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LRM --> Curv
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@@ -75,7 +75,7 @@ We multiply by square-root of volume on each side of the tensor conductivity to
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.. math::
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\mathbf{J}_c = \mathbf{Q}_{(i)}\mathbf{J}_\text{TENSOR} \\
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\mathbf{J}_c = \mathbf{N}_{(i)}^{-1}\mathbf{Q}_{(i)}\mathbf{J}_\text{LRM}
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\mathbf{J}_c = \mathbf{N}_{(i)}^{-1}\mathbf{Q}_{(i)}\mathbf{J}_\text{Curv}
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Here the \\\(i\\\) index refers to where we choose to approximate this integral, as discussed in the note above.
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We will approximate this integral by taking the fluxes clustered around every node of the cell, there are 8 combinations in 3D, and 4 in 2D. We will use a projection matrix \\\( \\mathbf{Q}_{(i)} \\\) to pick the appropriate fluxes. So, now that we have 8 approximations of this integral, we will just take the average. For the TensorMesh, this looks like:
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@@ -114,7 +114,7 @@ Here each \\( \\mathbf{P} \\in \\mathbb{R}^{(d*nC, nF)} \\\) is a combination of
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.. math::
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\mathbf{P}_{(i)} = \sqrt{ \frac{1}{2^d} \mathbf{I}^d \otimes \text{diag}(\mathbf{v})} \overbrace{\mathbf{N}_{(i)}^{-1}}^{\text{LRM only}} \mathbf{Q}_{(i)}
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\mathbf{P}_{(i)} = \sqrt{ \frac{1}{2^d} \mathbf{I}^d \otimes \text{diag}(\mathbf{v})} \overbrace{\mathbf{N}_{(i)}^{-1}}^{\text{Curv only}} \mathbf{Q}_{(i)}
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.. note::
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+1
-1
@@ -23,7 +23,7 @@ Solver Utilities
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:members:
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:undoc-members:
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LRM Utilities
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Curv Utilities
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=============
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.. automodule:: SimPEG.Utils.lrmutils
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