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Next: HaarSmoothing.m Up: Haar and Multiwavelet homogenization Previous: HaarFormulaY.m


HaarFormulaZ.m

Usage : HaarFormulaZ(a1x,a2x,a3x,a4x,a1y,a2y,a3y,a4y,b1,b2,b3,b4)
   
Input : Haar wavelet coefficients corresponding to
   
  \( a_{1}^{x}\ldots a_{4}^{x} \) the \( (x,x) \) diffusion coefficient
   
  \( a_{1}^{y}\ldots a_{4}^{y} \) the \( (y,y) \) diffusion coefficient
   
  \( b_{1}\ldots b_{4} \) the \( (x,y) \) diffusion coefficient


The output is the \( (x,y) \) Haar homogenized diffusion coefficient.


See also HaarSmoothing (Paragraph A.7), HaarFormulaX (Paragraph A.4) and HaarFormulaY (Paragraph A.5). The formula is

\begin{displaymath}
(-(a_{2}^{y}a_{3}^{x}a_{3}^{y}b_{2})+a_{1}^{y}a_{3}^{x}a_{4}...
...y}b_{1}-a_{2}^{y}b_{2})+(a_{2}^{x})^{2}(-(a_{1}^{y}b_{1})\dots \end{displaymath}


\begin{displaymath}
+a_{2}^{y}b_{2})-(a_{1}^{y})^{2}a_{3}^{x}b_{3}+a_{3}^{x}(a_{...
...{3}-a_{3}^{y}b_{2}^{2}b_{3}+2a_{3}^{x}a_{3}^{y}b_{3}^{2}\ldots \end{displaymath}


\begin{displaymath}
-b_{2}^{2}b_{3}^{2}+a_{3}^{x}b_{3}^{3}+(a_{1}^{y}a_{2}^{y}a_...
...y}a_{4}^{x}b_{2}+2a_{3}^{y}b_{1}b_{2}-a_{4}^{y}b_{2}^{2}\ldots \end{displaymath}


\begin{displaymath}
-(a_{3}^{y}a_{4}^{x}+a_{3}^{x}a_{4}^{y}-2(a_{1}^{y}+2b_{1})b...
...{4}^{y})+b_{1}(a_{1}^{y}+2b_{1})+b_{2}(a_{2}^{y}+b_{2})+\ldots \end{displaymath}


\begin{displaymath}
(a_{3}^{x}+b_{3})(a_{3}^{y}+b_{3}))b_{4}^{2}+(a_{4}^{x}+a_{4...
...}^{y})^{2}b_{1}-(a_{3}^{y})^{2}b_{1}+2a_{1}^{y}b_{1}^{2}\ldots \end{displaymath}


\begin{displaymath}
-a_{1}^{y}a_{2}^{y}b_{2}+a_{3}^{y}a_{4}^{y}b_{2}-2a_{2}^{y}b...
...-2a_{3}^{y}b_{1}b_{3}+a_{4}^{y}b_{2}b_{3}-b_{1}b_{3}^{2}\ldots \end{displaymath}


\begin{displaymath}
+(a_{2}^{y}a_{3}^{x}+a_{2}^{y}a_{3}^{y}-a_{1}^{y}(a_{4}^{x}+...
...}+b_{1})b_{4}^{2})+a_{2}^{x}(a_{1}^{y}a_{3}^{x}a_{4}^{y}\ldots \end{displaymath}


\begin{displaymath}
-2a_{1}^{y}b_{1}b_{2}+a_{1}^{y}a_{4}^{x}b_{3}-a_{3}^{y}b_{2}...
...4}^{y}b_{2}+2b_{1}b_{3}+a_{1}^{y}(a_{3}^{x}+b_{3}))b_{4}\ldots \end{displaymath}


\begin{displaymath}
-b_{2}b_{4}^{2}-a_{2}^{y}(-2b_{2}^{2}+a_{3}^{x}(a_{3}^{y}+b_{3})+b_{4}(a_{4}^{x}+b_{4}))))/\end{displaymath}


\begin{displaymath}
((a_{1}^{x})^{2}a_{1}^{y}-a_{1}^{y}(a_{2}^{x}+b_{2})^{2}+2(a...
...{3})b_{4}-(a_{1}^{y}+2b_{1})b_{4}^{2}+a_{1}^{x}((a_{1}^{y})^{2}\end{displaymath}


\begin{displaymath}
+2a_{1}^{y}b_{1}-(a_{3}^{y}+b_{3})^{2}-b_{4}^{2}))\end{displaymath}


next up previous
Next: HaarSmoothing.m Up: Haar and Multiwavelet homogenization Previous: HaarFormulaY.m
Yves Capdeboscq 2002-01-15