Static class containing useful routines for (weighted) least squares polynomial reconstruction. More...

#include <CD_LeastSquares.H>

Public Types
using	CellLocation = Location::Cell

using	FaceLocation = Location::Face

using	Connectivity = VofUtils::Connectivity

using	Neighborhood = VofUtils::Neighborhood

Public Member Functions
	LeastSquares ()=delete
	Static class, no construction here.

	~LeastSquares ()=delete
	Static class, no destruction here.

Static Public Member Functions
static VoFStencil	getInterpolationStencil (const CellLocation a_cellPos, const CellLocation a_otherCellsPos, const Connectivity a_connectivity, const VolIndex &a_startVof, const EBISBox &a_ebisbox, const Real a_dx, const int a_p, const int a_radius, const int a_order, const bool a_addStartingVof)
	Get an interpolation stencil to a point in a cell with a specified order and radius.

static VoFStencil	getGradSten (const VolIndex &a_vof, const CellLocation a_gradLocation, const CellLocation a_cellLocation, const EBISBox &a_ebisbox, const Real a_dx, const int a_radius, const int a_p, const int a_order, const IntVectSet a_knownTerms=IntVectSet())
	Compute a least squares gradient stencil in a cell.

static VoFStencil	getGradSten (const FaceIndex &a_face, const FaceLocation a_gradLocation, const CellLocation a_cellLocation, const EBISBox &a_ebisbox, const Real a_dx, const int a_radius, const int a_p, const int a_order, const IntVectSet a_knownTerms=IntVectSet())
	Compute a least squares gradient stencil on a grid face.

static VoFStencil	getBndryGradSten (const VolIndex &a_vof, const Neighborhood a_neighborhood, const CellLocation a_cellPositions, const EBISBox &a_ebisbox, const Real a_dx, const int a_radius, const int a_p, const int a_order, const bool a_addStartingVof)
	Compute a least squares gradient stencil on the EB centroid with specified order.

static Real	sumWeights (const VoFStencil &a_stencil, const int a_variable)
	Return the sum of weights in the stencil, for a specific variable.

static Real	sumAllWeights (const VoFStencil &a_stencil)
	Compute the sum of all weights in a stencil.

static VoFStencil	projectGradSten (const VoFStencil &a_stencil, const RealVect &a_projection)
	Assuming that a_stencil is a gradient stencil, project it along a direction.

static RealVect	displacement (const CellLocation a_from, const CellLocation a_to, const VolIndex &a_fromVof, const VolIndex &a_toVof, const EBISBox &a_ebisbox, const Real &a_dx)
	Computes the distance between two Vofs that are defined on the same grid level.

static RealVect	displacement (const FaceLocation a_fromLoc, const CellLocation a_toLoc, const FaceIndex &a_fromFace, const VolIndex &a_toVof, const EBISBox &a_ebisbox, const Real &a_dx)
	Computes the distance between a vof and and a face.

static RealVect	displacement (const CellLocation a_from, const CellLocation a_to, const VolIndex &a_fromVof, const VolIndex &a_toVof, const EBISBox &a_ebisboxFrom, const EBISBox &a_ebisboxTo, const Real &a_dxFrom, const Real &a_dxTo)
	Computes the distance between two Vofs that are defined on two different grid levels.

static Vector< RealVect >	getDisplacements (const CellLocation a_from, const CellLocation a_to, const VolIndex &a_fromVof, const Vector< VolIndex > &a_toVofs, const EBISBox &a_ebisbox, const Real &a_dx)
	Get displacement vectors from a cell position to another cell position for a list of Vofs, i.e. x = (xFrom - xTo).

static Vector< RealVect >	getDisplacements (const FaceLocation a_fromLoc, const CellLocation a_to, const FaceIndex &a_fromFace, const Vector< VolIndex > &a_toVofs, const EBISBox &a_ebisbox, const Real &a_dx)
	Get displacement vectors from a cell position to another cell position for a list of Vofs, i.e. x = (xFrom - xTo).

static Vector< Real >	makeDiagWeights (const Vector< RealVect > &a_displacements, const int a_pow)
	Create a list of weights. This routine returns a list of diagonal weights for a least squares system. The weights are given as 1/\|\|x1-x0\|\|^a where a is the power.

static VoFStencil	computeGradSten (const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const int a_p, const int a_order, const IntVectSet a_knownTerms)
	Get a least squares gradient stencil solution for computing the gradient at a point. This routine eliminates the value in the point where the gradient is computed (which is assumed to be known.)

static VoFStencil	computeGradSten (const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const Vector< Real > &a_weights, const int a_order, const IntVectSet a_knownTerms)
	Get a least squares gradient stencil solution for a system of first-order Taylor extrapolation for computing the gradient at a point.

static int	getTaylorExpansionSize (const int a_order)
	Get the size of a Taylor expansion for a given order.

static VoFStencil	computeInterpolationStencil (const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const int a_pow, const int a_order)
	Compute an interpolation stencil to specified order by solving a least squares system.

static VoFStencil	computeInterpolationStencil (const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const Vector< Real > &a_weights, const int a_order)
	Compute an interpolation stencil to specified order by solving a least squares system.

static std::map< IntVect, VoFStencil >	computeSingleLevelStencils (const IntVectSet &a_derivs, const IntVectSet &a_knownTerms, const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const int a_p, const int a_order)
	Compute a least squares interpolation to a specified order.

static std::map< IntVect, VoFStencil >	computeSingleLevelStencils (const IntVectSet &a_derivs, const IntVectSet &a_knownTerms, const Vector< VolIndex > &a_allVofs, const Vector< RealVect > &a_displacements, const Vector< Real > &a_weights, const int a_order)
	Compute a least squares interpolation to a specified order.

template<typename T >
static std::map< IntVect, std::pair< VoFStencil, VoFStencil > >	computeDualLevelStencils (const IntVectSet &a_derivs, const IntVectSet &a_knownTerms, const Vector< VolIndex > &a_fineVofs, const Vector< VolIndex > &a_coarVofs, const Vector< RealVect > &a_fineDisplacements, const Vector< RealVect > &a_coarDisplacements, const int a_p, const int a_order)
	Compute a least squares interpolation to a specified order. This version separates the stencils into two levels.

template<typename T >
static std::map< IntVect, std::pair< VoFStencil, VoFStencil > >	computeDualLevelStencils (const IntVectSet &a_derivs, const IntVectSet &a_knownTerms, const Vector< VolIndex > &a_fineVofs, const Vector< VolIndex > &a_coarVofs, const Vector< RealVect > &a_fineDisplacements, const Vector< RealVect > &a_coarDisplacements, const Vector< Real > &a_fineWeights, const Vector< Real > &a_coarWeights, const int a_order)
	Compute a least squares interpolation to a specified order. This version separates the stencils into two levels.

Detailed Description

Static class containing useful routines for (weighted) least squares polynomial reconstruction.

Member Function Documentation

◆ computeDualLevelStencils() [1/2]

template<typename T >

std::map< IntVect, std::pair< VoFStencil, VoFStencil > > LeastSquares::computeDualLevelStencils	(	const IntVectSet &	a_derivs,
		const IntVectSet &	a_knownTerms,
		const Vector< VolIndex > &	a_fineVofs,
		const Vector< VolIndex > &	a_coarVofs,
		const Vector< RealVect > &	a_fineDisplacements,
		const Vector< RealVect > &	a_coarDisplacements,
		const int	a_p,
		const int	a_order
	)

static

Compute a least squares interpolation to a specified order. This version separates the stencils into two levels.

This is the general version which lets the caller specify why derivatives he wants out of the interpolation. The user specifies this via a_derivs where each IntVect represent a differentiation. E.g. IntVect(0,0,0) is just f, IntVect(1,0,0) = d/dx, IntVect(1,1,2) = (d^4)/(dx dy dz^2) and so on. The stencils for the directional derivatives are coded onto the return map. E.g. if a_derivs contains IntVect(1,0,0) the stencil for d/dx is found in map.at(IntVect(1,0,0)). The user can solve a smaller system if some of the terms in the expansion are known, typically used when computing an approximation to the gradient at a point in space where the scalar value is known. Note that this will modify the right hand side of the system, and the user will have to figure out how to make sense of the stencil.

Parameters

[in]	a_derivs	Specification of which unknowns in the Taylor series will be returned.
[in]	a_knownTerms	Which terms in the Taylor series are known.
[in]	a_fineVofs	Fine-level vofs to include in the interpolation method.
[in]	a_coarVofs	Coar-level vofs to include in the interpolation method.
[in]	a_fineDisplacements	Displacement vectors from the fine Vofs to the interpolation point
[in]	a_coarDisplacements	Displacement vectors from the coar Vofs to the interpolation point
[in]	a_p	Weighting factor for weighted least squares
[in]	a_order	Order of the interpolation.

Returns: Stencils for each of the derivatives specified in the input argument. The first entry in the pair contains fine-grid vofs only, and the second entry contains the coar vofs.

Note: This will throw an error if you don't have enough equations for obtaining the specified order.; The return map is always initialized with empty stencils. If computing the pseudoinverse fails, the returned stencils are all empty.; T is the precision used by LAPACK

◆ computeDualLevelStencils() [2/2]

template<typename T >

std::map< IntVect, std::pair< VoFStencil, VoFStencil > > LeastSquares::computeDualLevelStencils	(	const IntVectSet &	a_derivs,
		const IntVectSet &	a_knownTerms,
		const Vector< VolIndex > &	a_fineVofs,
		const Vector< VolIndex > &	a_coarVofs,
		const Vector< RealVect > &	a_fineDisplacements,
		const Vector< RealVect > &	a_coarDisplacements,
		const Vector< Real > &	a_fineWeights,
		const Vector< Real > &	a_coarWeights,
		const int	a_order
	)

static

Compute a least squares interpolation to a specified order. This version separates the stencils into two levels.

This is the general version which lets the caller specify why derivatives he wants out of the interpolation. The user specifies this via a_derivs where each IntVect represent a differentiation. E.g. IntVect(0,0,0) is just f, IntVect(1,0,0) = d/dx, IntVect(1,1,2) = (d^4)/(dx dy dz^2) and so on. The stencils for the directional derivatives are coded onto the return map. E.g. if a_derivs contains IntVect(1,0,0) the stencil for d/dx is found in map.at(IntVect(1,0,0)). The user can solve a smaller system if some of the terms in the expansion are known, typically used when computing an approximation to the gradient at a point in space where the scalar value is known. Note that this will modify the right hand side of the system, and the user will have to figure out how to make sense of the stencil.

Parameters

[in]	a_derivs	Specification of which unknowns in the Taylor series will be returned.
[in]	a_knownTerms	Which terms in the Taylor series are known.
[in]	a_fineVofs	Fine-level vofs to include in the interpolation method.
[in]	a_coarVofs	Coar-level vofs to include in the interpolation method.
[in]	a_fineDisplacements	Displacement vectors from the fine Vofs to the interpolation point
[in]	a_coarDisplacements	Displacement vectors from the coar Vofs to the interpolation point
[in]	a_fineWeights	Weights for the fine level
[in]	a_coarWeights	Weights for the coarse level
[in]	a_order	Order of the interpolation.

Returns: Stencils for each of the derivatives specified in the input argument. The first entry in the pair contains fine-grid vofs only, and the second entry contains the coar vofs.

Note: This will throw an error if you don't have enough equations for obtaining the specified order.; The return map is always initialized with empty stencils. If computing the pseudoinverse fails, the returned stencils are all empty.; T is the precision used by LAPACK

◆ computeGradSten() [1/2]

VoFStencil LeastSquares::computeGradSten	(	const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const int	a_p,
		const int	a_order,
		const IntVectSet	a_knownTerms
	)

static

Get a least squares gradient stencil solution for computing the gradient at a point. This routine eliminates the value in the point where the gradient is computed (which is assumed to be known.)

Parameters

[in]	a_allVofs	Vofs for which the displacement vectors were computed.
[in]	a_displacements	Displacement vectors from Vofs to the interpolation point
[in]	a_p	Weighting exponent for system
[in]	a_order	Desired order.

Note: This computes weights using makeDiagWeights(a_displacements, a_p) and then calls the other version.

Returns: Stencil for obtaining the gradient in a point. Stencils for each direction are put in the VoFStencil.variable(i).

◆ computeGradSten() [2/2]

VoFStencil LeastSquares::computeGradSten	(	const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const Vector< Real > &	a_weights,
		const int	a_order,
		const IntVectSet	a_knownTerms
	)

static

Get a least squares gradient stencil solution for a system of first-order Taylor extrapolation for computing the gradient at a point.

This routine eliminates the value in the point where the gradient is computed (which is assumed to be known.)

Parameters

[in]	a_allVofs	Vofs for which the displacement vectors were computed.
[in]	a_displacements	Displacement vectors from Vofs to the interpolation point
[in]	a_weights	Weights for each system of equations.
[in]	a_order	Interpolation order

Returns: Stencil for obtaining the gradient in a point. Stencils for each direction are put in the VoFStencil.variable(i).

Note: This routine will cause a run-time error if you have less than SpaceDim equations, which is the minimum number of equations needed for obtaining a gradient. However, the routine does not check if the inputs are degenerate.

◆ computeInterpolationStencil() [1/2]

VoFStencil LeastSquares::computeInterpolationStencil	(	const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const int	a_pow,
		const int	a_order
	)

static

Compute an interpolation stencil to specified order by solving a least squares system.

Parameters

[in]	a_allVofs	Vofs to include in the interpolation method.
[in]	a_displacements	Displacement vectors from the Vofs to the interpolation point
[in]	a_order	Order of the interpolation.
[in]	a_weightP	Weighting order for the least squares system. Must be > 0 to have an effect.

Returns: Stencil for the least squares solution to the interpolation problem.

Note: This computes weights using makeDiagWeights(a_displacements, a_pow) and then calls the other version.

◆ computeInterpolationStencil() [2/2]

VoFStencil LeastSquares::computeInterpolationStencil	(	const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const Vector< Real > &	a_weights,
		const int	a_order
	)

static

Compute an interpolation stencil to specified order by solving a least squares system.

Parameters

[in]	a_allVofs	Vofs to include in the interpolation method.
[in]	a_displacements	Displacement vectors from the Vofs to the interpolation point
[in]	a_order	Order of the interpolation.
[in]	a_weightP	Weighting order for the least squares system. Must be > 0 to have an effect.

Returns: Stencil for the least squares solution to the interpolation problem.

Note: This calls the more general version with a_derivs = IntVectSet(IntVect(0,0)).; This will throw an error if you don't have enough equations for obtaining the specified order.

◆ computeSingleLevelStencils() [1/2]

std::map< IntVect, VoFStencil > LeastSquares::computeSingleLevelStencils	(	const IntVectSet &	a_derivs,
		const IntVectSet &	a_knownTerms,
		const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const int	a_p,
		const int	a_order
	)

static

Compute a least squares interpolation to a specified order.

This is the general version which lets the caller specify why derivatives he wants out of the interpolation. The user specifies this via a_derivs where each IntVect represent a differentiation. E.g. IntVect(0,0,0) is just f, IntVect(1,0,0) = d/dx, IntVect(1,1,2) = (d^4)/(dx dy dz^2) and so on. The stencils for the directional derivatives are coded onto the return map. E.g. if a_derivs contains IntVect(1,0,0) the stencil for d/dx is found in map.at(IntVect(1,0,0)). The user can solve a smaller system if some of the terms in the expansion are known, typically used when computing an approximation to the gradient at a point in space where the scalar value is known. Note that this will modify the right hand side of the system, and the user will have to figure out how to make sense of the stencil.

Parameters

[in]	a_derivs	Specification of which terms to obtain from the series.
[in]	a_knownTerms	Which terms in the Taylor series are known, and will be eliminated from the least squares system.
[in]	a_allVofs	Vofs to include in the interpolation method.
[in]	a_displacements	Displacement vectors from the Vofs to the interpolation point
[in]	a_p	Weighting order for the least squares system. Must be > 0 to have an effect.
[in]	a_order	Order of the interpolation.

Returns: Stencils for each of the derivatives specified in the input argument.

Note: This calls the more general version.

◆ computeSingleLevelStencils() [2/2]

std::map< IntVect, VoFStencil > LeastSquares::computeSingleLevelStencils	(	const IntVectSet &	a_derivs,
		const IntVectSet &	a_knownTerms,
		const Vector< VolIndex > &	a_allVofs,
		const Vector< RealVect > &	a_displacements,
		const Vector< Real > &	a_weights,
		const int	a_order
	)

static

Compute a least squares interpolation to a specified order.

This is the general version which lets the caller specify why derivatives he wants out of the interpolation. The user specifies this via a_derivs where each IntVect represent a differentiation. E.g. IntVect(0,0,0) is just f, IntVect(1,0,0) = d/dx, IntVect(1,1,2) = (d^4)/(dx dy dz^2) and so on. The stencils for the directional derivatives are coded onto the return map. E.g. if a_derivs contains IntVect(1,0,0) the stencil for d/dx is found in map.at(IntVect(1,0,0)). The user can solve a smaller system if some of the terms in the expansion are known, typically used when computing an approximation to the gradient at a point in space where the scalar value is known. Note that this will modify the right hand side of the system, and the user will have to figure out how to make sense of the stencil.

Parameters

[in]	a_derivs	Specification of which unknowns in the Taylor series will be returned.
[in]	a_knownTerms	Which terms in the Taylor series are known.
[in]	a_allVofs	Vofs to include in the interpolation method.
[in]	a_displacements	Displacement vectors from the Vofs to the interpolation point
[in]	a_weights	Weights for the least squares system.
[in]	a_order	Order of the returned interpolation.

Returns: Stencils for each of the derivatives specified in the input argument.

Note: This will throw an error if you don't have enough equations for obtaining the specified order.; The return map is always initialized with empty stencils. If computing the pseudoinverse fails, the returned stencils are all empty.

◆ displacement() [1/3]

RealVect LeastSquares::displacement	(	const CellLocation	a_from,
		const CellLocation	a_to,
		const VolIndex &	a_fromVof,
		const VolIndex &	a_toVof,
		const EBISBox &	a_ebisbox,
		const Real &	a_dx
	)

static

Computes the distance between two Vofs that are defined on the same grid level.

Parameters

[in]	a_from	Specifying position in the cell defined by a_fromVof
[in]	a_to	Specifying position in the cell defined by a_toVof
[in]	a_fromVof	Vof to compute the distance from
[in]	a_toVof	Vof to compute the distance to
[in]	a_ebisbox	EBISBox
[in]	a_dx	Grid resolution

Returns: The vector pos(a_toVof) - pos(a_fromVof).

◆ displacement() [2/3]

RealVect LeastSquares::displacement	(	const CellLocation	a_from,
		const CellLocation	a_to,
		const VolIndex &	a_fromVof,
		const VolIndex &	a_toVof,
		const EBISBox &	a_ebisboxFrom,
		const EBISBox &	a_ebisboxTo,
		const Real &	a_dxFrom,
		const Real &	a_dxTo
	)

static

Computes the distance between two Vofs that are defined on two different grid levels.

Parameters

[in]	a_from	Specifying position in the cell defined by a_fromVof
[in]	a_to	Specifying position in the cell defined by a_toVof
[in]	a_fromVof	Vof to compute the distance from
[in]	a_toVof	Vof to compute the distance to
[in]	a_ebisboxFrom	EBISBox which can reach a_fromVof
[in]	a_ebisboxTo	EBISBox which can reach a_toVof
[in]	a_dxFrom	Grid resolution for the a_fromVof vof
[in]	a_dxTo	Grid resolution for the a_toVof vof

Returns: The vector pos(a_toVof) - pos(a_fromVof).

◆ displacement() [3/3]

RealVect LeastSquares::displacement	(	const FaceLocation	a_fromLoc,
		const CellLocation	a_toLoc,
		const FaceIndex &	a_fromFace,
		const VolIndex &	a_toVof,
		const EBISBox &	a_ebisbox,
		const Real &	a_dx
	)

static

Computes the distance between a vof and and a face.

Parameters

[in]	a_fromLoc	Specifying position in the cell defined by a_fromVof
[in]	a_toLoc	Specifying position in the cell defined by a_toVof
[in]	a_fromFace	face to compute the distance from
[in]	a_toVof	Vof to compute the distance to
[in]	a_ebisbox	EBISBox
[in]	a_dx	Grid resolution

Returns: The vector pos(a_toVof) - pos(a_fromVof).

◆ getBndryGradSten()

VoFStencil LeastSquares::getBndryGradSten	(	const VolIndex &	a_vof,
		const Neighborhood	a_neighborhood,
		const CellLocation	a_cellPositions,
		const EBISBox &	a_ebisbox,
		const Real	a_dx,
		const int	a_radius,
		const int	a_p,
		const int	a_order,
		const bool	a_addStartingVof
	)

static

Compute a least squares gradient stencil on the EB centroid with specified order.

This routine eliminates the value on the boundary and the user will have to fetch the weight for this point from the returned stencil.

Parameters

[in]	a_vof	Input vof
[in]	a_neighborhood	Neighboorhood specification
[in]	a_cellPositions	How to interpret cell positions
[in]	a_ebisbox	ebisbox
[in]	a_radius	Stencil radius
[in]	a_dx	Resolution
[in]	a_p	Weight scaling
[in]	a_order	Order of the gradient.
[in]	a_addStartingVof	Use a_vof in the expression for the gradient. This can be ill-conditioned for cell-centered expressions.

Returns: Returns a least squares stencil for evaluating an approximation normal derivative on the boundary centroid.

◆ getDisplacements() [1/2]

Vector< RealVect > LeastSquares::getDisplacements	(	const CellLocation	a_from,
		const CellLocation	a_to,
		const VolIndex &	a_fromVof,
		const Vector< VolIndex > &	a_toVofs,
		const EBISBox &	a_ebisbox,
		const Real &	a_dx
	)

static

Get displacement vectors from a cell position to another cell position for a list of Vofs, i.e. x = (xFrom - xTo).

Parameters

[in]	a_from	From this position
[in]	a_to	To this position.
[in]	a_curVof	Origin vof
[in]	a_toVofs	Vofs to compute the distance to/from
[in]	a_ebisbox	EBISBox
[in]	a_dx	Grid resolution

◆ getDisplacements() [2/2]

Vector< RealVect > LeastSquares::getDisplacements	(	const FaceLocation	a_fromLoc,
		const CellLocation	a_to,
		const FaceIndex &	a_fromFace,
		const Vector< VolIndex > &	a_toVofs,
		const EBISBox &	a_ebisbox,
		const Real &	a_dx
	)

static

Get displacement vectors from a cell position to another cell position for a list of Vofs, i.e. x = (xFrom - xTo).

Parameters

[in]	a_fromLoc	Location on face
[in]	a_toLoc	Location in Vofs
[in]	a_fromFace	Origin face
[in]	a_toVofs	Vofs to compute the distance to/from
[in]	a_ebisbox	EBISBox
[in]	a_dx	Grid resolution

◆ getGradSten() [1/2]

VoFStencil LeastSquares::getGradSten	(	const FaceIndex &	a_face,
		const FaceLocation	a_gradLocation,
		const CellLocation	a_cellLocation,
		const EBISBox &	a_ebisbox,
		const Real	a_dx,
		const int	a_radius,
		const int	a_p,
		const int	a_order,
		const IntVectSet	a_knownTerms = `IntVectSet()`
	)

static

Compute a least squares gradient stencil on a grid face.

This routine computes grad(phi) using a least squares reconstruction to specified order.

Parameters

[in]	a_face	Input face
[in]	a_gradLocation	Where (on the face) the gradient will be computed
[in]	a_cellLocation	Cell location
[in]	a_ebisbox	ebisbox
[in]	a_dx	Resolution
[in]	a_radius	Stencil radius
[in]	a_p	Weighting factor for least squares
[in]	a_order	Truncation order.

Returns: Returns a least squares stencil for computing the gradient. The directional derivatives are in the components of the returned stencil.

◆ getGradSten() [2/2]

VoFStencil LeastSquares::getGradSten	(	const VolIndex &	a_vof,
		const CellLocation	a_gradLocation,
		const CellLocation	a_cellLocation,
		const EBISBox &	a_ebisbox,
		const Real	a_dx,
		const int	a_radius,
		const int	a_p,
		const int	a_order,
		const IntVectSet	a_knownTerms = `IntVectSet()`
	)

static

Compute a least squares gradient stencil in a cell.

This routine computes grad(phi) using a least squares reconstruction to specified order.

Parameters

[in]	a_vof	Input vof
[in]	a_gradLocation	Where (in the vof) the gradient is evaluated
[in]	a_cellLocation	Cell locations
[in]	a_ebisbox	ebisbox
[in]	a_dx	Resolution
[in]	a_radius	Stencil radius
[in]	a_p	Weighting factor for least squares
[in]	a_order	Truncation order.

Returns: Returns a least squares stencil for computing the gradient. The directional derivatives are in the components of the returned stencil.

◆ getInterpolationStencil()

VoFStencil LeastSquares::getInterpolationStencil	(	const CellLocation	a_cellPos,
		const CellLocation	a_otherCellsPos,
		const Connectivity	a_connectivity,
		const VolIndex &	a_startVof,
		const EBISBox &	a_ebisbox,
		const Real	a_dx,
		const int	a_p,
		const int	a_radius,
		const int	a_order,
		const bool	a_addStartingVof
	)

static

Get an interpolation stencil to a point in a cell with a specified order and radius.

Parameters

[in]	a_cellPos	Position in the cell of the starting Vof.
[in]	a_otherCellsPos	Positions in the other cells.
[in]	a_startVof	The vof to compute for.
[in]	a_ebisbox	EBISBox.
[in]	a_dx	Grid resolution.
[in]	a_p	Power factor for weights.
[in]	a_radius	Stencil radius.
[in]	a_order	Interpolation order.
[in]	a_addStartingVof	Add starting vof or not (can't be used with a_p > 0) as it would lead to ill-conditioned systems.

◆ getTaylorExpansionSize()

int LeastSquares::getTaylorExpansionSize ( const int a_order )

static

Get the size of a Taylor expansion for a given order.

Parameters

[in] a_order Desired order in Taylor expansion

Returns: Returns number of terms in Taylor expansion.

◆ makeDiagWeights()

Vector< Real > LeastSquares::makeDiagWeights	(	const Vector< RealVect > &	a_displacements,
		const int	a_pow
	)

inlinestatic

Create a list of weights. This routine returns a list of diagonal weights for a least squares system. The weights are given as 1/||x1-x0||^a where a is the power.

Parameters

[in]	a_displacements	Displacement vectors, i.e. (x1-x0,x2-x0, x3-x0,...,(xN-x0)^T.
[in]	a_power	Power factor for weights.

◆ projectGradSten()

VoFStencil LeastSquares::projectGradSten	(	const VoFStencil &	a_stencil,
		const RealVect &	a_projection
	)

static

Assuming that a_stencil is a gradient stencil, project it along a direction.

Parameters

[in]	a_stencil	Stencil describing a gradient.
[in]	a_projection	Vector to project stencil along.

Returns: Returns gradient stencil projected along a_project.

Note: Users need to make sure ||a_projection|| = 1 for this routine to make sense.

◆ sumAllWeights()

Real LeastSquares::sumAllWeights ( const VoFStencil & a_stencil )

static

Compute the sum of all weights in a stencil.

Parameters

[in] a_stencil Stencil

Returns: Returns sum of weights in a_stencil (over all variables).

◆ sumWeights()

Real LeastSquares::sumWeights	(	const VoFStencil &	a_stencil,
		const int	a_variable
	)

static

Return the sum of weights in the stencil, for a specific variable.

Parameters

[in]	a_stencil	Stencil
[in]	a_variable	Which variable to sum.

Returns: Returns sum of weights for a specific variable in the stencil.

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

Source/Utilities/CD_LeastSquares.H
Source/Utilities/CD_LeastSquares.cpp
Source/Utilities/CD_LeastSquaresImplem.H

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ computeDualLevelStencils() [1/2]

◆ computeDualLevelStencils() [2/2]

◆ computeGradSten() [1/2]

◆ computeGradSten() [2/2]

◆ computeInterpolationStencil() [1/2]

◆ computeInterpolationStencil() [2/2]

◆ computeSingleLevelStencils() [1/2]

◆ computeSingleLevelStencils() [2/2]

◆ displacement() [1/3]

◆ displacement() [2/3]

◆ displacement() [3/3]

◆ getBndryGradSten()

◆ getDisplacements() [1/2]

◆ getDisplacements() [2/2]

◆ getGradSten() [1/2]

◆ getGradSten() [2/2]

◆ getInterpolationStencil()

◆ getTaylorExpansionSize()

◆ makeDiagWeights()

◆ projectGradSten()

◆ sumAllWeights()

◆ sumWeights()