`specfem::algorithms::gradient`¶

template<typename ChunkIndexType, typename VectorFieldType, typename QuadratureType, typename CallbackFunctor, std::enable_if_t<specfem::data_access::is_chunk_element<VectorFieldType>::value && VectorFieldType::dimension_tag == specfem::dimension::type::dim2, int> = 0> void gradient(const ChunkIndexType &chunk_index, const specfem::assembly::jacobian_matrix<specfem::dimension::type::dim2> &jacobian_matrix, const QuadratureType &quadrature, const VectorFieldType &f, const CallbackFunctor &callback)¶

Compute the gradient of a scalar field f using the spectral element formulation (eqn: 29 in Komatitsch and Tromp, 1999)

Template Parameters:

ChunkIndexType – Chunk index type
VectorFieldType – Field view type (Chunk view)
QuadratureType – Quadrature view type
CallbackFunctor – Callback functor type

Parameters:

chunk_index – Chunk index specifying the elements within this chunk
jacobian_matrix – Jacobian matrix of basis functions
quadrature – Integration quadrature
f – Field to compute the gradient of

callback – Callback functor. Callback signature must be:

 void(const typename IteratorType::index_type, const
specfem::datatype::TensorPointViewType<type_real, 2,
VectorFieldType::components>)

Compute the gradient of a field f & g using the spectral element formulation (eqn: 29 in Komatitsch and Tromp, 1999)

Template Parameters:

ChunkIndexType – Chunk index type
VectorFieldType – Field view type (Chunk view)
QuadratureType – Quadrature view type
CallbackFunctor – Callback functor type

Parameters:

chunk_index – Chunk index specifying the elements within this chunk
jacobian_matrix – Jacobian matrix of basis functions
quadrature – Integration quadrature
f – Field to compute the gradient of
g – Field to compute the gradient of

callback – Callback functor. Callback signature must be:

 void(const typename IteratorType::index_type, const
specfem::datatype::TensorPointViewType<type_real, 2,
VectorFieldType::components>, const
specfem::datatype::TensorPointViewType<type_real, 2,
VectorFieldType::components>)

template<typename ChunkIndexType, typename VectorFieldType, typename QuadratureType, typename CallbackFunctor, std::enable_if_t<specfem::data_access::is_chunk_element<VectorFieldType>::value && VectorFieldType::dimension_tag == specfem::dimension::type::dim3, int> = 0> void gradient(const ChunkIndexType &chunk_index, const specfem::assembly::jacobian_matrix<specfem::dimension::type::dim3> &jacobian_matrix, const QuadratureType &quadrature, const VectorFieldType &f, const CallbackFunctor &callback)¶

Compute the gradient of a scalar field f using the spectral element formulation for 3D elements.

Template Parameters:

ChunkIndexType – Chunk index type
VectorFieldType – Field view type (Chunk view)
QuadratureType – Quadrature view type
CallbackFunctor – Callback functor type

Parameters:

chunk_index – Chunk index specifying the elements within this chunk
jacobian_matrix – Jacobian matrix of basis functions
quadrature – Integration quadrature
f – Field to compute the gradient of

callback – Callback functor. Callback signature must be:

 void(const typename IteratorType::index_type, const
specfem::datatype::TensorPointViewType<type_real, 3,
VectorFieldType::components>)

template<typename ChunkIndexType, typename VectorFieldType, typename QuadratureType, typename CallbackFunctor, std::enable_if_t<specfem::data_access::is_chunk_element<VectorFieldType>::value && VectorFieldType::dimension_tag == specfem::dimension::type::dim3, int> = 0> void gradient(const ChunkIndexType &chunk_index, const specfem::assembly::jacobian_matrix<specfem::dimension::type::dim3> &jacobian_matrix, const QuadratureType &quadrature, const VectorFieldType &f, const VectorFieldType &g, const CallbackFunctor &callback)¶

Compute the gradient of a field f & g using the spectral element formulation for 3D elements.

Template Parameters:

ChunkIndexType – Chunk index type
VectorFieldType – Field view type (Chunk view)
QuadratureType – Quadrature view type
CallbackFunctor – Callback functor type

Parameters:

chunk_index – Chunk index specifying the elements within this chunk
jacobian_matrix – Jacobian matrix of basis functions
quadrature – Integration quadrature
f – Field to compute the gradient of
g – Field to compute the gradient of

callback – Callback functor. Callback signature must be:

 void(const typename IteratorType::index_type, const
specfem::datatype::TensorPointViewType<type_real, 3,
VectorFieldType::components>, const
specfem::datatype::TensorPointViewType<type_real, 3,
VectorFieldType::components>)

Implementation Details¶

template<typename VectorFieldType, typename QuadratureType, typename std::enable_if_t<VectorFieldType::dimension_tag == specfem::dimension::type::dim2, int> = 0> auto specfem::algorithms::impl::element_gradient(const VectorFieldType &f, const specfem::point::index<specfem::dimension::type::dim2, VectorFieldType::using_simd> &local_index, const specfem::point::jacobian_matrix<specfem::dimension::type::dim2, false, VectorFieldType::using_simd> &point_jacobian_matrix, const QuadratureType &lagrange_derivative, typename VectorFieldType::simd::datatype (&df_dxi)[VectorFieldType::components], typename VectorFieldType::simd::datatype (&df_dgamma)[VectorFieldType::components])¶

Compute the gradient of a vector field at a specific point in a 2D spectral element.

Template Parameters:

VectorFieldType – Type of the vector field (must be 2D)
QuadratureType – Type of the Lagrange derivative polynomial

Parameters:

f – Vector field to compute gradient of
local_index – Local indices within the spectral element
point_jacobian_matrix – Jacobian matrix for coordinate transformation
lagrange_derivative – Lagrange derivative polynomials for differentiation
df_dxi – Output array for derivatives with respect to xi
df_dgamma – Output array for derivatives with respect to gamma

Returns:

Auto-deduced return type containing the gradient values

template<typename VectorFieldType, typename QuadratureType, typename std::enable_if_t<VectorFieldType::dimension_tag == specfem::dimension::type::dim3, int> = 0> auto specfem::algorithms::impl::element_gradient(const VectorFieldType &f, const specfem::point::index<specfem::dimension::type::dim3, VectorFieldType::using_simd> &local_index, const specfem::point::jacobian_matrix<specfem::dimension::type::dim3, false, VectorFieldType::using_simd> &point_jacobian_matrix, const QuadratureType &lagrange_derivative, typename VectorFieldType::simd::datatype (&df_dxi)[VectorFieldType::components], typename VectorFieldType::simd::datatype (&df_deta)[VectorFieldType::components], typename VectorFieldType::simd::datatype (&df_dgamma)[VectorFieldType::components])¶

Compute the gradient of a vector field at a specific point in a 3D spectral element.

Template Parameters:

VectorFieldType – Type of the vector field (must be 3D)
QuadratureType – Type of the Lagrange derivative polynomial

Parameters:

f – Vector field to compute gradient of
local_index – Local indices within the spectral element
point_jacobian_matrix – Jacobian matrix for coordinate transformation
lagrange_derivative – Lagrange derivative polynomials for differentiation
df_dxi – Output array for derivatives with respect to xi
df_deta – Output array for derivatives with respect to eta
df_dgamma – Output array for derivatives with respect to gamma

Returns:

Auto-deduced return type containing the gradient values

specfem::algorithms::gradient¶

Implementation Details¶

`specfem::algorithms::gradient`¶