Yves Capdeboscq - Michael Vogelius
This Document and the M-files mentioned within can be found
here in tgz format (or in zip format)
All files described in part A can be run with Matlab 5 or 6, without the PDE Toolbox. To run the demos listed in part B, the PDE Toolbox is required.
The implementation examples available in the Examples directory require the Matlab PDE Toolbox. The results of these computations are in the directory ExamplesResults.
These informations are also available as line commands: type help <function> to obtain help.
Usage : | [RH,RMW,RT]=WaveHom(M,N) |
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Input : | and , by matrices |
the periodic diffusion coefficient | |
the periodic diffusion coefficient | |
RH, | a 3 row column containing the |
homogenized coefficients according to the Haar Wavelets | |
RMW, | a 3 row column containing the |
homogenized coefficients according to the Legendre-2 Multiwavelet | |
RT, | a 3 row column containing the |
exact homogenized formulas in the case . |
Usage : | RES=AsymptoticRationalReduction(O) |
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Input : | a array, |
constructed by MRADecompositionMatrix (Paragraph A.8). |
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 |
Usage : | Extension(sig) |
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Input : | sig a array corresponding to |
the , and diffusion coefficient | |
Usage : | HaarFormulaX(a1x,a2x,a3x,a4x,a1y,a2y,a3y,a4y,b1,b2,b3,b4) |
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Input : | Haar wavelet coefficients corresponding to |
the diffusion coefficient | |
the diffusion coefficient | |
the diffusion coefficient |
Usage : | HaarFormulaY(a1x,a2x,a3x,a4x,a1y,a2y,a3y,a4y,b1,b2,b3,b4) |
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Input : | Haar wavelet coefficients corresponding to |
the diffusion coefficient | |
the diffusion coefficient | |
the diffusion coefficient |
Usage : | HaarFormulaZ(a1x,a2x,a3x,a4x,a1y,a2y,a3y,a4y,b1,b2,b3,b4) |
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Input : | Haar wavelet coefficients corresponding to |
the diffusion coefficient | |
the diffusion coefficient | |
the diffusion coefficient |
Usage : | HaarSmoothing(sig,EType) |
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Input : | sig, a dimensional array |
EType, an optional parameter. | |
The first matrix represents the diffusion coefficient | |
The second matrix represents the diffusion coefficient | |
The third matrix represents the diffusion coefficient | |
If Etype is set to , PeriodicExtension (Paragraph A.10) is used | |
instead of Extension (Paragraph A.3). |
Usage : | MRADecompositionMatrix(sig) |
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Input : | an array, where |
is the kth Haar wavelet coefficient of the | |
-th diffusion coefficient: | |
corresponds to (x,x) | |
corresponds to (y,y) | |
corresponds to (x,y) | |
at the point . |
Usage : | MWSmoothing(sig,EType) |
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Input : | sig, a dimensional array |
EType, an optional parameter. | |
The first matrix represents the diffusion coefficient | |
The second matrix represents the diffusion coefficient | |
The third matrix represents the diffusion coefficient | |
If Etype is set to , PeriodicExtension (Paragraph A.10) is used | |
instead of Extension (Paragraph A.3). |
Usage : | PeriodicExtension(sig) |
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Input : | sig a array corresponding to |
the , and diffusion coefficients. |
Usage : | resu=Smoothing(sig,Type,NbIter,BType) |
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e.g. resu=Smoothing(A,'Haar','auto') | |
Input : | sig a array representing |
an isotropic diffusion operator coefficient | |
a diagonal diffusion operator coefficient | |
a symmetric diffusion operator coefficient | |
type can be 'Haar' or 'MW' | |
NbIter can be any number or 'auto' which means the smoothing method | |
determines itself when to stop (variations between two steps less than ) | |
BType (optional), if set to 2, sets globally periodic boundary | |
condition instead of local ones. |
Usage : | WaveletSquare(sig) |
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Input : | sig an array corresponding to |
the , and diffusion coefficients. |
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The translation was initiated by Yves Capdeboscq on 2002-01-15