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u_f , u, are these two the same?

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Old   September 16, 2013, 05:20
Default u_f , u, are these two the same?
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Dongyue Li
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Hi guys,

Wonderful day!

While Im digging into fvc::reconstruct(), after lots of effort, I made a little progress, Now Im confusing that:
\sum {{n_f}\left( {{S_f} \cdot u} \right)}  = \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)}

namely:
u_f = u

Is this rite? Only by this I can get the same equation as fvc::reconstruct().
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Old   September 16, 2013, 05:41
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Bernhard
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Can you add some linenumbers of relevant files? u and u_f are definitely not the same, as one would be a surface field and the other a volume field.
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Old   September 16, 2013, 05:46
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Dongyue Li
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Quote:
Originally Posted by Bernhard View Post
Can you add some linenumbers of relevant files? u and u_f are definitely not the same, as one would be a surface field and the other a volume field.
I will make it more clear later, texting these equations in mathtype is time-consuming. Thank you very much. U help me alot...
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Old   September 16, 2013, 20:37
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Sorry, so late!

\begin{array}{l}
\sum {{n_f}\left( {{S_f} \cdot u} \right) = } \sum {{n_f}\left( {{S_f} \cdot {u_f}} \right)} \\
\sum {\left[ {\left( {{n_F} \otimes {S_f}} \right) \cdot u} \right]}  = \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} \left( {{S_f} \cdot {u_f}} \right)\\
\sum {\left[ {\left( {\frac{{{S_f}}}{{\left| {{S_f}} \right|}} \otimes {S_f}} \right) \cdot u} \right]}  = \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} {\phi _f}\\
u = \underbrace {{{\left\{ {\sum {\left[ {\left( {\frac{{{S_f}}}{{\left| {{S_f}} \right|}} \otimes {S_f}} \right)} \right]} } \right\}}^{ - 1}} \cdot \sum {\frac{{{S_f}}}{{\left| {{S_f}} \right|}}} {\phi _f}}_{weller's\;fvc::reconstruct()}
\end{array}

this might be clear. Any ideas?
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Old   September 22, 2013, 22:01
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any ideas?
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