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              : /// \cond
       9              : class DataVector;
      10              : template <size_t Dim>
      11              : class Mesh;
      12              : /// \endcond
      13              : 
      14              : namespace domain {
      15              : /*!
      16              :  * \brief Estimate of how much a function can exceed its extrema over the
      17              :  * grid points of an element anywhere inside the element, given its
      18              :  * `grid_point_values`.
      19              :  *
      20              :  * The extrema of a coordinate (or of the distance from a point) over the grid
      21              :  * points of a curved element can be smaller than over the whole element, e.g.
      22              :  * because the center of a curved face is not a grid point. Between
      23              :  * neighboring grid points, a function exceeds the linear interpolant between
      24              :  * them by at most \f$h^2 \max|f''|/8\f$, where \f$h\f$ is the spacing in the
      25              :  * logical coordinate and \f$f''\f$ is the second derivative with respect to
      26              :  * it. The padding is the sum of this bound over the logical dimensions, with
      27              :  * the second derivatives estimated by divided differences, so it vanishes for
      28              :  * functions that are linear in the logical coordinates (e.g. the coordinates of
      29              :  * elements with straight edges). For quadratures whose grid points don't
      30              :  * include the element boundaries (e.g. Gauss), a term for the parts of the
      31              :  * element beyond the outermost grid points is included. It should be used as a
      32              :  * cheap test whether a point can be in the element.
      33              :  *
      34              :  * \param mesh the mesh of the element, at whose grid points
      35              :  * `grid_point_values` are given
      36              :  * \param grid_point_values the values at the grid points of `mesh` of a
      37              :  * function that is smooth in the element, e.g. a coordinate or the distance
      38              :  * from a point
      39              :  */
      40            1 : double extrema_padding(const Mesh<3>& mesh,
      41              :                        const DataVector& grid_point_values);
      42              : }  // namespace domain