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Reference documentation for deal.II version GIT 8e09676776 2023-03-27 21:15:01+00:00
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#include <deal.II/matrix_free/fe_point_evaluation.h>
Public Types | |
using | value_type = typename internal::FEPointEvaluation::EvaluatorTypeTraits< dim, n_components, Number >::value_type |
using | gradient_type = typename internal::FEPointEvaluation::EvaluatorTypeTraits< dim, n_components, Number >::gradient_type |
Public Member Functions | |
FEPointEvaluation (const Mapping< dim > &mapping, const FiniteElement< dim > &fe, const UpdateFlags update_flags, const unsigned int first_selected_component=0) | |
FEPointEvaluation (NonMatching::MappingInfo< dim, spacedim > &mapping_info, const FiniteElement< dim > &fe, const unsigned int first_selected_component=0) | |
void | reinit (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const ArrayView< const Point< dim >> &unit_points) |
void | reinit (const unsigned int cell_index) |
void | reinit (const unsigned int cell_index, const unsigned int face_number) |
void | evaluate (const ArrayView< const Number > &solution_values, const EvaluationFlags::EvaluationFlags &evaluation_flags) |
void | integrate (const ArrayView< Number > &solution_values, const EvaluationFlags::EvaluationFlags &integration_flags) |
const value_type & | get_value (const unsigned int point_index) const |
void | submit_value (const value_type &value, const unsigned int point_index) |
const gradient_type & | get_gradient (const unsigned int point_index) const |
const gradient_type & | get_unit_gradient (const unsigned int point_index) const |
void | submit_gradient (const gradient_type &, const unsigned int point_index) |
DerivativeForm< 1, dim, spacedim > | jacobian (const unsigned int point_index) const |
DerivativeForm< 1, spacedim, dim > | inverse_jacobian (const unsigned int point_index) const |
Number | JxW (const unsigned int point_index) const |
Tensor< 1, spacedim > | normal_vector (const unsigned int point_index) const |
Point< spacedim > | real_point (const unsigned int point_index) const |
Point< dim > | unit_point (const unsigned int point_index) const |
std_cxx20::ranges::iota_view< unsigned int, unsigned int > | quadrature_point_indices () const |
Private Member Functions | |
void | setup (const unsigned int first_selected_component) |
This class provides an interface to the evaluation of interpolated solution values and gradients on cells on arbitrary reference point positions. These points can change from cell to cell, both with respect to their quantity as well to the location. The two typical use cases are evaluations on non-matching grids and particle simulations.
The use of this class is similar to FEValues or FEEvaluation: The class is first initialized to a cell by calling FEPointEvaluation::reinit(cell, unit_points)
, with the main difference to the other concepts that the underlying points in reference coordinates need to be passed along. Then, upon call to evaluate() or integrate(), the user can compute information at the give points. Eventually, the access functions get_value() or get_gradient() allow to query this information at a specific point index.
The functionality is similar to creating an FEValues object with a Quadrature object on the unit_points
on every cell separately and then calling FEValues::get_function_values or FEValues::get_function_gradients, and for some elements and mappings this is what actually happens internally. For specific combinations of Mapping and FiniteElement realizations, however, there is a much more efficient implementation that avoids the memory allocation and other expensive start-up cost of FEValues. Currently, the functionality is specialized for mappings derived from MappingQ and MappingCartesian and for finite elements with tensor product structure that work with the Matrix-free infrastructure module. In those cases, the cost implied by this class is similar (or sometimes even somewhat lower) than using FEValues::reinit(cell)
followed by FEValues::get_function_gradients
.
Definition at line 407 of file fe_point_evaluation.h.
using FEPointEvaluation< n_components, dim, spacedim, Number >::value_type = typename internal::FEPointEvaluation:: EvaluatorTypeTraits<dim, n_components, Number>::value_type |
Definition at line 410 of file fe_point_evaluation.h.
using FEPointEvaluation< n_components, dim, spacedim, Number >::gradient_type = typename internal::FEPointEvaluation:: EvaluatorTypeTraits<dim, n_components, Number>::gradient_type |
Definition at line 412 of file fe_point_evaluation.h.
FEPointEvaluation< n_components, dim, spacedim, Number >::FEPointEvaluation | ( | const Mapping< dim > & | mapping, |
const FiniteElement< dim > & | fe, | ||
const UpdateFlags | update_flags, | ||
const unsigned int | first_selected_component = 0 |
||
) |
Constructor.
mapping | The Mapping class describing the actual geometry of a cell passed to the evaluate() function. |
fe | The FiniteElement object that is used for the evaluation, which is typically the same on all cells to be evaluated. |
update_flags | Specify the quantities to be computed by the mapping during the call of reinit(). During evaluate() or integrate(), this data is queried to produce the desired result (e.g., the gradient of a finite element solution). |
first_selected_component | For multi-component FiniteElement objects, this parameter allows to select a range of n_components components starting from this parameter. |
Definition at line 784 of file fe_point_evaluation.h.
FEPointEvaluation< n_components, dim, spacedim, Number >::FEPointEvaluation | ( | NonMatching::MappingInfo< dim, spacedim > & | mapping_info, |
const FiniteElement< dim > & | fe, | ||
const unsigned int | first_selected_component = 0 |
||
) |
Constructor to make the present class able to re-use the geometry data also used by other FEPointEvaluation
objects.
mapping_info | The MappingInfo class describes the geometry-related data for evaluating finite-element solutions. This object enables to construct such an object on the outside, possibly re-using it between several objects or between several calls to the same cell and unit points. |
fe | The FiniteElement object that is used for the evaluation, which is typically the same on all cells to be evaluated. |
first_selected_component | For multi-component FiniteElement objects, this parameter allows to select a range of n_components components starting from this parameter. |
Definition at line 807 of file fe_point_evaluation.h.
void FEPointEvaluation< n_components, dim, spacedim, Number >::reinit | ( | const typename Triangulation< dim, spacedim >::cell_iterator & | cell, |
const ArrayView< const Point< dim >> & | unit_points | ||
) |
Set up the mapping information for the given cell, e.g., by computing the Jacobian of the mapping for the given points if gradients of the functions are requested.
[in] | cell | An iterator to the current cell |
[in] | unit_points | List of points in the reference locations of the current cell where the FiniteElement object should be evaluated/integrated in the evaluate() and integrate() functions. |
Definition at line 897 of file fe_point_evaluation.h.
void FEPointEvaluation< n_components, dim, spacedim, Number >::reinit | ( | const unsigned int | cell_index | ) |
Reinitialize the evaluator to point to the correct precomputed mapping of the cell in the MappingInfo object.
Definition at line 931 of file fe_point_evaluation.h.
void FEPointEvaluation< n_components, dim, spacedim, Number >::reinit | ( | const unsigned int | cell_index, |
const unsigned int | face_number | ||
) |
Reinitialize the evaluator to point to the correct precomputed mapping of the face in the MappingInfo object.
Definition at line 953 of file fe_point_evaluation.h.
void FEPointEvaluation< n_components, dim, spacedim, Number >::evaluate | ( | const ArrayView< const Number > & | solution_values, |
const EvaluationFlags::EvaluationFlags & | evaluation_flags | ||
) |
This function interpolates the finite element solution, represented by solution_values
, on the cell and unit_points
passed to reinit().
[in] | solution_values | This array is supposed to contain the unknown values on the element as returned by cell->get_dof_values(global_vector, solution_values) . |
[in] | evaluation_flags | Flags specifying which quantities should be evaluated at the points. |
Definition at line 976 of file fe_point_evaluation.h.
void FEPointEvaluation< n_components, dim, spacedim, Number >::integrate | ( | const ArrayView< Number > & | solution_values, |
const EvaluationFlags::EvaluationFlags & | integration_flags | ||
) |
This function multiplies the quantities passed in by previous submit_value() or submit_gradient() calls by the value or gradient of the test functions, and performs summation over all given points. This is similar to the integration of a bilinear form in terms of the test function, with the difference that this formula does not include a JxW
factor. This allows the class to naturally embed point information (e.g. particles) into a finite element formulation. Of course, by multiplication of a JxW
information of the data given to submit_value(), the integration can also be represented by this class.
[out] | solution_values | This array will contain the result of the integral, which can be used to during cell->set_dof_values(solution_values, global_vector) or cell->distribute_local_to_global(solution_values, global_vector) . Note that for multi-component systems where only some of the components are selected by the present class, the entries not touched by this class will be zeroed out. |
[in] | integration_flags | Flags specifying which quantities should be integrated at the points. |
Definition at line 1119 of file fe_point_evaluation.h.
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inline |
Return the value at quadrature point number point_index
after a call to FEPointEvaluation::evaluate() with EvaluationFlags::values set, or the value that has been stored there with a call to FEPointEvaluation::submit_value(). If the object is vector-valued, a vector-valued return argument is given.
Definition at line 1285 of file fe_point_evaluation.h.
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inline |
Write a value to the field containing the values on points with component point_index. Access to the same field as through get_value(). If applied before the function FEPointEvaluation::integrate() with EvaluationFlags::values set is called, this specifies the value which is tested by all basis function on the current cell and integrated over.
Definition at line 1324 of file fe_point_evaluation.h.
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inline |
Return the gradient in real coordinates at the point with index point_index
after a call to FEPointEvaluation::evaluate() with EvaluationFlags::gradients set, or the gradient that has been stored there with a call to FEPointEvaluation::submit_gradient(). The gradient in real coordinates is obtained by taking the unit gradient (also accessible via get_unit_gradient()) and applying the inverse Jacobian of the mapping. If the object is vector-valued, a vector-valued return argument is given.
Definition at line 1297 of file fe_point_evaluation.h.
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inline |
Return the gradient in unit coordinates at the point with index point_index
after a call to FEPointEvaluation::evaluate() with EvaluationFlags::gradients set, or the gradient that has been stored there with a call to FEPointEvaluation::submit_gradient(). If the object is vector-valued, a vector-valued return argument is given. Note that when vectorization is enabled, values from several points are grouped together.
Definition at line 1309 of file fe_point_evaluation.h.
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inline |
Write a contribution that is tested by the gradient to the field containing the values on points with the given point_index
. Access to the same field as through get_gradient(). If applied before the function FEPointEvaluation::integrate(EvaluationFlags::gradients) is called, this specifies what is tested by all basis function gradients on the current cell and integrated over.
Definition at line 1336 of file fe_point_evaluation.h.
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inline |
Return the Jacobian of the transformation on the current cell with the given point index. Prerequisite: This class needs to be constructed with UpdateFlags containing update_jacobian
.
Definition at line 1348 of file fe_point_evaluation.h.
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inline |
Return the inverse of the Jacobian of the transformation on the current cell with the given point index. Prerequisite: This class needs to be constructed with UpdateFlags containing update_inverse_jacobian
or update_gradients
.
Definition at line 1361 of file fe_point_evaluation.h.
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inline |
Return the Jacobian determinant multiplied by the quadrature weight. This class or the MappingInfo object passed to this function needs to be constructed with UpdateFlags containing update_JxW_values
.
Definition at line 1374 of file fe_point_evaluation.h.
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inline |
Return the normal vector. This class or the MappingInfo object passed to this function needs to be constructed with UpdateFlags containing update_normal_vectors
.
Definition at line 1386 of file fe_point_evaluation.h.
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Return the position in real coordinates of the given point index among the points passed to reinit().
Definition at line 1399 of file fe_point_evaluation.h.
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Return the position in unit/reference coordinates of the given point index, i.e., the respective point passed to the reinit() function.
Definition at line 1412 of file fe_point_evaluation.h.
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Return an object that can be thought of as an array containing all indices from zero to n_quadrature_points. This allows to write code using range-based for loops.
Definition at line 1425 of file fe_point_evaluation.h.
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Common setup function for both constructors. Does the setup for both fast and slow path.
first_selected_component | For multi-component FiniteElement objects, this parameter allows to select a range of n_components components starting from this parameter. |
Definition at line 827 of file fe_point_evaluation.h.
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Number of quadrature points of the current cell/face.
Definition at line 655 of file fe_point_evaluation.h.
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Pointer to the Mapping object passed to the constructor.
Definition at line 660 of file fe_point_evaluation.h.
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Pointer to the FiniteElement object passed to the constructor.
Definition at line 665 of file fe_point_evaluation.h.
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Description of the 1d polynomial basis for tensor product elements used for the fast path of this class using tensor product evaluators.
Definition at line 671 of file fe_point_evaluation.h.
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Store whether the polynomials are linear with nodes at 0 and 1.
Definition at line 676 of file fe_point_evaluation.h.
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Renumbering between the unknowns of unknowns implied by the FiniteElement class and a lexicographic numbering used for the tensorized code path.
Definition at line 682 of file fe_point_evaluation.h.
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Temporary array to store the solution_values
passed to the evaluate() function in a format compatible with the tensor product evaluators. For vector-valued setups, this array uses a Tensor<1, n_components>
type to collect the unknowns for a particular basis function.
Definition at line 690 of file fe_point_evaluation.h.
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Temporary array to store a vectorized version of the solution_values
computed during integrate()
in a format compatible with the tensor product evaluators. For vector-valued setups, this array uses a Tensor<1, n_components, VectorizedArray<Number>>
format.
Definition at line 702 of file fe_point_evaluation.h.
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Temporary array to store the values at the points.
Definition at line 707 of file fe_point_evaluation.h.
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Temporary array to store the gradients in unit coordinates at the points.
Definition at line 712 of file fe_point_evaluation.h.
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Temporary array to store the gradients in real coordinates at the points.
Definition at line 717 of file fe_point_evaluation.h.
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Number of unknowns per component, i.e., number of unique basis functions, for the chosen FiniteElement (or base element).
Definition at line 723 of file fe_point_evaluation.h.
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The first selected component in the active base element.
Definition at line 728 of file fe_point_evaluation.h.
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For complicated FiniteElement objects this variable informs us about which unknowns actually carry degrees of freedom in the selected components.
Definition at line 735 of file fe_point_evaluation.h.
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The desired update flags for the evaluation.
Definition at line 740 of file fe_point_evaluation.h.
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The FEValues object underlying the slow evaluation path.
Definition at line 745 of file fe_point_evaluation.h.
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Pointer to mapping info on the fly computed during reinit.
Definition at line 751 of file fe_point_evaluation.h.
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Pointer to currently used mapping info (either on the fly or external precomputed).
Definition at line 757 of file fe_point_evaluation.h.
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The current cell index to access mapping data from mapping info.
Definition at line 762 of file fe_point_evaluation.h.
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The current face number to access mapping data from mapping info.
Definition at line 767 of file fe_point_evaluation.h.
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Bool indicating if fast path is chosen.
Definition at line 772 of file fe_point_evaluation.h.
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Bool indicating if class is reinitialized and data vectors a resized.
Definition at line 777 of file fe_point_evaluation.h.