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As in the rest of Chombo, data are held on rectangular patches. In the mapped multiblock framework, each patch must be contained in only one block. In other words, no patch may straddle two or more blocks.
Examples
Advanced Tables  Table Plus 

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Domain in 2D mapped space: five squares  Range in 2D real space: disk 

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Advanced Tables  Table Plus 

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Domain in 2D mapped space: eight squares  Range in 2D real space: singlenull edge plasma geometry 

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Advanced Tables  Table Plus 

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Domain in 2D mapped space: six squares  Range in 3D real space: surface of sphere 

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Advection on a sphere, with one level of refinement
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Exchanging data between blocks
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The ghost cells of a patch that lie outside the block containing the patch will be called extrablock ghost cells of the patch. Two layers of extrablock ghost cells of block 2 of the disk example are outlined with dotted blue lines below, in both mapped space and real space. The centers of four of them are marked with blue *. The cells of the interpolation stencils of these four ghost cells are shown with thicker outlines, each with the color of its block.
Advanced Tables  Table Plus 

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In mapped space: four ghost cells with their interpolation stencils 

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The function value for each extrablock ghost cell is interpolated from function values for the valid cells in its stencil.
Around each ghost cell, we approximate the function by a Taylor polynomial in real coordinates, of degree P. This polynomial has different coefficients for each ghost cell. In 2D the polynomial is of the form:
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$$f(X, Y) = \sum_{p, q \geq 0: p + q \leq P} a_{pq} \left(\frac{X  X_{\boldsymbol{g}}}{R}\right)^p \left(\frac{Y  Y_{\boldsymbol{g}}}{R}\right)^q$$ 
where (X_{g}, Y_{g}) is the center of the ghost cell in real coordinates, and R is the mean distance from (X_{g}, Y_{g}) to the centers in real space of the stencil cells of g.
Starting with averaged values of f over each valid cell, then the coefficients a_{pq} come from solving the overdetermined system of equations
LaTeX Formatting 

$$\sum_{p, q \geq 0; p + q \leq P} a_{pq} \left\langle \left(\frac{X  X_{\boldsymbol{g}}}{R}\right)^p \left(\frac{Y  Y_{\boldsymbol{g}}}{R}\right)^q \right \rangle_{\boldsymbol{j}} = \left\langle f \right\rangle_{\boldsymbol{j}}$$ 
where there is an equation for every cell j in the selected neighborhood of valid cells of the ghost cell. The notation
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$\langle \cdot \rangle_{\boldsymbol{j}}$ 
indicates an average over cell j.
The average value of f on the ghost cell is then obtained by
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$$\left\langle f \right\rangle_{\boldsymbol{g}} = \sum_{p, q \geq 0; p + q \leq P} a_{pq} \left\langle \left(\frac{X  X_{\boldsymbol{g}}}{R}\right)^p \left(\frac{Y  Y_{\boldsymbol{g}}}{R}\right)^q \right \rangle_{\boldsymbol{g}}$$ 
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