Mapping with radial basis functions using the Petsc library to solve the resulting system. More...

#include <PetRadialBasisFctMapping.hpp>

Inheritance diagram for precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >:

Collaboration diagram for precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >:

Public Member Functions
	PetRadialBasisFctMapping (Mapping::Constraint constraint, int dimensions, const RADIAL_BASIS_FUNCTION_T &function, std::array< bool, 3 > deadAxis, double solverRtol=1e-9, Polynomial polynomial=Polynomial::SEPARATE)
	Constructor.

	~PetRadialBasisFctMapping () override
	Deletes the PETSc objects and the _deadAxis array.

void	computeMapping () final override
	Computes the mapping coefficients from the in- and output mesh.

void	clear () final override
	Removes a computed mapping.

std::string	getName () const final override
	name of the rbf mapping

Public Member Functions inherited from precice::mapping::RadialBasisFctBaseMapping< RADIAL_BASIS_FUNCTION_T >
	RadialBasisFctBaseMapping (Constraint constraint, int dimensions, const RADIAL_BASIS_FUNCTION_T &function, std::array< bool, 3 > deadAxis, InitialGuessRequirement mappingType)
	Constructor.

virtual	~RadialBasisFctBaseMapping ()=default

virtual void	tagMeshFirstRound () final
	Method used by partition. Tags vertices that could be owned by this rank.

virtual void	tagMeshSecondRound () final
	Method used by partition. Tags vertices that can be filtered out.

Public Member Functions inherited from precice::mapping::Mapping
	Mapping (Constraint constraint, int dimensions, bool requiresGradientData, InitialGuessRequirement initialGuessRequirement)
	Constructor, takes mapping constraint.

Mapping &	operator= (Mapping &&)=delete

virtual	~Mapping ()=default
	Destructor, empty.

void	setMeshes (const mesh::PtrMesh &input, const mesh::PtrMesh &output)
	Sets input and output meshes carrying data to be mapped.

const mesh::PtrMesh &	getInputMesh () const

const mesh::PtrMesh &	getOutputMesh () const

Constraint	getConstraint () const
	Returns the constraint (consistent/conservative) of the mapping.

MeshRequirement	getInputRequirement () const
	Returns the requirement on the input mesh.

MeshRequirement	getOutputRequirement () const
	Returns the requirement on the output mesh.

bool	hasComputedMapping () const
	Returns true, if the mapping has been computed.

virtual bool	hasConstraint (const Constraint &constraint) const
	Checks whether the mapping has the given constraint or not.

bool	isScaledConsistent () const
	Returns true if mapping is a form of scaled consistent mapping.

bool	requiresInitialGuess () const
	Return true if the mapping requires an initial guess.

const Eigen::VectorXd &	initialGuess () const
	Return the provided initial guess of a mapping using an initialGuess.

Eigen::VectorXd &	initialGuess ()

bool	hasInitialGuess () const
	True if initialGuess().size() == 0.

void	map (int inputDataID, int outputDataID)

void	map (int inputDataID, int outputDataID, Eigen::VectorXd &initialGuess)

void	map (const time::Sample &input, Eigen::VectorXd &output)
	Maps an input Sample to output data from input mesh to output mesh.

void	map (const time::Sample &input, Eigen::VectorXd &output, Eigen::VectorXd &initialGuess)
	Maps an input Sample to output data from input mesh to output mesh, given an initialGuess.

virtual void	scaleConsistentMapping (const Eigen::VectorXd &input, Eigen::VectorXd &output, Constraint type) const
	Scales the consistently mapped output data such that the surface integral of the values on input mesh and output mesh are equal.

bool	requiresGradientData () const
	Returns whether the mapping requires gradient data.

Private Types
using	VertexData = std::vector<std::vector<std::pair<int, double>>>
	Stores col -> value for each row. Used to return the already computed values from the preconditioning.

Private Member Functions
void	mapConservative (const time::Sample &inData, Eigen::VectorXd &outData) final override
	Maps data using a conservative constraint.

void	mapConsistent (const time::Sample &inData, Eigen::VectorXd &outData) final override
	Maps data using a consistent constraint.

void	printMappingInfo (int dim) const
	Prints an INFO about the current mapping.

VertexData	bgPreallocationMatrixC (const mesh::PtrMesh inMesh)
	Preallocate matrix C and saves the coefficients using a boost::geometry spatial tree for neighbor search.

VertexData	bgPreallocationMatrixA (const mesh::PtrMesh inMesh, const mesh::PtrMesh outMesh)

void	loadInitialGuessForDim (int dimension, int allDimensions, petsc::Vector &destination)

void	storeInitialGuessForDim (int dimension, int allDimensions, petsc::Vector &source)

Private Attributes
logging::Logger	_log {"mapping::PetRadialBasisFctMapping"}

petsc::Matrix	_matrixC
	Interpolation system matrix. Evaluated basis function on the input mesh.

petsc::Matrix	_matrixQ
	Vandermonde Matrix for linear polynomial, constructed from vertices of the input mesh.

petsc::Matrix	_matrixA
	Interpolation evaluation matrix. Evaluated basis function on the output mesh.

petsc::Matrix	_matrixV
	Coordinates of the output mesh to evaluate the separated polynomial.

petsc::Vector	oneInterpolant
	Interpolant of g(x) = 1 evaluated at output sites, used for rescaling.

petsc::KSPSolver	_solver
	Used to solve matrixC for the RBF weighting factors.

petsc::KSPSolver	_QRsolver
	Used to solve the under-determined system for the separated polynomial.

AO	_AOmapping
	Maps globalIndex to local index.

const double	_solverRtol

Polynomial	_polynomial
	Toggles the use of the additional polynomial.

bool	useRescaling = true
	Toggles use of rescaled basis functions, only active when Polynomial == SEPARATE.

size_t	polyparams
	Number of coefficients for the integrated polynomial. Depends on dimension and number of dead dimensions.

size_t	sepPolyparams
	Number of coefficients for the separated polynomial. Depends on dimension and number of dead dimensions.

size_t	localPolyparams
	Equals to polyparams if rank == 0. Is 0 everywhere else.

utils::Parallel::CommStatePtr	_commState
	The CommState used to communicate.

Additional Inherited Members
Public Types inherited from precice::mapping::Mapping
enum	Constraint { CONSISTENT , CONSERVATIVE , SCALED_CONSISTENT_SURFACE , SCALED_CONSISTENT_VOLUME }
	Specifies additional constraints for a mapping. More...

enum class	MeshRequirement { UNDEFINED = 0 , VERTEX = 1 , FULL = 2 }
	Specifies requirements for the input and output meshes of a mapping. More...

enum class	InitialGuessRequirement : bool { Required = true , None = false }
	Specifies whether the mapping requires an initial guess. More...

Protected Member Functions inherited from precice::mapping::RadialBasisFctBaseMapping< RADIAL_BASIS_FUNCTION_T >
int	getPolynomialParameters () const
	Computes the number of polynomial degrees of freedom based on the problem dimension and the dead axis.

Protected Member Functions inherited from precice::mapping::Mapping
mesh::PtrMesh	input () const
	Returns pointer to input mesh.

mesh::PtrMesh	output () const
	Returns pointer to output mesh.

void	setInputRequirement (MeshRequirement requirement)
	Sets the mesh requirement for the input mesh.

void	setOutputRequirement (MeshRequirement requirement)
	Sets the mesh requirement for the output mesh.

int	getDimensions () const

Protected Attributes inherited from precice::mapping::RadialBasisFctBaseMapping< RADIAL_BASIS_FUNCTION_T >
RADIAL_BASIS_FUNCTION_T	_basisFunction
	Radial basis function type used in interpolation.

std::vector< bool >	_deadAxis
	true if the mapping along some axis should be ignored

Protected Attributes inherited from precice::mapping::Mapping
bool	_hasComputedMapping = false
	Flag to indicate whether computeMapping() has been called.

bool	_requiresGradientData
	Flag if gradient data is required for the mapping.

Detailed Description

template<typename RADIAL_BASIS_FUNCTION_T>
class precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >

Mapping with radial basis functions using the Petsc library to solve the resulting system.

With help of the input data points and values an interpolant is constructed. The interpolant is formed by a weighted sum of conditionally positive radial basis functions and a (low order) polynomial, and evaluated at the output data points.

The radial basis function type has to be given as template parameter.

Definition at line 52 of file PetRadialBasisFctMapping.hpp.

Member Typedef Documentation

◆ VertexData

template<typename RADIAL_BASIS_FUNCTION_T >

using precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::VertexData = std::vector<std::vector<std::pair<int, double>>>

private

Stores col -> value for each row. Used to return the already computed values from the preconditioning.

Definition at line 94 of file PetRadialBasisFctMapping.hpp.

Constructor & Destructor Documentation

◆ PetRadialBasisFctMapping()

template<typename RADIAL_BASIS_FUNCTION_T >

precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::PetRadialBasisFctMapping	(	Mapping::Constraint	constraint,
		int	dimensions,
		const RADIAL_BASIS_FUNCTION_T &	function,
		std::array< bool, 3 >	deadAxis,
		double	solverRtol = 1e-9,
		Polynomial	polynomial = Polynomial::SEPARATE )

Constructor.

Parameters

[in]	constraint	Specifies mapping to be consistent or conservative.
[in]	dimensions	Dimensionality of the meshes
[in]	function	Radial basis function used for mapping.
[in]	xDead,yDead,zDead	Deactivates mapping along an axis
[in]	solverRtol	Relative tolerance for the linear solver.
[in]	polynomial	Type of polynomial augmentation

For description on convergence testing and meaning of solverRtol see http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPConvergedDefault.html#KSPConvergedDefault

Definition at line 170 of file PetRadialBasisFctMapping.hpp.

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◆ ~PetRadialBasisFctMapping()

template<typename RADIAL_BASIS_FUNCTION_T >

precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::~PetRadialBasisFctMapping ( )

override

Deletes the PETSc objects and the _deadAxis array.

Definition at line 195 of file PetRadialBasisFctMapping.hpp.

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Member Function Documentation

◆ bgPreallocationMatrixA()

template<typename RADIAL_BASIS_FUNCTION_T >

PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::VertexData precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::bgPreallocationMatrixA	(	const mesh::PtrMesh	inMesh,
		const mesh::PtrMesh	outMesh )

private

Definition at line 922 of file PetRadialBasisFctMapping.hpp.

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◆ bgPreallocationMatrixC()

template<typename RADIAL_BASIS_FUNCTION_T >

PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::VertexData precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::bgPreallocationMatrixC ( const mesh::PtrMesh inMesh )

private

Preallocate matrix C and saves the coefficients using a boost::geometry spatial tree for neighbor search.

Definition at line 842 of file PetRadialBasisFctMapping.hpp.

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◆ clear()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::clear ( )

finaloverridevirtual

Removes a computed mapping.

Implements precice::mapping::RadialBasisFctBaseMapping< RADIAL_BASIS_FUNCTION_T >.

Definition at line 505 of file PetRadialBasisFctMapping.hpp.

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◆ computeMapping()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::computeMapping ( )

finaloverridevirtual

Computes the mapping coefficients from the in- and output mesh.

Implements precice::mapping::RadialBasisFctBaseMapping< RADIAL_BASIS_FUNCTION_T >.

Definition at line 201 of file PetRadialBasisFctMapping.hpp.

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◆ getName()

template<typename RADIAL_BASIS_FUNCTION_T >

std::string precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::getName ( ) const

finaloverridevirtual

name of the rbf mapping

Implements precice::mapping::Mapping.

Definition at line 521 of file PetRadialBasisFctMapping.hpp.

◆ loadInitialGuessForDim()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::loadInitialGuessForDim	(	int	dimension,
		int	allDimensions,
		petsc::Vector &	destination )

private

load the initialGuess for a given dimension or allocates the storage for the first iteration

The initialGuess passed to Mapping::map contains one guess for each data dimension as the mapping is evaluated for each dimension. As an examples, a 3D vector thus contains 3 initialGuesses, one for each solver. This extracts it from the overall initialGuess.

Definition at line 527 of file PetRadialBasisFctMapping.hpp.

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◆ mapConservative()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::mapConservative	(	const time::Sample &	inData,
		Eigen::VectorXd &	outData )

finaloverrideprivatevirtual

Maps data using a conservative constraint.

Parameters

[in]	input	Sample to map data from
[in]	output	Values to map to

If requiresInitialGuess(), then the initial guess is available via initialGuess(). Provide a new initial guess by overwriting it. The mapping has full control over its size.

See also: For mappings requiring an initialGuess: initialGuess() hasInitialGuess()

Implements precice::mapping::Mapping.

Definition at line 691 of file PetRadialBasisFctMapping.hpp.

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◆ mapConsistent()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::mapConsistent	(	const time::Sample &	inData,
		Eigen::VectorXd &	outData )

finaloverrideprivatevirtual

Maps data using a consistent constraint.

Parameters

[in]	input	Sample to map data from
[in]	output	Values to map to

If requiresInitialGuess(), then the initial guess is available via initialGuess(). Provide a new initial guess by overwriting it. The mapping has full control over its size.

See also: For mappings requiring an initialGuess: initialGuess() hasInitialGuess()

Implements precice::mapping::Mapping.

Definition at line 564 of file PetRadialBasisFctMapping.hpp.

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◆ printMappingInfo()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::printMappingInfo ( int dim ) const

private

Prints an INFO about the current mapping.

Definition at line 821 of file PetRadialBasisFctMapping.hpp.

◆ storeInitialGuessForDim()

template<typename RADIAL_BASIS_FUNCTION_T >

void precice::mapping::PetRadialBasisFctMapping< RADIAL_BASIS_FUNCTION_T >::storeInitialGuessForDim	(	int	dimension,
		int	allDimensions,
		petsc::Vector &	source )

private

stores the initialGuess for a given dimension

The initialGuess passed to Mapping::map contains one guess for each data dimension as the mapping is evaluated for each dimension. As an examples, a 3D vector thus contains 3 initialGuesses, one for each solver. This stores the initialGuess of a given dimension into the overall initialGuess.

Definition at line 548 of file PetRadialBasisFctMapping.hpp.

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