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2/3. Add to pseudo Cartesian domain center function in mappings
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@EmilyBourne
EmilyBourne committed Oct 31, 2023
1 parent ddfc169 commit 031183c
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107 changes: 107 additions & 0 deletions vendor/sll/include/sll/mapping/circular_to_cartesian.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -202,4 +202,111 @@ class CircularToCartesian
assert(fabs(r) >= 1e-15);
return 1 / r * std::cos(p);
}



/**
* @brief Compute the full Jacobian matrix from the mapping to the pseudo-Cartesian mapping at the central point.
*
*
* Here, as @f$ \mathcal{G} = \mathcal{F} @f$ (see DiscreteToCartesian), the Jacobian matrix of
* @f$(\mathcal{F} \circ \mathcal{G}^{-1})^{-1} @f$ is the identity matrix.
* So, the pseudo-Cartesian Jacobian matrix for a circular mapping is given by :
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{11}(0, \theta) = 1, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{12}(0, \theta) = 0, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{21}(0, \theta) = 0, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{22}(0, \theta) = 1. @f$
*
*
*
* @param[in] grid
* The domain where the mapping is defined.
* @param[out] matrix
* The pseudo-Cartesian matrix evaluated at the central point.
*
*
* @see DiscreteToCartesian
* @see BslAdvection
* @see AdvectionDomain
*/
template <class Domain>
void to_pseudo_cartesian_jacobian_center_matrix(Domain const& grid, Matrix_2x2& matrix) const
{
matrix[0][0] = 1.;
matrix[0][1] = 0.;
matrix[1][0] = 0.;
matrix[1][1] = 1.;
}

/**
* @brief Compute the (1,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{11}(0, \theta) = 1. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (1,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see CircularToCartesian::to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_11_center(Domain const& grid) const
{
return 1.;
};

/**
* @brief Compute the (1,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{12}(0, \theta) = 0. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (1,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see CircularToCartesian::to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_12_center(Domain const& grid) const
{
return 0.;
};

/**
* @brief Compute the (2,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{21}(0, \theta) = 0. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (2,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see CircularToCartesian::to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_21_center(Domain const& grid) const
{
return 0.;
};

/**
* @brief Compute the (2,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{22}(0, \theta) = 1. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (2,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see CircularToCartesian::to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_22_center(Domain const& grid) const
{
return 1.;
};
};
108 changes: 108 additions & 0 deletions vendor/sll/include/sll/mapping/czarny_to_cartesian.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -346,4 +346,112 @@ class CzarnyToCartesian
const double fact_3 = m_e * xi / divisor;
return 1 / r * cos_theta / fact_3;
}


/**
* @brief Compute the full Jacobian matrix from the mapping to the pseudo-Cartesian mapping at the central point.
*
*
* The pseudo-Cartesian Jacobian matrix for a Czarny mapping is given by :
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{11}(0, \theta) = - \sqrt{1 + \varepsilon^2}, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{12}(0, \theta) = 0, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{21}(0, \theta) = 0, @f$
* - @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{22}(0, \theta) = \frac{2 - \sqrt{1 + \varepsilon^2}}{e \xi}. @f$
*
*
*
*
* @param[in] grid
* The domain where the mapping is defined.
* @param[out] matrix
* The pseudo-Cartesian matrix at the central point evaluated.
*
*
* @see DiscreteToCartesian
* @see BslAdvection
* @see AdvectionDomain
*/
template <class Domain>
void to_pseudo_cartesian_jacobian_center_matrix(Domain const& grid, Matrix_2x2& matrix) const
{
const double xi = std::sqrt(1. / (1. - m_epsilon * m_epsilon * 0.25));
const double sqrt_eps_2 = std::sqrt(1. + m_epsilon * m_epsilon);
matrix[0][0] = -sqrt_eps_2;
matrix[0][1] = 0.;
matrix[1][0] = 0.;
matrix[1][1] = (2 - sqrt_eps_2) / m_e / xi;
}

/**
* @brief Compute the (1,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{11}(0, \theta) = - \sqrt{1 + \varepsilon^2}. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (1,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_11_center(Domain const& grid) const
{
return -std::sqrt(1 + m_epsilon * m_epsilon);
}

/**
* @brief Compute the (1,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{12}(0, \theta) = 0. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (1,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_12_center(Domain const& grid) const
{
return 0;
}

/**
* @brief Compute the (2,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{21}(0, \theta) = 0. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (2,1) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_21_center(Domain const& grid) const
{
return 0;
}

/**
* @brief Compute the (2,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @f$ (J_{\mathcal{F}}J_{\mathcal{G}}^{-1})^{-1}_{22}(0, \theta) = \frac{2 - \sqrt{1 + \varepsilon^2}}{e \xi}. @f$
*
* @param[in] grid
* The domain where the mapping is defined.
*
* @return A double with the (2,2) coefficient of the pseudo-Cartesian Jacobian matrix at the central point.
*
* @see to_pseudo_cartesian_jacobian_center_matrix
*/
template <class Domain>
double to_pseudo_cartesian_jacobian_22_center(Domain const& grid) const
{
const double xi = std::sqrt(1. / (1. - m_epsilon * m_epsilon * 0.25));
return (2 - std::sqrt(1 + m_epsilon * m_epsilon)) / m_e / xi;
}
};
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