       tmpl::bind<hypersurface_computation, tmpl::_1>>,
       Actions::FilterSwshVolumeQuantity<Tags::BondiH>,
@@ -126,6 +131,10 @@ struct KleinGordonCharacteristicEvolution
                           Actions::CalculatePsi0AndDerivAtInnerBoundary,
                           tmpl::list<>>,
       Actions::PrecomputeKleinGordonSourceVariables,
+      tmpl::transform<
+          bondi_hypersurface_step_tags,
+          tmpl::bind<::Actions::MutateApply,
+                     tmpl::bind<ComputeKleinGordonSource, tmpl::_1>>>,
       tmpl::transform<bondi_hypersurface_step_tags,
                       tmpl::bind<hypersurface_computation, tmpl::_1>>,
       Actions::FilterSwshVolumeQuantity<Tags::BondiH>,

src/Evolution/Systems/Cce/KleinGordonSource.cpp

@@ -0,0 +1,57 @@
+// Distributed under the MIT License.
+// See LICENSE.txt for details.
+
+#include "Evolution/Systems/Cce/KleinGordonSource.hpp"
+
+namespace Cce {
+
+void ComputeKleinGordonSource<Tags::BondiBeta>::apply(
+    gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_source_beta,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& dy_kg_psi,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& one_minus_y) {
+  get(*kg_source_beta) = 2. * M_PI * get(one_minus_y) * square(get(dy_kg_psi));
+}
+
+void ComputeKleinGordonSource<Tags::BondiQ>::apply(
+    gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> kg_source_q,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& dy_kg_psi,
+    const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi) {
+  get(*kg_source_q) = 16. * M_PI * get(eth_kg_psi) * get(dy_kg_psi);
+}
+
+void ComputeKleinGordonSource<Tags::BondiU>::apply(
+    gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> kg_source_u,
+    const size_t l_max, const size_t number_of_radial_points) {
+  const size_t volume_size =
+      Spectral::Swsh::number_of_swsh_collocation_points(l_max) *
+      number_of_radial_points;
+  get(*kg_source_u) = SpinWeighted<ComplexDataVector, 1>{volume_size, 0.0};
+}
+
+void ComputeKleinGordonSource<Tags::BondiW>::apply(
+    gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_source_w,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& exp_2_beta,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_k,
+    const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
+    const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi) {
+  SpinWeighted<ComplexDataVector, 0> complex_part;
+  SpinWeighted<ComplexDataVector, 0> real_part;
+
+  complex_part.data() =
+      2.0 * real(get(bondi_j).data() * square(conj(get(eth_kg_psi))).data());
+  real_part.data() =
+      -2.0 * get(bondi_k).data() * square(abs(get(eth_kg_psi).data()));
+  get(*kg_source_w) =
+      M_PI * get(exp_2_beta) / get(bondi_r) * (complex_part + real_part);
+}
+
+void ComputeKleinGordonSource<Tags::BondiH>::apply(
+    gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> kg_source_h,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& exp_2_beta,
+    const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
+    const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi) {
+  get(*kg_source_h) =
+      2 * M_PI * get(exp_2_beta) / get(bondi_r) * square(get(eth_kg_psi));
+}
+}  // namespace Cce

src/Evolution/Systems/Cce/KleinGordonSource.hpp

@@ -0,0 +1,139 @@
+// Distributed under the MIT License.
+// See LICENSE.txt for details.
+
+#pragma once
+
+#include "Evolution/Systems/Cce/OptionTags.hpp"
+#include "Evolution/Systems/Cce/Tags.hpp"
+#include "Utilities/Gsl.hpp"
+#include "Utilities/TMPL.hpp"
+
+namespace Cce {
+
+/*!
+ * \brief Computes `Tags::KleinGordonSource<Tag>` for the tags evolved by
+ * Klein-Gordon Cce.
+ *
+ * \details In scalar-tensor theory, the Cce hypersurface equations get
+ * additional source terms contributed by the stress-energy tensor of the scalar
+ * field. The tag `Tags::KleinGordonSource<Tag>` stores the corresponding volume
+ * data.
+ */
+template <typename Tag>
+struct ComputeKleinGordonSource;
+
+/*!
+ * \brief Computes the Klein-Gordon source of the Bondi \f$\beta\f$
+ *
+ * \details The source reads:
+ *
+ * \f{align*}{
+ * 2 \pi (1-y) (\partial_y\psi)^2,
+ * \f}
+ * where \f$\psi\f$ is the Klein-Gordon (scalar) field.
+ */
+template <>
+struct ComputeKleinGordonSource<Tags::BondiBeta> {
+  using return_tags = tmpl::list<Tags::KleinGordonSource<Tags::BondiBeta>>;
+  using argument_tags =
+      tmpl::list<Tags::Dy<Tags::KleinGordonPsi>, Tags::OneMinusY>;
+  static void apply(
+      gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_source_beta,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& dy_kg_psi,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& one_minus_y);
+};
+
+/*!
+ * \brief Computes the Klein-Gordon source of the Bondi \f$Q\f$
+ *
+ * \details Following the nomenclature of \cite Moxon2020gha and their Eq. (49),
+ * the scalar field contributes only to the regular part of the source term
+ * \f$S_2^R\f$. The expression reads:
+ *
+ * \f{align*}{
+ * 16 \pi \eth\psi \partial_y\psi,
+ * \f}
+ * where \f$\psi\f$ is the Klein-Gordon (scalar) field.
+ */
+template <>
+struct ComputeKleinGordonSource<Tags::BondiQ> {
+  using return_tags = tmpl::list<Tags::KleinGordonSource<Tags::BondiQ>>;
+  using argument_tags =
+      tmpl::list<Tags::Dy<Tags::KleinGordonPsi>,
+                 Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
+                                                  Spectral::Swsh::Tags::Eth>>;
+  static void apply(
+      gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> kg_source_q,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& dy_kg_psi,
+      const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi);
+};
+
+/*!
+ * \brief Computes the Klein-Gordon source of the Bondi \f$U\f$
+ *
+ * \details The source vanishes.
+ */
+template <>
+struct ComputeKleinGordonSource<Tags::BondiU> {
+  using return_tags = tmpl::list<Tags::KleinGordonSource<Tags::BondiU>>;
+  using argument_tags = tmpl::list<Tags::LMax, Tags::NumberOfRadialPoints>;
+  static void apply(
+      gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 1>>*> kg_source_u,
+      size_t l_max, size_t number_of_radial_points);
+};
+
+/*!
+ * \brief Computes the Klein-Gordon source of the Bondi \f$W\f$
+ *
+ * \details Following the nomenclature of \cite Moxon2020gha and their Eq. (49),
+ * the scalar field contributes only to the regular part of the source term
+ * \f$S_2^R\f$. The expression reads:
+ *
+ * \f{align*}{
+ * \frac{\pi e^{2\beta}}{R} \left[J(\bar{\eth}\psi)^2 + \bar{J}(\eth
+ * \psi)^2-2K \eth\psi\bar{\eth}\psi\right],
+ * \f}
+ * where \f$\psi\f$ is the Klein-Gordon (scalar) field.
+ */
+template <>
+struct ComputeKleinGordonSource<Tags::BondiW> {
+  using return_tags = tmpl::list<Tags::KleinGordonSource<Tags::BondiW>>;
+  using argument_tags =
+      tmpl::list<Tags::Exp2Beta, Tags::BondiR, Tags::BondiK, Tags::BondiJ,
+                 Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
+                                                  Spectral::Swsh::Tags::Eth>>;
+  static void apply(
+      gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 0>>*> kg_source_w,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& exp_2_beta,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_k,
+      const Scalar<SpinWeighted<ComplexDataVector, 2>>& bondi_j,
+      const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi);
+};
+
+/*!
+ * \brief Computes the Klein-Gordon source of the Bondi \f$H\f$
+ *
+ * \details Following the nomenclature of \cite Moxon2020gha and their Eq. (50),
+ * the scalar field contributes only to the regular part of the source term
+ * \f$S_3^R\f$. The expression reads:
+ *
+ * \f{align*}{
+ * 2 \pi \frac{e^{2\beta}}{R}(\eth\psi)^2,
+ * \f}
+ * where \f$\psi\f$ is the Klein-Gordon (scalar) field.
+ */
+template <>
+struct ComputeKleinGordonSource<Tags::BondiH> {
+  using return_tags = tmpl::list<Tags::KleinGordonSource<Tags::BondiH>>;
+  using argument_tags =
+      tmpl::list<Tags::Exp2Beta, Tags::BondiR,
+                 Spectral::Swsh::Tags::Derivative<Tags::KleinGordonPsi,
+                                                  Spectral::Swsh::Tags::Eth>>;
+  static void apply(
+      gsl::not_null<Scalar<SpinWeighted<ComplexDataVector, 2>>*> kg_source_h,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& exp_2_beta,
+      const Scalar<SpinWeighted<ComplexDataVector, 0>>& bondi_r,
+      const Scalar<SpinWeighted<ComplexDataVector, 1>>& eth_kg_psi);
+};
+}  // namespace Cce

tests/Unit/Evolution/Systems/Cce/Actions/CMakeLists.txt

@@ -17,6 +17,7 @@ set(LIBRARY_SOURCES
   Test_InitializeKleinGordonFirstHypersurface.cpp
   Test_InitializeKleinGordonWorldtubeBoundary.cpp
   Test_InitializeWorldtubeBoundary.cpp
+  Test_KleinGordonCceCalculations.cpp
   Test_KleinGordonH5BoundaryCommunication.cpp
   Test_Psi0Matching.cpp
   Test_RequestBoundaryData.cpp