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Blitz Devel : |
From: Axel Thimm (Axel.Thimm_at_[hidden])
Date: 1998-06-26 05:30:00
Hello,
On Thu, Jun 25, 1998 at 05:25:30PM -0400, Todd Veldhuizen wrote:
> I'm going to implement the following stencil operators:
>
> backward differences with accuracy O(h) and O(h^2)
> central differences with accuracy O(h^2) and O(h^4)
> forward differences with accuracy O(H) and O(h^2)
>
> for the first through fourth derivatives (altogether, 24 stencil
> operators).
>
> Question: naming conventions.
On lattices we call them forward, backward and symmetric (or antihermitian)
derivatives. It (falsely ?) resembles continuum, but so do names like Laplace
or d'Alembert.
Are there thoughts, or better said wishes, for introducing connections? I.e.
-2*A(0,0) + U(1,1) * A(1,0) + U(1,-1) * A(-1,0) etc.
I do not know, if this is used in FEM, but it makes sense on differential
operators over manifolds with connections, e.g. lattice gauge theory or
general relativity on the lattice. Perhaps Hydrodynamics also use this concept
in defining their covariant derivative including the current etc., do they?
Another extension (for fermionic field theories) could be Dirac operators
linear operators that should give a Laplacian/d'Alembert when squared, thus
introducing Clifford algebras.
At this stage all of this may be still too academic to discuss for
implemenation into Blitz++, but perhaps it would be good to know where the
extensions should be made in the future and not to block that way.
Regards, Axel.
-- Axel Thimm Axel.Thimm_at_[hidden] Axel.Thimm_at_[hidden] --------------------- blitz-dev list -------------------------------- * To subscribe/unsubscribe: mail to majordomo_at_[hidden], with "subscribe blitz-dev" or "unsubscribe blitz-dev" in the body of the message * Blitz++ web page: http://oonumerics.org/blitz/