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 {}