AbstractAssembler< VectorType, SparseMatrixType, dim > Class Template Reference#

DiFfRG: DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim > Class Template Reference

DiFfRG

This is the general assembler interface for any kind of discretization. An assembler is responsible for calculating residuals and their jacobians for any given discretization, including both the spatial part and any further variables. Any assembler for a specific spatial discretization must fully implement this interface. More...

#include <abstract_assembler.hh>

Public Types
using	NumberType = typename get_type::NumberType<VectorType>

Public Member Functions
virtual void	attach_data_output (DataOutput< dim, VectorType > &data_out, const VectorType &solution, const VectorType &variables=VectorType(), const VectorType &dt_solution=VectorType(), const VectorType &residual=VectorType())=0
	Attach any data output to the DataOutput object provided. This can be used to extract additional data from the solution and write it to the output file. This includes both derivatives and other spatial functions, as well as single values that can be appended to the .csv file.

virtual void	reinit ()=0
	Reinitialize the assembler. This is necessary if the mesh has changed, e.g. after a mesh refinement.

virtual void	set_time (double t)=0
	Set the current time. The assembler should usually just forward this to the numerical model.

virtual const get_type::SparsityPattern< SparseMatrixType > &	get_sparsity_pattern_jacobian () const =0
	Obtain the sparsity pattern of the jacobian matrix.

virtual IndexSet	get_differential_indices () const =0
	Obtain the dofs which contain time derivatives.

virtual void	reinit_vector (VectorType &vector) const =0
	Reinitialize an arbitrary vector so that it has the correct size and structure.

virtual const SparseMatrixType &	get_mass_matrix () const =0
	Obtain the mass matrix.

Residual and jacobian functions
virtual void	residual_variables (VectorType &residual, const VectorType &variables, const VectorType &spatial_solution)
	When coupling the spatial discretization to additional variables, this function should calculate the residual for the additional variables.

virtual void	jacobian_variables (FullMatrix< NumberType > &jacobian, const VectorType &variables, const VectorType &spatial_solution)
	When coupling the spatial discretization to additional variables, this function should calculate the jacobian for the additional variables.

void	mass (VectorType &mass, const VectorType &solution_global, NumberType weight)
	Calculates the mass \(m_i(u)\) for an ODE.

virtual void	mass (VectorType &mass, const VectorType &solution_global, const VectorType &solution_global_dot, NumberType weight)=0
	Calculates the mass \(m(u, \partial_t u)\) for a DAE.

void	residual (VectorType &residual, const VectorType &solution_global, NumberType weight, NumberType weight_mass, const VectorType &variables=VectorType())
	Calculates the residual for an ODE.

virtual void	residual (VectorType &residual, const VectorType &solution_global, NumberType weight, const VectorType &solution_global_dot, NumberType weight_mass, const VectorType &variables=VectorType())=0
	Calculates the residual for a DAE.

void	jacobian_mass (SparseMatrixType &jacobian, const VectorType &solution_global, NumberType mass_weight=1.)
	Calculates the jacobian of the mass function for an ODE.

virtual void	jacobian_mass (SparseMatrixType &jacobian, const VectorType &solution_global, const VectorType &solution_global_dot, NumberType alpha=1., NumberType beta=1.)=0
	Calculates the jacobian of the mass function for a DAE.

void	jacobian (SparseMatrixType &jacobian, const VectorType &solution_global, NumberType weight, NumberType mass_weight, const VectorType &variables=VectorType())
	Calculates the jacobian of the residual function for an ODE.

virtual void	jacobian (SparseMatrixType &jacobian, const VectorType &solution_global, NumberType weight, const VectorType &solution_global_dot, NumberType alpha, NumberType beta, const VectorType &variables=VectorType())=0
	Calculates the jacobian of the residual function for a DAE.

Detailed Description

template<typename VectorType, typename SparseMatrixType, uint dim>
class DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >

This is the general assembler interface for any kind of discretization. An assembler is responsible for calculating residuals and their jacobians for any given discretization, including both the spatial part and any further variables. Any assembler for a specific spatial discretization must fully implement this interface.

In general, we have either a system of differential and algebraic equations which can be written as

\[\large m_i(u, \partial_t u) + \partial_x F_i(u, \dots) + s_i(u, \dots) = 0\,,i\in \{0, \dots, N_f-1\}\,, \]

or a system of differential equations which can be written as

\[\large m_{ij}\partial_t u_j + \partial_x F_i(u, \dots) + s_i(u, \dots) = 0\,,i\in \{0, \dots, N_f-1\}\,. \]

Here, \(u_i\) is the solution vector, \(\partial_t u_i\) is the time derivative of the solution vector, \(m_i\) is the mass function and \(m_{ij}\) the mass matrix, \(F_i\) is called the flux, and \(s_i\) is the source term. We will henceforth call the first equation a DAE (differential algebraic equation) and the second equation an ODE (ordinary differential equation).

For more information, please also refer to the guide and the documentation of DiFfRG::def::AbstractModel.

The second equation is used in all residual and jacobian functions which do not take the time derivative as an explicit argument, while the first equation is used in all other methods.

Template Parameters

VectorType	The vector type used in the spatial discretization
dim	The dimension of the spatial discretization

Member Typedef Documentation

◆ NumberType

template<typename VectorType , typename SparseMatrixType , uint dim>

using DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::NumberType = typename get_type::NumberType<VectorType>

Member Function Documentation

◆ attach_data_output()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::attach_data_output	(	DataOutput< dim, VectorType > &	data_out,
		const VectorType &	solution,
		const VectorType &	variables = VectorType(),
		const VectorType &	dt_solution = VectorType(),
		const VectorType &	residual = VectorType() )

pure virtual

Attach any data output to the DataOutput object provided. This can be used to extract additional data from the solution and write it to the output file. This includes both derivatives and other spatial functions, as well as single values that can be appended to the .csv file.

Parameters

data_out	The DataOutput object to attach the data to
solution	The spatial solution vector
variables	The additional variables vector

Implemented in DiFfRG::Variables::Assembler< Model_ >.

◆ get_differential_indices()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual IndexSet DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::get_differential_indices ( ) const

pure virtual

Obtain the dofs which contain time derivatives.

Returns: IndexSet The indices of the dofs which contain time derivatives

Implemented in DiFfRG::FEMAssembler< Discretization_, Model_ >, DiFfRG::FV::KurganovTadmor::Assembler< Discretization_, Model_ >, DiFfRG::LDG::LDGAssemblerBase< Discretization_, Model_ >, and DiFfRG::Variables::Assembler< Model_ >.

◆ get_mass_matrix()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual const SparseMatrixType & DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::get_mass_matrix ( ) const

pure virtual

Obtain the mass matrix.

Returns: const SparseMatrixType& The mass matrix

Implemented in DiFfRG::CG::Assembler< Discretization_, Model_ >, DiFfRG::dDG::Assembler< Discretization_, Model_ >, DiFfRG::DG::Assembler< Discretization_, Model_ >, DiFfRG::FV::KurganovTadmor::Assembler< Discretization_, Model_ >, DiFfRG::LDG::Assembler< Discretization_, Model_ >, and DiFfRG::Variables::Assembler< Model_ >.

◆ get_sparsity_pattern_jacobian()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual const get_type::SparsityPattern< SparseMatrixType > & DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::get_sparsity_pattern_jacobian ( ) const

pure virtual

Obtain the sparsity pattern of the jacobian matrix.

Returns: const SparsityPattern<VectorType>& The sparsity pattern of the jacobian matrix

Implemented in DiFfRG::CG::Assembler< Discretization_, Model_ >, DiFfRG::dDG::Assembler< Discretization_, Model_ >, DiFfRG::DG::Assembler< Discretization_, Model_ >, DiFfRG::FV::KurganovTadmor::Assembler< Discretization_, Model_ >, DiFfRG::LDG::Assembler< Discretization_, Model_ >, and DiFfRG::Variables::Assembler< Model_ >.

◆ jacobian() [1/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::jacobian	(	SparseMatrixType &	jacobian,
		const VectorType &	solution_global,
		NumberType	weight,
		const VectorType &	solution_global_dot,
		NumberType	alpha,
		NumberType	beta,
		const VectorType &	variables = VectorType() )

pure virtual

Calculates the jacobian of the residual function for a DAE.

Parameters

jacobian
solution_global
weight
solution_global_dot
alpha
beta

◆ jacobian() [2/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::jacobian	(	SparseMatrixType &	jacobian,
		const VectorType &	solution_global,
		NumberType	weight,
		NumberType	mass_weight,
		const VectorType &	variables = VectorType() )

inline

Calculates the jacobian of the residual function for an ODE.

Parameters

jacobian
solution_global
weight
mass_weight

◆ jacobian_mass() [1/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::jacobian_mass	(	SparseMatrixType &	jacobian,
		const VectorType &	solution_global,
		const VectorType &	solution_global_dot,
		NumberType	alpha = 1.,
		NumberType	beta = 1. )

pure virtual

Calculates the jacobian of the mass function for a DAE.

This function calculates the jacobian of the mass, i.e.

\[\large \alpha\, \int_\Omega\, \frac{\partial m_i(u_k, \partial_t u_k)}{\partial (\partial_t u_j)} \phi_i + \beta\, \int_\Omega\, \frac{\partial m_i(u_k, \partial_t u_k)}{\partial u_j} \phi_i \]

.

Parameters

jacobian	The jacobian matrix to be filled. This function adds to the matrix.
solution_global	The spatial solution vector
solution_global_dot	The spatial solution vector time derivative
alpha	The weight \( \alpha \) for the derivative with respect to \( \partial_t \)
beta	The weight \( \beta \) for the derivative with respect to \( u \)

◆ jacobian_mass() [2/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::jacobian_mass	(	SparseMatrixType &	jacobian,
		const VectorType &	solution_global,
		NumberType	mass_weight = 1. )

inline

Calculates the jacobian of the mass function for an ODE.

This function calculates the jacobian of the mass, i.e.

\[\large w_m\, \int_\Omega\, m_{ij} \phi_i \]

.

Parameters

jacobian	The jacobian matrix to be filled. This function adds to the matrix.
solution_global	The spatial solution vector
mass_weight	The weight for the mass \( w_m \)

◆ jacobian_variables()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::jacobian_variables	(	FullMatrix< NumberType > &	jacobian,
		const VectorType &	variables,
		const VectorType &	spatial_solution )

inlinevirtual

When coupling the spatial discretization to additional variables, this function should calculate the jacobian for the additional variables.

Parameters

jacobian	The jacobian matrix of the additional variables
variables	The current additional variables vector
spatial_solution	The spatial solution vector, which is needed for the calculation of the jacobian

◆ mass() [1/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::mass	(	VectorType &	mass,
		const VectorType &	solution_global,
		const VectorType &	solution_global_dot,
		NumberType	weight )

pure virtual

Calculates the mass \(m(u, \partial_t u)\) for a DAE.

This function calculates the mass as \( w_m \, \int_\Omega\, m_i(u_j, \partial_t u_j) \phi_i\).

Parameters

mass	The mass vector to be filled
solution_global	The spatial solution vector
solution_global_dot	The spatial solution vector time derivative
weight	The weight for the mass \( w_m \)

◆ mass() [2/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::mass	(	VectorType &	mass,
		const VectorType &	solution_global,
		NumberType	weight )

inline

Calculates the mass \(m_i(u)\) for an ODE.

This function calculates the mass as \( w_m \, \int_\Omega\, m_ij \partial_t u_j \phi_i\).

Parameters

mass	The mass vector to be filled
solution_global	The spatial solution vector
weight	The weight for the mass \( w_m \)

◆ reinit()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::reinit ( )

pure virtual

Reinitialize the assembler. This is necessary if the mesh has changed, e.g. after a mesh refinement.

Implemented in DiFfRG::CG::Assembler< Discretization_, Model_ >, DiFfRG::dDG::Assembler< Discretization_, Model_ >, DiFfRG::DG::Assembler< Discretization_, Model_ >, DiFfRG::FEMAssembler< Discretization_, Model_ >, DiFfRG::FV::KurganovTadmor::Assembler< Discretization_, Model_ >, DiFfRG::LDG::Assembler< Discretization_, Model_ >, DiFfRG::LDG::LDGAssemblerBase< Discretization_, Model_ >, and DiFfRG::Variables::Assembler< Model_ >.

◆ reinit_vector()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::reinit_vector ( VectorType & vector ) const

pure virtual

Reinitialize an arbitrary vector so that it has the correct size and structure.

Parameters

vector The vector to be reinitialized

Implemented in DiFfRG::Variables::Assembler< Model_ >.

◆ residual() [1/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::residual	(	VectorType &	residual,
		const VectorType &	solution_global,
		NumberType	weight,
		const VectorType &	solution_global_dot,
		NumberType	weight_mass,
		const VectorType &	variables = VectorType() )

pure virtual

Calculates the residual for a DAE.

This function calculates the sum

\[\large \int_\Omega\, \bigg(w_m m_i(u_j, \partial_t u_j) \phi_i - w_r F_i(u_j, \dots) \partial_x \phi_i + w_r s_i(u_j, \dots) \phi_i \bigg) + \int_{\partial\Omega}\, w_r \widehat{F}_i(u_j, \dots) \phi_i \]

.

Here, \(w_r\) is the residual weight, \(w_m\,\,\) is the weight for the mass, and \(\widehat{F}_i\) are the boundary terms picked up by the partial integration of the flux.

Parameters

residual	The residual vector to be filled
solution_global	The spatial solution vector
weight	The weight for the residual \( w_r \)
solution_global_dot	The spatial solution vector time derivative
weight_mass	The weight for the mass \( w_m \)

◆ residual() [2/2]

template<typename VectorType , typename SparseMatrixType , uint dim>

void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::residual	(	VectorType &	residual,
		const VectorType &	solution_global,
		NumberType	weight,
		NumberType	weight_mass,
		const VectorType &	variables = VectorType() )

inline

Calculates the residual for an ODE.

This function calculates the sum

\[\large \int_\Omega\, \bigg(w_m m_ij \partial_t u_j \phi_i - w_r F_i(u_j, \dots) \partial_x \phi_i + w_r s_i(u_j, \dots) \phi_i \bigg) + \int_{\partial\Omega}\, w_r \widehat{F}_i(u_j, \dots) \phi_i \]

.

Here, \(w_r\) is the residual weight, \(w_m\,\,\) is the weight for the mass, and \(\widehat{F}_i\) are any boundary terms picked up by the partial integration of the flux.

Parameters

residual	The residual vector to be filled
solution_global	The spatial solution vector
weight	The weight for the residual \( w_r \)
weight_mass	The weight for the mass \( w_m \)

◆ residual_variables()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::residual_variables	(	VectorType &	residual,
		const VectorType &	variables,
		const VectorType &	spatial_solution )

inlinevirtual

When coupling the spatial discretization to additional variables, this function should calculate the residual for the additional variables.

Parameters

residual	The residual vector of the additional variables
variables	The current additional variables vector
spatial_solution	The spatial solution vector, which is needed for the calculation of the residual

Reimplemented in DiFfRG::Variables::Assembler< Model_ >.

◆ set_time()

template<typename VectorType , typename SparseMatrixType , uint dim>

virtual void DiFfRG::AbstractAssembler< VectorType, SparseMatrixType, dim >::set_time ( double t )

pure virtual

Set the current time. The assembler should usually just forward this to the numerical model.

Parameters

t	The current time

Implemented in DiFfRG::FEMAssembler< Discretization_, Model_ >, DiFfRG::FV::KurganovTadmor::Assembler< Discretization_, Model_ >, DiFfRG::LDG::LDGAssemblerBase< Discretization_, Model_ >, and DiFfRG::Variables::Assembler< Model_ >.

The documentation for this class was generated from the following file:

/home/runner/work/DiFfRG_current/DiFfRG_current/DiFfRG/include/DiFfRG/discretization/common/abstract_assembler.hh

AbstractAssembler&lt; VectorType, SparseMatrixType, dim &gt; Class Template Reference#

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ NumberType

Member Function Documentation

◆ attach_data_output()

◆ get_differential_indices()

◆ get_mass_matrix()

◆ get_sparsity_pattern_jacobian()

◆ jacobian() [1/2]

◆ jacobian() [2/2]

◆ jacobian_mass() [1/2]

◆ jacobian_mass() [2/2]

◆ jacobian_variables()

◆ mass() [1/2]

◆ mass() [2/2]

◆ reinit()

◆ reinit_vector()

◆ residual() [1/2]

◆ residual() [2/2]

◆ residual_variables()

◆ set_time()

AbstractAssembler< VectorType, SparseMatrixType, dim > Class Template Reference#