Line data    Source code

       1           1 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : /// \file
       5             : /// Defines ScalarWave::Solutions and SecondOrderScalarWave::Solutions
       6             : 
       7             : #pragma once
       8             : 
       9             : namespace ScalarWave {
      10             : /*!
      11             :  * \ingroup AnalyticSolutionsGroup
      12             :  * \brief Holds analytic solutions to the first-order reduction of the
      13             :  * Euclidean wave equation.
      14             :  *
      15             :  * The first-order system evolves \f$\Psi\f$, \f$\Pi\f$, and \f$\Phi_j\f$:
      16             :  * \f{align*}
      17             :  * \partial_t \Psi &= -\Pi, \\
      18             :  * \partial_t \Pi &= -\delta^{ij}\partial_i\Phi_j, \\
      19             :  * \partial_t \Phi_j &= -\partial_j\Pi.
      20             :  * \f}
      21             :  */
      22             : namespace Solutions {}
      23             : }  // namespace ScalarWave
      24             : 
      25             : /*!
      26             :  * \ingroup AnalyticSolutionsGroup
      27             :  * \brief Holds analytic solutions to the second-order-in-space formulation of
      28             :  * the Euclidean wave equation.
      29             :  *
      30             :  * The second-order-in-space system evolves \f$\Psi\f$ and \f$\Pi\f$, while
      31             :  * \f$\Phi_j\f$ is auxiliary:
      32             :  * \f{align*}
      33             :  * \partial_t \Psi &= -\Pi, \\
      34             :  * \partial_t \Pi &= -\delta^{ij}\partial_i\Phi_j, \\
      35             :  * \Phi_j &= \partial_j\Psi.
      36             :  * \f}
      37             :  */
      38             : namespace SecondOrderScalarWave::Solutions {}