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AsymptoticRationalReduction.m

Usage : RES=AsymptoticRationalReduction(O)
   
Input : a \( L\times L\times 3\times 6\times 16\times 16 \) array,
   
  constructed by MRADecompositionMatrix (Paragraph A.8).


Part of MWSmoothing (Paragraph A.9).


The output of this function is an \( L\times L\times 3 \) array corresponding to the second order coefficients of the reduced operator taking the limit of the differentiation parameter \( \theta =1/2+\epsilon \) when epsilon tends to zero.


RES(:,:,1) corresponds to the (x,x) diffusion coefficient
   
RES(:,:,2) corresponds to the (y,y) diffusion coefficient
   
RES(:,:,3) corresponds to the (x,y) diffusion coefficient


\begin{displaymath}
\frac{d}{dx} \textrm{RES}(x,y,1)\frac{d}{dx} + \frac{d}{dy} \textrm{RES}(x,y,2)\frac{d}{dy}
\end{displaymath}


\begin{displaymath}
+\frac{d}{dy} \textrm{RES}(x,y3) \frac{d}{dx} +\frac{d}{dx} \textrm{RES}(x,y,3) \frac{d}{dy}
\end{displaymath}


See also MWSmoothing (Paragraph A.9) and MRADecompositionMatrix (Paragraph A.8).



Yves Capdeboscq 2002-01-15