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Assembler

The purpose of an assembler is to assemble local quantities (local stiffness matrix, local force vector, local energy, etc.) by looping over finite elements and thereby arriving at a global structure. This page describes the available assemblers and how they can be used.

Each of the assemblers is constructed as follows: 

AssemblerName(const Basis& basis, const FEContainer& fes, const std::vector<bool>& dirichletFlags)

  • basis is the basis that was used to construct the finite elements. The implementation of the bases involves four different strategies: BlockedLexicographic, BlockedInterleaved, FlatLexicographic and FlatInterleaved. These strategies are to be considered while creating the assembler. For further information on these strategies, refer to Chapter 10 of DUNE1.
  • fes is a container that contains all the finite elements that should be assembled.
  • dirichletFlags is a std::vector<bool> type. The i-th degree of freedom is fixed when dirichletFlags[i] = true. When a reduced matrix or vector is chosen, the corresponding row and column entries are removed.

Base class for flat assemblers

The FlatAssemblerBase is the base class for all assemblers currently available. All other assemblers inherit from this one, i.e., their interface includes the following functions: 

size_t size() // (1)!
size_t reducedSize() // (2)!
auto &finiteElements() const // (3)!
Eigen::VectorXd createFullVector(const Eigen::VectorXd &reducedVector) // (4)!
size_t constraintsBelow(size_t i) // (5)!
bool isConstrained(size_t i) // (6)!
size_t estimateOfConnectivity() // (7)!

  1. Returns the number of degrees of freedom.
  2. Returns the number of degrees of freedom that are not constrained by a Dirichlet boundary condition.
  3. Returns a reference to the finite element container, which was passed to the assembler.
  4. Gets a reduced vector and returns a full vector. Entries corresponding to fixed dofs are set to 0. The values of the other entries are obtained from the reduced vector.
  5. Indicates how many degrees of freedom {0,1,...i-1} are fixed.
  6. Indicates whether the degree of freedom i is fixed.
  7. Returns 8x the number of grid elements, which is an estimate for the connectivity. It can be used to allocate vectors.

Scalar assembler

It has the capabilities of FlatAssemblerBase plus one additional function: 

double& getScalar(const RequirementType& fErequirements)
This assembler can be used when only a scalar quantity is of interest and the assembly of matrices or vectors is irrelevant. The available requirements are explained on the FE requirements page. dirichletFlags is not used in this assembler.

It assembles the requested scalar quantity. A call to this function could look like this: 

ScalarAssembler myAssembler(...) // (1)!
const auto& K = myAssembler.getScalar(feRequirements) // (2)!

  1. Represents the construction of the desired assembler.
  2. To learn more about the available alternatives to energy and how this works, read the FE requirements page.

Flat vector assembler

It has all the features of ScalarAssembler plus more, like: 

Eigen::VectorXd& getRawVector(const FERequirementType &feRequirements)
Eigen::VectorXd& getVector(const FERequirementType& feRequirements)
Eigen::VectorXd& getReducedVector(const FERequirementType& feRequirements)
The first one returns a vector without considering the boundary conditions. The remaining, as the name suggests, returns a full vector or a reduced vector considering boundary conditions. They work in the same way as the scalar assembly functions of ScalarAssembler. The available FE requirements are explained on the FE requirements page.

Flat sparse assembler

It offers the functions of VectorFlatAssembler plus more, like: 

Eigen::SparseMatrix<double> &getRawMatrix(const FERequirementType &feRequirements) 
Eigen::SparseMatrix<double> &getMatrix(const FERequirementType &feRequirements)
Eigen::SparseMatrix<double> &getReducedMatrix(const FERequirementType &feRequirements)
A sparse matrix is returned. They work in the same way as the vector assembly functions of VectorFlatAssembler. The available FE requirements are explained on the FE requirements page.

Flat dense assembler

The only difference between the SparseFlatAssembler and the DenseFlatAssembler is that the DenseFlatAssembler returns a dense matrix. 

Eigen::MatrixXd &getRawMatrix(const FERequirementType &feRequirements)
Eigen::MatrixXd &getMatrix(const FERequirementType &feRequirements)
Eigen::MatrixXd &getReducedMatrix(const FERequirementType &feRequirements)

  1. Oliver Sander. DUNE—The Distributed and Unified Numerics Environment. Volume 140. Springer Nature, 2020. doi:10.1007/978-3-030-59702-3. ↩