MoFEM::AdJoint< EleOp >::Integration< I > Struct Template Reference

#include "src/finite_elements/adJoint.hpp"

Public Types
template<int SPACE_DIM>
using	OpGetCoFactor = OpGetCoFactorImpl< SPACE_DIM, I, EleOp >
	Operator to compute cofactor matrix derivatives for higher-order geometry.

Detailed Description

template<typename EleOp>
template<IntegrationType I>
struct MoFEM::AdJoint< EleOp >::Integration< I >

Examples

mofem/tutorials/vec-7/adjoint.cpp.

Definition at line 16 of file adJoint.hpp.

Member Typedef Documentation

OpGetCoFactor

template<typename EleOp >

template<IntegrationType I>

template<int SPACE_DIM>

using MoFEM::AdJoint< EleOp >::Integration< I >::OpGetCoFactor = OpGetCoFactorImpl<SPACE_DIM, I, EleOp>

Operator to compute cofactor matrix derivatives for higher-order geometry.

The cofactor matrix \(\text{cof}(\mathbf{J})\) of the Jacobian matrix \(\mathbf{J}\) is defined as:

\[ \text{cof}(\mathbf{J}) = \det(\mathbf{J}) \cdot \mathbf{J}^{-T} \]

where \(\mathbf{J}^{-T} = (\mathbf{J}^{-1})^T\) is the transpose of the inverse Jacobian.

For a 2D case with Jacobian matrix:

\[ \mathbf{J} = \begin{pmatrix} J_{11} & J_{12} \\ J_{21} & J_{22} \end{pmatrix} \]

The cofactor matrix is:

\[ \text{cof}(\mathbf{J}) = \begin{pmatrix} J_{22} & -J_{12} \\ -J_{21} & J_{11} \end{pmatrix} \]

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:

\[ \frac{d}{d\alpha}\text{cof}(\mathbf{J}) = \frac{d}{d\alpha}(\det(\mathbf{J}) \cdot \mathbf{J}^{-T}) \]

Template Parameters

SPACE_DIM

Spatial dimension (2D or 3D)

Definition at line 54 of file adJoint.hpp.

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The documentation for this struct was generated from the following file:

• src/finite_elements/adJoint.hpp