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LEAST ASYMMETRIC DAUBECHIES-16
1.5
scaling function
wavelet
1
0.5
0
-0.5
-1
-1.5
-6
-4
-2
0
2
4
6
Figure 2.1: Daubechies Scaling Function and Wavelet of order 16
If a grid point carries the 7 wavelets in addition to the scaling function, it belongs
to the high resolution region. In the low resolution region a grid point carries only
a single scaling function. In the high resolution region, the resolution is doubled
in each direction with respect to the low resolution region. The grid spacing is
specified by the parameters hgridx, hgridy, hgridz. The low resolution region is
constructed in the following way. Around each atom one draws a sphere whose
radii are the ’size of the atom’ times the adimensional parameter crmult. All the
grid points being contained in the union of all these spheres form the low resolution
region. The high resolution is constructed in a similar way. One draws spheres
whose radii are the ’size of the bonding region’ times the parameter frmult around
each atom. All the grid points being contained in the union of all these spheres form
the high resolution region. Default values for the ’size of the atom’ and the ’size
of the bonding region’ are contained in the package. The user can however choose
different values and these values can be specified by adding an additional line at
the end of the pseudopotential parameter files which contain first the alternative
values of crmult and then frmult.
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