NodeQuadCFInterp2 Class Reference

#include <NodeQuadCFInterp2.H>

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.

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)

Constructor & Destructor Documentation

NodeQuadCFInterp2::NodeQuadCFInterp2 ( )

Default constructor. User must subsequently call define().

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::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 ( )

Destructor.

Member Function Documentation

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

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

bool NodeQuadCFInterp2::isDefined ( ) const

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

void NodeQuadCFInterp2::setVerbose ( bool a_verbose )

Set whether to give output. Default is false.

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

void NodeQuadCFInterp2::clearMemory ( ) [private]

void NodeQuadCFInterp2::setDefaultValues ( ) [private]

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

DisjointBoxLayout NodeQuadCFInterp2::m_grids [protected]

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

ProblemDomain NodeQuadCFInterp2::m_domain [protected]

CELL-centered physical domain of this level

Box NodeQuadCFInterp2::m_domainCoarseNodes [protected]

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

DisjointBoxLayout NodeQuadCFInterp2::m_coarsenedGrids [protected]

CELL-centered m_grids coarsened by 2

LevelData<NodeFArrayBox> NodeQuadCFInterp2::m_coarseCopy [protected]

copy of coarse phi, used in CFInterp().

bool NodeQuadCFInterp2::m_interfaceOnly [protected]

interpolating from interface only?

int NodeQuadCFInterp2::m_interpolationDegree [protected]

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

int NodeQuadCFInterp2::m_ncomp [protected]

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

bool NodeQuadCFInterp2::m_isDefined [protected]

has full define function been called?

const LayoutData<NodeCFIVS>* NodeQuadCFInterp2::m_loCFIVS [protected]

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

const LayoutData<NodeCFIVS>* NodeQuadCFInterp2::m_hiCFIVS [protected]

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

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
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)