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AnalyticWaveHom.m

Usage : [RH,RMW,RT]=WaveHom(M,N)
   
Input : \( M \) and \( N \), \( 2 \) by \( 2 \) matrices
   
  \( M \) the \( (x,x) \) periodic diffusion coefficient
   
  \( N \) the \( (y,y) \) periodic diffusion coefficient
   
  \( \frac{d}{dx}M\frac{d}{dx}+\frac{d}{dy}N\frac{d}{dy} \)


For a general symmetric periodic matrix use HaarSmoothing instead.


The output of this function is the same as the output of the HaarSmoothing function, in periodic 2 by 2 case. Here the formulas are implemented in their simpler form (in terms of the \( X,Y,Z \) variables) without explicitly using wavelet coefficients.


The output is composed of 3 row column vectors


RH, a 3 row column containing the \( ((x,x),(x,y),(y,y)) \)
  homogenized coefficients according to the Haar Wavelets
   
RMW, a 3 row column containing the \( ((x,x),(x,y),(y,y)) \)
  homogenized coefficients according to the Legendre-2 Multiwavelet
   
RT, a 3 row column containing the \( ((x,x),(x,y),(y,y)) \)
  exact homogenized formulas in the case \( M=N \).


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