A general (interface) class for DOF handling, see Lecture Document Paragraph 2.7.4.13. More...
#include <lf/assemble/dofhandler.h>
Public Member Functions | |
| virtual | ~DofHandler ()=default |
| virtual Destructor More... | |
| virtual size_type | NumDofs () const =0 |
| total number of dof's handled by the object More... | |
| virtual size_type | NumLocalDofs (const lf::mesh::Entity &entity) const =0 |
| tells the number of degrees of freedom subordinate/_belonging_ to to an entity More... | |
| virtual size_type | NumInteriorDofs (const lf::mesh::Entity &entity) const =0 |
| provides number of shape functions associated with an entity More... | |
| virtual nonstd::span< const gdof_idx_t > | GlobalDofIndices (const lf::mesh::Entity &entity) const =0 |
| access to indices of global dof's belonging to an entity More... | |
| virtual nonstd::span< const gdof_idx_t > | InteriorGlobalDofIndices (const lf::mesh::Entity &entity) const =0 |
| global indices of shape functions associated with an entity_ More... | |
| virtual const lf::mesh::Entity & | Entity (gdof_idx_t dofnum) const =0 |
| retrieve unique entity at which a basis function is located More... | |
| virtual std::shared_ptr< const lf::mesh::Mesh > | Mesh () const =0 |
| Acess to underlying mesh object. More... | |
Protected Member Functions | |
| DofHandler ()=default | |
| Default constructor, can only be called from derived class. More... | |
Protected constructors | |
Copying and assignment do not make sense for DofHandler objects, but derived classes may be copied/assigned | |
| DofHandler (const DofHandler &)=default | |
| DofHandler (DofHandler &&)=default | |
| DofHandler & | operator= (const DofHandler &)=default |
| DofHandler & | operator= (DofHandler &&)=default |
Related Functions | |
(Note that these are not member functions.) | |
| void | PrintInfo (std::ostream &stream, const DofHandler &dof_handler, unsigned int ctrl=0) |
| Output information about the given dof handler to the given stream object. More... | |
Detailed Description
A general (interface) class for DOF handling, see Lecture Document Paragraph 2.7.4.13.
Objects of this class provide the local-to-global map for indices of local/global shape functions.
Some terminology
- The terms "degrees of freedom", "global basis functions", and "global shape functions are synomymous. - Every global and local shape function is <em>associated</em> with a unique geometric entity. - The global/local shape functions associated with a mesh entity are called its <strong>interior</strong> shape functions/degrees of freedom. - The shape functions/degrees of freedom <strong>belonging</strong> to a mesh entity or <strong>subordinate</strong> to a mesh entity are those whose supports cover that entity. Hence all interior d.o.f. must also belong to an entity. <h2>Rules for ordering global shape functions <-> degrees of freedom (dof)</h2> Note that every global shape (dof) function belongs to a unique mesh entity. Ordering them means assigning a unique (vector component) index starting from zero until <tt>NumDofs-1</tt>. -# Dofs belonging to entities of a larger co-dimension are arranged before dofs associated with entities of a smaller co-dimension: This means <strong>First dofs on nodes, then dofs on edges, then dofs on cells</strong> -# Dofs owned by the same mesh entity are numbered contiguously. -# if two entities have the same co-dimension, then the dofs of that with the lower index are numbered before the dofs of that with the higher index: <em>dof numbering is compatible with indexing</em> <h2>Rules for numbering local shape functions (local dof)</h2> -# As above, Dofs belonging to <em>sub-entities</em> of a larger (relative) co-dimension are arranged before dofs associated with <em>sub-entities</em> of a smaller co-dimension. -# As above, dofs belonging to the same sub-entity are numbered contiguously. -# dofs for <em>sub-entities</em> of the same co-dimension are taken into account in the order given by the <em>local indexing</em> of the sub-entities. <h2>Local-to-global dof index mapping for entities of higher co-dimension</h2> The method getGlobalDofs() is available for entities of <em>any co-dimension</em>. For instance, this allows assembly of contributions from low-dimensional manifolds like boundaries or interfaces. However, the consistency of the local numbering of dofs has to be ensured. In two dimensions this is an issue for edges only and can be resolved by taking into account the orientation (direction) of the edge: dofs are ordered along the edge and those "closer to endpoint 0" are numbered first. In 3D many more situations have to be dealt with. The local numbering conventions are also defined in <a href="https://www.sam.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf" >Lecture Document</a> Paragraph 2.7.4.11 and illustrated in <a href="https://www.sam.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf" >Lecture Document</a> Example 2.7.4.12. <h4>Demonstration code</h4> (<a href="https://www.sam.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf" >Lecture Document</a> Code 2.7.4.15) @snippet dofhandleruse.cc pdi <h3>Conventions for numbering global shape functions</h3> Though not important for most finite element computations, the <strong>current implementations</strong> of the local-to-global d.o.f. mapping interface comply with the following rules: -# The shape functions associated to entities of higher co-dimension have smaller indices than those blonding to entities of lower co-dimension. This means that for 2D meshes d.o.f. for nodes are numbered first, then those for edges, finally those for cells. -# Within entities of the same co-dimension the <em>numbering follows their indexing</em> through the member function @ref lf::mesh::Mesh::Index(). Also refer to <a href="https://www.sam.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf" >Lecture Document Remark 2.7.4.17.
Definition at line 109 of file dofhandler.h.
Constructor & Destructor Documentation
◆ DofHandler() [1/3]
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protecteddefault |
Default constructor, can only be called from derived class.
◆ DofHandler() [2/3]
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protecteddefault |
◆ DofHandler() [3/3]
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protecteddefault |
◆ ~DofHandler()
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virtualdefault |
virtual Destructor
Member Function Documentation
◆ Entity()
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pure virtual |
retrieve unique entity at which a basis function is located
- Parameters
-
dofnum global index of the basis function/degree of freedom
This function returns the unique geometric entity to which a particular basis function = degree of freedom is associated.
This function is hardly ever needed in finite element codes and is supplied for debugging purposes.
- See also
- GlobalDofIndices()
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by projects::ipdg_stokes::assemble::buildSystemMatrixInOutFlow(), projects::ipdg_stokes::assemble::buildSystemMatrixNoFlow(), and lf::assemble::PrintInfo().
◆ GlobalDofIndices()
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pure virtual |
access to indices of global dof's belonging to an entity
- Parameters
-
entity reference to the entity for which the dof's are to be fetched. This entity must belong to the underlying mesh.
- Returns
- cardinal number range of global dof indices, see std::span data type documentation.
The basis functions of every finite element space must be associated with a unique geometric entity. Conversely, every entity can possess a finite number of basis functions = degrees of freedom. This member function returns the global indices of all basis functions associated with the entity and its sub-entitites (the covering local shape functions).
The size of the returned range must agree with the value returned by NumLocalDofs() when supplied with the same arguments.
Consult Lecture Document Paragraph 2.7.4.13 for more information.
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by lf::assemble::AssembleMatrixLocally(), lf::assemble::AssembleVectorLocally(), projects::ipdg_stokes::assemble::createOffsetFunction(), projects::ipdg_stokes::post_processing::extractBasisFunctionCoefficients(), projects::ipdg_stokes::post_processing::extractVelocity(), lf::fe::InitEssentialConditionFromFunction(), and lf::assemble::PrintInfo().
◆ InteriorGlobalDofIndices()
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pure virtual |
global indices of shape functions associated with an entity_
- Parameters
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entity entity for which shape functin indices are queried
- Returns
- cardinal number range of global indices of shape functions, see std::span data type documentation.
Each global shape function is associated with a unique mesh entity. This method provides all the global indices of the shape function associated to the entity specified by the function arguments, see Lecture Document Paragraph 2.7.4.13 for additional explanations.
- Note
- Be aware of the difference of GlobalDofIndices() and InteriorGlobalDofIndices()
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by lf::assemble::PrintInfo().
◆ Mesh()
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pure virtual |
Acess to underlying mesh object.
Every DofHandler object has to be associated with a unique mesh. All entities passed to the DofHandler object must belong to that mesh.
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by FisherKPP::assembleGalerkinMatrices(), lf::assemble::AssembleMatrixLocally(), lf::assemble::AssembleVectorLocally(), and lf::assemble::PrintInfo().
◆ NumDofs()
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pure virtual |
total number of dof's handled by the object
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by FisherKPP::assembleGalerkinMatrices(), lf::assemble::AssembleMatrixLocally(), lf::assemble::AssembleVectorLocally(), projects::ipdg_stokes::assemble::buildSystemMatrixInOutFlow(), projects::ipdg_stokes::assemble::buildSystemMatrixNoFlow(), projects::hldo_sphere::operators::DiracOperator::Compute(), projects::hldo_sphere::operators::DiracOperatorSourceProblem::Compute(), projects::hldo_sphere::operators::HodgeLaplaciansSourceProblems< SCALAR >::Compute(), projects::hldo_sphere::operators::WhitneyOneHodgeLaplace< SCALAR >::Compute(), projects::hldo_sphere::operators::WhitneyTwoHodgeLaplace< SCALAR >::Compute(), projects::hldo_sphere::operators::WhitneyZeroHodgeLaplace< SCALAR >::Compute(), projects::hldo_sphere::debugging::WhitneyOneCurlTest::Compute(), projects::ipdg_stokes::assemble::createOffsetFunction(), lf::fe::InitEssentialConditionFromFunction(), lf::uscalfe::PrintInfo(), lf::assemble::PrintInfo(), and lf::fe::prolongate().
◆ NumInteriorDofs()
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pure virtual |
provides number of shape functions associated with an entity
- Parameters
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entity entity of underlying mesh whose number of shape functions is queried
The return value of this method must be equal to the length of the range built by InteriorGlobalDofIndices().
- See also
- InteriorGlobalDofIndices()
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
◆ NumLocalDofs()
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pure virtual |
tells the number of degrees of freedom subordinate/_belonging_ to to an entity
- Parameters
-
entity reference to an entity of the underlying mesh
This method informs about the length of the vector returned by GlobalDofIndices().
- See also
- GlobalDofIndices()
Implemented in lf::assemble::UniformFEDofHandler, lf::assemble::DynamicFEDofHandler, and projects::dpg::ProductUniformFEDofHandler.
Referenced by lf::assemble::AssembleMatrixLocally(), lf::assemble::AssembleVectorLocally(), lf::fe::InitEssentialConditionFromFunction(), and lf::assemble::PrintInfo().
◆ operator=() [1/2]
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protecteddefault |
◆ operator=() [2/2]
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protecteddefault |
Friends And Related Function Documentation
◆ PrintInfo()
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related |
Output information about the given dof handler to the given stream object.
- Parameters
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stream The stream to which we should print dof_handler The dof handler that should be printed ctrl controls the level of detail of the printed output (see below)
The following output levels are supported
- if = 0: minimal out: just prints global no of dofs
- if > 0 and divisible by 2: print dofs associated with all entities
- if > 0 and divisible by 3: print entities belonging to dofs
- if > 0 and divisible by 10: also print interior dof indices
The documentation for this class was generated from the following file:
- /home/nico/bildung/SemVI/thesis/lehrfempp/lib/lf/assemble/dofhandler.h
