Re: Irregularly gridded Discrete Laplacian Operator

[David Bateman]

Marco Caliari wrote:
> On 18/07/07, David Bateman <David.Bateman at motorola.com> wrote:
>
>   
>> whereas the equivalent in Matlab appears to be
>>
>> D(2:end-1) = ((M(3:end) - M(2:end-1)) ./  dx(2:end) + (M(1:end-2) -
>> M(2:end-1)) ./ dx(1:end-1)) ./ (dx(1:end-1) + dx(2:end))
>>     
>
> A factor 2 is missing. In any case, it is a first order approximation of
> the second derivative. 
No the factor of 2 is implicit in the addition "(dx(1:end-1) +
dx(2:end))" . Try setting dx(i) = dx(i+1) for all i (ie a uniform grid)
and you'll see that the Octave and Matlab definitions are the same.. In
any case in terms of the graph a constant scaling factor makes no
difference :-)

> Better approximations can be obtained by taking a
> larger stencil, see, e.g.,
> http://www.damtp.cam.ac.uk/user/na/PartII/Lect15.pdf
>   
Thanks Marco, but as far as I can tell the dx here is always uniform, it
however confirms the correctness of the Octave and Matlab definitions
for uniform grids...

Cheers
David

-- 
David Bateman                                address@hidden
Motorola Labs - Paris                        +33 1 69 35 48 04 (Ph) 
Parc Les Algorithmes, Commune de St Aubin    +33 6 72 01 06 33 (Mob) 
91193 Gif-Sur-Yvette FRANCE                  +33 1 69 35 77 01 (Fax) 

The information contained in this communication has been classified as: 

[x] General Business Information 
[ ] Motorola Internal Use Only 
[ ] Motorola Confidential Proprietary