/*
This file is part of t8code.
t8code is a C library to manage a collection (a forest) of multiple
connected adaptive space-trees of general element classes in parallel.
Copyright (C) 2015 the developers
t8code is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
t8code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with t8code; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/** file t8_example_common.hxx
* This header declares datatypes and functions that are used by multiple
* examples of t8code. This includes adaptation function to adapt at a zero
* level-set of a level-set function and various 2 and 3 dimensional vector
* fields that can serve as fluid velocities.
*/
#ifndef T8_EXAMPLE_COMMON_H
#define T8_EXAMPLE_COMMON_H
#include <t8.h>
#include <t8_forest/t8_forest_general.h>
#include <t8_types/t8_vec.hxx>
/** A levelset function in 3+1 space dimensions. */
typedef double (*t8_example_level_set_fn) (const t8_3D_point &, double, void *);
/** Struct to handle refinement around a level-set function. */
typedef struct
{
t8_example_level_set_fn L; /**< The level set function. */
void *udata; /**< Data pointer that is passed to L */
double band_width; /**< Width of max_level elements around the zero-level set */
double t; /**< Time value passed to levelset function */
int min_level; /**< The minimal refinement level. Elements with this level will not be coarsened. */
int max_level; /**< The maximum refinement level. Elements with this level will not be refined. */
} t8_example_level_set_struct_t;
/** Function pointer for real valued functions from d+1 space dimensions
* functions f: R^d x R -> R */
typedef double (*t8_scalar_function_1d_fn) (double x, double t);
typedef double (*t8_scalar_function_2d_fn) (const t8_point<2> &x, const double t);
typedef double (*t8_scalar_function_3d_fn) (const t8_3D_point &x, const double t);
/** Function pointer for a vector valued function f: R^3 x R -> R */
typedef void (*t8_flow_function_3d_fn) (const t8_3D_point &x_in, const double t, t8_3D_vec &x_out);
/* function declarations */
/** Query whether a given element is within a prescribed distance to the zero level-set
* of a level-set function.
* \param [in] forest The forest.
* \param [in] ltreeid A local tree in \a forest.
* \param [in] element An element of tree \a ltreeid in \a forest.
* \param [in] levelset The level-set function.
* \param [in] band_width Check whether the element is within a band of
* \a band_width many elements of its size.
* \param [in] t Time value passed to \a levelset.
* \param [in] udata User data passed to \a levelset.
* \return True if the absolute value of \a levelset at \a element's midpoint
* is smaller than \a band_width * \a element's diameter.
* False otherwise.
* If \a band_width = 0 then the return value is true if and only if
* the zero level-set passes through \a element.
*/
int
t8_common_within_levelset (t8_forest_t forest, const t8_locidx_t ltreeid, const t8_element_t *element,
t8_example_level_set_fn levelset, double band_width, double t, void *udata);
/** Adapt a forest such that always the second child of the first
* tree is refined and no other elements. This results in a highly
* imbalanced forest.
*/
int
t8_common_adapt_balance (t8_forest_t forest, t8_forest_t forest_from, t8_locidx_t which_tree,
const t8_eclass_t tree_class, t8_locidx_t lelement_id, const t8_scheme_c *scheme,
const int is_family, const int num_elements, t8_element_t *elements[]);
/** Adapt a forest along a given level-set function.
* The user data of forest must be a pointer to a \a t8_example_level_set_struct_t.
* An element in the forest is refined, if it is in a band of \a band_with many
* \a max_level elements around the zero level-set Gamma = { x | L(x) = 0}
*/
/* TODO: Currently the band_width control is not working yet.
* if band_with = 0, then all elements that are touched by the zero LS are refined. */
int
t8_common_adapt_level_set (t8_forest_t forest, t8_forest_t forest_from, t8_locidx_t which_tree,
const t8_eclass_t tree_class, t8_locidx_t lelement_id, const t8_scheme_c *scheme,
const int is_family, const int num_elements, t8_element_t *elements[]);
/** Real valued functions defined in t8_example_common_functions.h */
typedef struct
{
t8_3D_point M;
/**< midpoint */
double radius;
/**< radius */
} t8_levelset_sphere_data_t;
/** Distance to a sphere with given midpoint and radius.
* data is interpreted as t8_levelset_sphere_data_t.
* \return dist (x,data->M) - data->radius
*/
double
t8_levelset_sphere (const t8_3D_point &x, double t, void *data);
/** Returns always 1.
* \return 1
*/
double
t8_scalar3d_constant_one (const double x[3], double t);
/** Returns always 0.
* \return 0
*/
double
t8_scalar3d_constant_zero (const double x[3], double t);
/** Return the x-coordinate of the input.
* \return x[0]
*/
double
t8_scalar3d_project_x (const double x[3], double t);
/** This function is =1 if the 0.25 <= x <= 0.75 and 0 else. */
double
t8_scalar3d_step_function (const double x[3], double t);
/** This function is =1 if 0.25 <= x <= 0.75,
* it is 0 outside of 0.25-eps and 0.75+eps,
* it interpolates linearly in between. eps = 0.1 **/
double
t8_scalar3d_almost_step_function (const double x[3], double t);
/** A 1-d Bell-curve centered around 0.5 */
double
t8_scalar3d_exp_distribution (const double x[3], double t);
/** Sinus of 2pi x_0
* \return sin (2pi x[0])
*/
double
t8_scalar3d_sinx (const double x[3], double t);
/** Sinus of x times cosinus of y
* \return sin (2pi x[0]) * cos (2pi x[1])
*/
double
t8_scalar3d_sinx_cosy (const double x[3], double t);
/** Sinus of 10 * x times cosinus of y times z
* \return 10 * sin (2pi x[0]) * cos (2pi x[1]) * x[3]
*/
double
t8_scalar3d_sinx_cosy_z (const double x[3], double t);
/** Sinus of t
* \return sin (2pi t)
*/
double
t8_scalar3d_sint (const double x[3], double t);
/** Level-set function of a sphere around origin with radius 0.75
* \return |x| - 0.75
*/
double
t8_scalar3d_sphere_75_radius (const t8_3D_vec &x, const double t);
/** Level-set function of a sphere around M = (0.5,0.5,0.5) with radius 0.375
* \return |x - M| - 0.375
*/
double
t8_scalar3d_sphere_05_midpoint_375_radius (const t8_3D_vec &x, const double t);
/** Level-set function of a sphere around M = (0.3,0.3,0.3) with radius 0.25
* \return |x - M| - 0.25
*/
double
t8_scalar3d_sphere_03_midpoint_25_radius (const t8_3D_vec &x, const double t);
/** Level-set function of a sphere around M = (0.5,0.5,0) with radius 0.375
* \return |x - M| - 0.375
*/
double
t8_scalar3d_sphere_05_0z_midpoint_375_radius (const t8_3D_vec &x, const double t);
/** Flow functions */
/** Returns always 1 in each coordinate.
*/
void
t8_flow_constant_one_vec (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
/** Sets the first coordinate to 1, all other to 0. */
void
t8_flow_constant_one_x_vec (const t8_3D_point &x, const double t, t8_3D_vec &x_ou);
/** Sets the first and second coordinate to 1, the third to 0. */
void
t8_flow_constant_one_xy_vec (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
/** Sets all coordinates to a nonzero constant. */
void
t8_flow_constant_one_xyz_vec (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
/** Transform the unit square to [-0.5,0.5]^2 and computes
* x = 2pi*y, y = -2pi*x
*/
void
t8_flow_rotation_2d (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
void
t8_flow_compressible (const t8_3D_point &x_in, const double t, t8_3D_vec &x_out);
/** Incompressible flow in unit cube */
void
t8_flow_incomp_cube_flow (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
/** 2d flow around a circle with radius R = 1 and
* constant inflow with x-speed U = 1.
* See https://doi.org/10.13140/RG.2.2.34714.11203 */
void
t8_flow_around_circle (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
void
t8_flow_stokes_flow_sphere_shell (const t8_3D_point &x_in, const double t, t8_3D_vec &x_out);
void
t8_flow_around_circle_with_angular_velocity (const t8_3D_point &x, const double t, t8_3D_vec &x_out);
#endif /* !T8_EXAMPLE_COMMON_H */
