#include <NodeQuadCFInterp2.H>
Public Methods | |
| NodeQuadCFInterp2 () | |
| {\bf constructors, destructor and defines} | |
| 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) | |
| 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) | |
| ~NodeQuadCFInterp2 () | |
| 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) |
| 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 | isDefined () const |
| void | coarseFineInterp (LevelData< NodeFArrayBox > &a_phi, const LevelData< NodeFArrayBox > &a_phiCoarse) |
| {\bf data modification functions} | |
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 |
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.
{\bf 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.\
{\bf 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: \begin{verbatim} o---o-x-o---o -1 0 1 2 \end{verbatim} 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: \begin{verbatim} o---o-x-o o -1 0 1 2 \end{verbatim} 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: \begin{verbatim} o o-x-o---o -1 0 1 2 \end{verbatim} then we approximate f''(1/2) by f''(1) and use f''(1) ~ (f(0) - 2 * f(1) + f(2)). \
{\bf 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). \begin{verbatim} (0,1) (1,1) o-------o | | | x | | | o-------o (0,0) (1,0) \end{verbatim} 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.
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{\bf constructors, destructor and defines} Default constructor. User must subsequently call define(). |
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Constructor calls setDefaultValues() and then calls define() with the same arguments. |
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Constructor calls setDefaultValues() and then calls define() with the same arguments. |
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Destructor. |
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{\bf data modification functions} Coarse / Fine (inhomogeneous) interpolation operator. Fill the nodes of a_phi on the coarse/fine interface with interpolated data from a_phiCoarse. {\bf Arguments:}\ a_phi (modified): the data at this level.\ a_phiCoarse (not modified): the data at the next coarser level.\ |
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Full define function. Makes all coarse-fine information and sets internal variables. The current level is taken to be the fine level. {\bf Arguments:}\ a_grids: domain of this level.\ a_domain: CELL-centered physical domain at this level.\ a_loCFIVS, a_hiCFIVS: pointers to objects used for figuring out which nodes lie on interface with the next coarser level. \ a_interfaceOnly: interpolating from interface only?\ a_interpolationDegree: 1 for (bi)linear, 2 for (bi)quadratic\ a_ncomp: number of components.\ |
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Full define function. Makes all coarse-fine information and sets internal variables. The current level is taken to be the fine level. {\bf Arguments:}\ a_grids: domain of this level.\ a_domain: CELL-centered physical domain at this level.\ a_loCFIVS, a_hiCFIVS: pointers to objects used for figuring out which nodes lie on interface with the next coarser level. \ a_interfaceOnly: interpolating from interface only?\ a_interpolationDegree: 1 for (bi)linear, 2 for (bi)quadratic\ a_ncomp: number of components.\ |
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Returns true if this object was created with the defining constructor or if define() has been called. |
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1.2.16