Class to interpolate quadratically at coarse/fine interface when refinement ratio is 2. More...

#include <NodeQuadCFInterp2.H>

Public Member Functions
Constructors, destructor and defines
	NodeQuadCFInterp2 ()

	NodeQuadCFInterp2 (const DisjointBoxLayout &a_grids, const Box &a_domain, const LayoutData< NodeCFIVS > const a_loCFIVS, const LayoutData< NodeCFIVS > const a_hiCFIVS, bool a_interfaceOnly, int a_interpolationDegree, int a_ncomp=1, bool a_verbose=false)

	NodeQuadCFInterp2 (const DisjointBoxLayout &a_grids, const ProblemDomain &a_domain, const LayoutData< NodeCFIVS > const a_loCFIVS, const LayoutData< NodeCFIVS > const a_hiCFIVS, bool a_interfaceOnly, int a_interpolationDegree, int a_ncomp=1, bool a_verbose=false)

	~NodeQuadCFInterp2 ()

void	define (const DisjointBoxLayout &a_grids, const ProblemDomain &a_domain, const LayoutData< NodeCFIVS > const a_loCFIVS, const LayoutData< NodeCFIVS > const a_hiCFIVS, bool a_interfaceOnly, int a_interpolationDegree, int a_ncomp=1, bool a_verbose=false)

void	define (const DisjointBoxLayout &a_grids, const Box &a_domain, const LayoutData< NodeCFIVS > const a_loCFIVS, const LayoutData< NodeCFIVS > const a_hiCFIVS, bool a_interfaceOnly, int a_interpolationDegree, int a_ncomp=1, bool a_verbose=false)

Access functions
bool	isDefined () const

Parameter-setting functions
void	setVerbose (bool a_verbose)

Data modification functions
void	coarseFineInterp (LevelData< NodeFArrayBox > &a_phi, const LevelData< NodeFArrayBox > &a_phiCoarse)

Protected Attributes
DisjointBoxLayout	m_grids

ProblemDomain	m_domain

Box	m_domainCoarseNodes

DisjointBoxLayout	m_coarsenedGrids

LevelData< NodeFArrayBox >	m_coarseCopy

bool	m_interfaceOnly

int	m_interpolationDegree

int	m_ncomp

bool	m_isDefined

const LayoutData< NodeCFIVS > *	m_loCFIVS

const LayoutData< NodeCFIVS > *	m_hiCFIVS

bool	m_verbose

Private Member Functions
void	clearMemory ()

void	setDefaultValues ()

void	interpLine (FArrayBox &a_fineFab, const FArrayBox &a_psiFab, const IntVectSet &a_psiFabNodes, const IntVect &a_iv, int a_idirOther)

Detailed Description

Class to interpolate quadratically at coarse/fine interface when refinement ratio is 2.

Class to interpolate quadratically at interface between this level and next coarser level, when the refinement ratio is 2. This class should be considered internal to NodeQuadCFInterp.

Long Description:

The interface has codimension one.
If a fine node coincides with a coarse node, then we merely project from the coarse node to the fine node.
Otherwise, we take the mean of the neighboring coarse nodes and subtract 1/8 * dx^2 times the sum of the second derivatives in the appropriate directions.

The interpolation is performed in function coarseFineInterp(). The constructor computes m_loCFIVS and m_hiCFIVS to determine the fine nodes at the interface with the coarse level.

The constructor also takes m_loCFIVS and m_hiCFIVS to determine the fine nodes at the interface with the coarse level. Calling getFineIVS() on m_loCFIVS[idir][dit()] gives us the IntVectSet of nodes of m_grids[dit()] on the face in the low direction in dimension idir, that lie on the interface with the coarser level. Similarly with m_hiCFIVS[idir][dit()] for the opposite face, in the high direction in dimension idir.

2-D Description:

In the 2-D problem, the interface is 1-D. Between coarse nodes at 0 and 1, we approximate the value at the fine node by
f(1/2) ~ (f(0) + f(1))/2 - 1/8 * f''(1/2)
where we estimate the second derivative f''(1/2) from the coarse values f(0), f(1), and either f(-1) or f(2) or both.

If the points -1 and 2 are both on the grid:

      o---o-x-o---o
     -1   0   1   2

then we use
f''(1/2) ~ (f(-1) - f(0) - f(1) + f(2))/2.

If the point -1 is on the grid but 2 is not:

      o---o-x-o   o
     -1   0   1   2

then we approximate f''(1/2) by f''(0) and use
f''(0) ~ (f(-1) - 2 * f(0) + f(1)).

If the point 2 is on the grid but -1 is not:

      o   o-x-o---o
     -1   0   1   2

then we approximate f''(1/2) by f''(1) and use
f''(1) ~ (f(0) - 2 * f(1) + f(2)).

3-D Description:

In the 3-D problem, the interface is 2-D. For any given fine node along the interface, look at its three coordinates. At least one of the coordinates is divisible by 2, meaning that it lies on a plane of coarse nodes. If all of the coordinates are even, then the fine node coincides with a coarse node, and we project the value. If only one coordinate is odd, then this reduces to the problem of a 1-D interface described above in the 2-D case.

We are left with the problem of interpolating f(1/2, 1/2).

    (0,1)   (1,1)
      o-------o
      |       |
      |   x   |
      |       |
      o-------o
    (0,0)   (1,0)

We use
f(1/2,1/2) ~ (f(0,0) + f(0,1) + f(1,0) + f(1,1))/4 - 1/8 * ( d^2 f/dx^2 (1/2,1/2) + d^2 f/dy^2 (1/2,1/2))
where the second derivatives are estimated from the four neighboring coarse nodes and their neighbors.

In particular, d^2 f/dx^2 (1/2,1/2) is approximated by the mean of d^2 f/dx^2 (1/2, 0) and d^2 f/dx^2 (1/2, 1).
These second derivatives are estimated in the same way as described above for the 1-D interface in the 2-D case.

Constructor & Destructor Documentation

◆ NodeQuadCFInterp2() [1/3]

NodeQuadCFInterp2::NodeQuadCFInterp2 ( )

Default constructor. User must subsequently call define().

◆ NodeQuadCFInterp2() [2/3]

NodeQuadCFInterp2::NodeQuadCFInterp2	(	const DisjointBoxLayout &	a_grids,
		const Box &	a_domain,
		const LayoutData< NodeCFIVS > *const	a_loCFIVS,
		const LayoutData< NodeCFIVS > *const	a_hiCFIVS,
		bool	a_interfaceOnly,
		int	a_interpolationDegree,
		int	a_ncomp = `1`,
		bool	a_verbose = `false`
	)

Constructor calls setDefaultValues() and then calls define() with the same arguments.

◆ NodeQuadCFInterp2() [3/3]

NodeQuadCFInterp2::NodeQuadCFInterp2	(	const DisjointBoxLayout &	a_grids,
		const ProblemDomain &	a_domain,
		const LayoutData< NodeCFIVS > *const	a_loCFIVS,
		const LayoutData< NodeCFIVS > *const	a_hiCFIVS,
		bool	a_interfaceOnly,
		int	a_interpolationDegree,
		int	a_ncomp = `1`,
		bool	a_verbose = `false`
	)

Constructor calls setDefaultValues() and then calls define() with the same arguments.

◆ ~NodeQuadCFInterp2()

NodeQuadCFInterp2::~NodeQuadCFInterp2 ( )

Destructor.

Member Function Documentation

◆ define() [1/2]

void NodeQuadCFInterp2::define	(	const DisjointBoxLayout &	a_grids,
		const ProblemDomain &	a_domain,
		const LayoutData< NodeCFIVS > *const	a_loCFIVS,
		const LayoutData< NodeCFIVS > *const	a_hiCFIVS,
		bool	a_interfaceOnly,
		int	a_interpolationDegree,
		int	a_ncomp = `1`,
		bool	a_verbose = `false`
	)

Full define function. Makes all coarse-fine information and sets internal variables. The current level is taken to be the fine level.

Parameters

a_grids	CELL-centered grids at this level
a_domain	CELL-centered physical domain at this level
a_loCFIVS	pointer to object storing coarse/fine interface nodes
a_hiCFIVS	pointer to object storing coarse/fine interface nodes
a_interfaceOnly	whether interpolation is from interface only, meaning that off-interface data should not be used
a_interpolationDegree	degree of interpolation; 1 for (bi)linear, 2 for (bi)quadratic
a_ncomp	number of components of data
a_verbose	verbose output flag

◆ define() [2/2]

void NodeQuadCFInterp2::define	(	const DisjointBoxLayout &	a_grids,
		const Box &	a_domain,
		const LayoutData< NodeCFIVS > *const	a_loCFIVS,
		const LayoutData< NodeCFIVS > *const	a_hiCFIVS,
		bool	a_interfaceOnly,
		int	a_interpolationDegree,
		int	a_ncomp = `1`,
		bool	a_verbose = `false`
	)

Full define function. Makes all coarse-fine information and sets internal variables. The current level is taken to be the fine level.

Parameters

a_grids	CELL-centered grids at this level
a_domain	CELL-centered physical domain at this level
a_loCFIVS	pointer to object storing coarse/fine interface nodes
a_hiCFIVS	pointer to object storing coarse/fine interface nodes
a_interfaceOnly	whether interpolation is from interface only, meaning that off-interface data should not be used
a_interpolationDegree	degree of interpolation; 1 for (bi)linear, 2 for (bi)quadratic
a_ncomp	number of components of data
a_verbose	verbose output flag

◆ isDefined()

bool NodeQuadCFInterp2::isDefined ( ) const

Returns true if this object was created with the defining constructor or if define() has been called.

◆ setVerbose()

void NodeQuadCFInterp2::setVerbose ( bool a_verbose )

Set whether to give output. Default is false.

◆ coarseFineInterp()

void NodeQuadCFInterp2::coarseFineInterp	(	LevelData< NodeFArrayBox > &	a_phi,
		const LevelData< NodeFArrayBox > &	a_phiCoarse
	)

Coarse / Fine (inhomogeneous) interpolation operator. Fill the nodes of a_phi on the coarse/fine interface with interpolated data from a_phiCoarse.

Parameters

a_phi	data at this level
a_phiCoarse	data at the next coarser level

◆ clearMemory()

void NodeQuadCFInterp2::clearMemory ( )

private

◆ setDefaultValues()

void NodeQuadCFInterp2::setDefaultValues ( )

private

◆ interpLine()

void NodeQuadCFInterp2::interpLine	(	FArrayBox &	a_fineFab,
		const FArrayBox &	a_psiFab,
		const IntVectSet &	a_psiFabNodes,
		const IntVect &	a_iv,
		int	a_idirOther
	)

private

Interpolate from a_psiFab to a_fineFab at a_iv along a line.

Parameters

a_fineFab	fine data on NODE-centered FAB
a_psiFab	coarse data on NODE-centered FAB
a_psiFabNodes	nodes of a_psiFab from which data can be used
a_iv	point at which to interpolate
a_idirOther	direction (0 to SpaceDim-1) along which to interpolate

Member Data Documentation

◆ m_grids

DisjointBoxLayout NodeQuadCFInterp2::m_grids

protected

CELL-centered grids at the current level (the finer level)

◆ m_domain

ProblemDomain NodeQuadCFInterp2::m_domain

protected

CELL-centered physical domain of this level

◆ m_domainCoarseNodes

Box NodeQuadCFInterp2::m_domainCoarseNodes

protected

NODE-centered box of nodes at physical domain at the coarser level

◆ m_coarsenedGrids

DisjointBoxLayout NodeQuadCFInterp2::m_coarsenedGrids

protected

CELL-centered m_grids coarsened by 2

◆ m_coarseCopy

LevelData<NodeFArrayBox> NodeQuadCFInterp2::m_coarseCopy

protected

copy of coarse phi, used in CFInterp().

◆ m_interfaceOnly

bool NodeQuadCFInterp2::m_interfaceOnly

protected

interpolating from interface only?

◆ m_interpolationDegree

int NodeQuadCFInterp2::m_interpolationDegree

protected

degree of interpolation: 1 for (bi)linear, 2 for (bi)quadratic

◆ m_ncomp

int NodeQuadCFInterp2::m_ncomp

protected

number of components of data, needed for setting size of work array

◆ m_isDefined

bool NodeQuadCFInterp2::m_isDefined

protected

has full define function been called?

◆ m_loCFIVS

const LayoutData<NodeCFIVS>* NodeQuadCFInterp2::m_loCFIVS

protected

pointer to object storing coarse/fine interface nodes between this level and next coarser level

◆ m_hiCFIVS

const LayoutData<NodeCFIVS>* NodeQuadCFInterp2::m_hiCFIVS

protected

pointer to object storing coarse/fine interface nodes between this level and next coarser level

◆ m_verbose

bool NodeQuadCFInterp2::m_verbose

protected

if true, print out extra information

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

NodeQuadCFInterp2.H

Public Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NodeQuadCFInterp2() [1/3]

◆ NodeQuadCFInterp2() [2/3]

◆ NodeQuadCFInterp2() [3/3]

◆ ~NodeQuadCFInterp2()

Member Function Documentation

◆ define() [1/2]

◆ define() [2/2]

◆ isDefined()

◆ setVerbose()

◆ coarseFineInterp()

◆ clearMemory()

◆ setDefaultValues()

◆ interpLine()

Member Data Documentation

◆ m_grids

◆ m_domain

◆ m_domainCoarseNodes

◆ m_coarsenedGrids

◆ m_coarseCopy

◆ m_interfaceOnly

◆ m_interpolationDegree

◆ m_ncomp

◆ m_isDefined

◆ m_loCFIVS

◆ m_hiCFIVS

◆ m_verbose