2D Elastic Isotropic Strain Computation

template<typename FieldDerivativesType, std::enable_if_t<FieldDerivativesType::medium_tag == specfem::element::medium_tag::elastic_psv, int> = 0>
specfem::datatype::TensorPointViewType<type_real, 2, 2, FieldDerivativesType::using_simd> impl_compute_strain(const FieldDerivativesType &field_derivatives)

Compute symmetric strain tensor for 2D elastic P-SV waves.

Computes the symmetric strain tensor \(\boldsymbol{\varepsilon}\) from displacement gradients:

\[\begin{split} \boldsymbol{\varepsilon} = \begin{pmatrix} \varepsilon_{xx} & \varepsilon_{xz} \\ \varepsilon_{xz} & \varepsilon_{zz} \end{pmatrix} = \begin{pmatrix} \frac{\partial u_x}{\partial x} & \frac{1}{2}\left(\frac{\partial u_x}{\partial z} + \frac{\partial u_z}{\partial x}\right) \\ \frac{1}{2}\left(\frac{\partial u_x}{\partial z} + \frac{\partial u_z}{\partial x}\right) & \frac{\partial u_z}{\partial z} \end{pmatrix} \end{split}\]

Template Parameters:

FieldDerivativesType – Point field-derivatives type (deduced)

Parameters:

field_derivatives – Displacement gradients \(\nabla \mathbf{u}\)

Returns:

2×2 symmetric strain tensor \(\boldsymbol{\varepsilon}\)

template<typename FieldDerivativesType, std::enable_if_t<FieldDerivativesType::medium_tag == specfem::element::medium_tag::elastic_psv, int> = 0>
specfem::datatype::TensorPointViewType<type_real, 2, 2, FieldDerivativesType::using_simd> impl_compute_deviatoric_strain(const FieldDerivativesType &field_derivatives)

Compute deviatoric strain tensor for 2D elastic P-SV waves.

Computes the deviatoric strain \(\boldsymbol{\varepsilon}'\) by removing the volumetric component:

\[ \boldsymbol{\varepsilon}' = \boldsymbol{\varepsilon} - \frac{\text{tr}(\boldsymbol{\varepsilon})}{3}\mathbf{I} \]

where \(\text{tr}(\boldsymbol{\varepsilon}) = \varepsilon_{xx} + \varepsilon_{zz}\).

Under plane-strain conditions, the missing \(\varepsilon'_{yy} = -\frac{\text{tr}(\boldsymbol{\varepsilon})}{3}\) ensures \(\text{tr}(\boldsymbol{\varepsilon}') = 0\) in 3D.

Template Parameters:

FieldDerivativesType – Point field-derivatives type (deduced)

Parameters:

field_derivatives – Displacement gradients \(\nabla \mathbf{u}\)

Returns:

2×2 deviatoric strain tensor \(\boldsymbol{\varepsilon}'\)

3D Elastic Isotropic Strain Computation

template<typename FieldDerivativesType, std::enable_if_t<FieldDerivativesType::medium_tag == specfem::element::medium_tag::elastic, int> = 0>
specfem::datatype::TensorPointViewType<type_real, 3, 3, FieldDerivativesType::using_simd> impl_compute_strain(const FieldDerivativesType &field_derivatives)

Compute symmetric strain tensor for 3D elastic media.

Template Parameters:

FieldDerivativesType – Point field-derivatives type (deduced)

Parameters:

field_derivatives – Displacement gradients

Returns:

3×3 symmetric strain tensor

template<typename FieldDerivativesType, std::enable_if_t<FieldDerivativesType::medium_tag == specfem::element::medium_tag::elastic, int> = 0>
specfem::datatype::TensorPointViewType<type_real, 3, 3, FieldDerivativesType::using_simd> impl_compute_deviatoric_strain(const FieldDerivativesType &field_derivatives)

Compute deviatoric strain tensor for 3D elastic media.

Subtracts trace/3 from diagonal. In 3D the deviatoric trace is exactly zero.

Template Parameters:

FieldDerivativesType – Point field-derivatives type (deduced)

Parameters:

field_derivatives – Displacement gradients

Returns:

3×3 deviatoric strain tensor

template<bool UseSIMD>
specfem::datatype::simd<type_real, UseSIMD>::datatype impl_trace(const specfem::datatype::TensorPointViewType<type_real, 3, 3, UseSIMD> &tensor)

Trace of a 3×3 elastic strain tensor (ε_xx + ε_yy + ε_zz).

Template Parameters:

UseSIMD – Enable SIMD vectorization

Parameters:

tensor – 3×3 strain tensor

Returns:

Scalar trace value