adJoint.hpp

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/** \file adJoint.hpp
  * \brief Operators managing HO geometry derivatives
 
*/
 
#ifndef __ADJOINT_HPP__
#define __ADJOINT_HPP__
 
namespace MoFEM {
 
template <typename EleOp> struct AdJoint {
 
  using EntData = EntitiesFieldData::EntData;
  using OpType = typename EleOp::OpType;
 
  template <IntegrationType I> struct Integration {
 
    /**
     * @brief Operator to compute cofactor matrix derivatives for higher-order geometry
     * 
     * The cofactor matrix \f$\text{cof}(\mathbf{J})\f$ of the Jacobian matrix \f$\mathbf{J}\f$ 
     * is defined as:
     * \f[
     * \text{cof}(\mathbf{J}) = \det(\mathbf{J}) \cdot \mathbf{J}^{-T}
     * \f]
     * where \f$\mathbf{J}^{-T} = (\mathbf{J}^{-1})^T\f$ is the transpose of the inverse Jacobian.
     * 
     * For a 2D case with Jacobian matrix:
     * \f[
     * \mathbf{J} = \begin{pmatrix} 
     * J_{11} & J_{12} \\ 
     * J_{21} & J_{22} 
     * \end{pmatrix}
     * \f]
     * 
     * The cofactor matrix is:
     * \f[
     * \text{cof}(\mathbf{J}) = \begin{pmatrix} 
     * J_{22} & -J_{12} \\ 
     * -J_{21} & J_{11} 
     * \end{pmatrix}
     * \f]
     * 
     * This operator computes the derivative of the cofactor with respect to 
     * geometry parameters, which is essential for higher-order geometry sensitivity analysis.
     * The computed quantity is:
     * \f[
     * \frac{d}{d\alpha}\text{cof}(\mathbf{J}) = \frac{d}{d\alpha}(\det(\mathbf{J}) \cdot \mathbf{J}^{-T})
     * \f]
     * 
     * @tparam SPACE_DIM Spatial dimension (2D or 3D)
     */
    template <int SPACE_DIM>
    using OpGetCoFactor = OpGetCoFactorImpl<SPACE_DIM, I, EleOp>;
 
  };
};
 
}; // namespace MoFEM
 
#endif