Re: request for algorithm

On 2006-01-12, Peter Spellucci <spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
>
> this is a wrong aproach: parallelization makes sense only for HPC
> and HPC applications always require that you consider quite carefully the
> properties of the specific problem, the properties of your computing equipment
> coming second

I know, and you are partly right, judging from the algorithmic
perspective. However, I was more interested to investigate specific
programming/hardware issues purely from the CS perspective, and the focus
was not on a particular class of applications. This research attracted
my interest in the field of numerical analysis, hence the reverse order
you spotted.

>
> no!
> laplacian(U(x,y,z))=F(x,y,z), domain [0,X]*[0,Y]*[0,Z]
> makes no sense without specifying boundary values (Dirichlet, von Neumann,
> Robin) on the complete boundary. the initial value problem for the
> laplacian is not well posed in the sense of Hadamard (existence, uniqueness of
> solution and continuous dependence of the solution from the problem data)
>

(Sorry for my ignorance, just curious so I took up the courage to ask)
What if we somehow know that we are looking for a periodic function,
and choose a domain, so that the required value at x=1 coincides with the
value at x=X? Then I could hypothetically use boundary values specified
on the complete domain.

>
> what you really want: all problems (?) where "new data" depend explicitly
> on the "old data" and there exist of course lots of problems which can be solved
> in this manner, for example all explicit iteration processes, and, as mentioned
> already, time stepping for hyperbolic equations
>

I noticed you mentioned first order hyperbolic equations, that means
second order is inappropriate? Also, if any other problem with the
desired properties falls in mind, I would be grateful if you let me
know. Finally, I would certainly be interested in any proposed reading
you would recommend on numerical analysis, discretization techniques
and iterative solvers.

Thank you very much for your time Professor!
.

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