On 5 Aug 2014, at 0:14, James Crist wrote:
@Tim:
They're for representing tensors. Of course, the can be used for a
number
of things, including calculating finite difference formulas. In my
case,
tensors are useful for stress analysis, especially in changing
reference
frames. Other uses I know about relate to various physics topics.
Oh neat! I took a class on finite elements, but we never referred to
them
as tensors. I'll have to look into that.
Not really, finite differences are a different approach to solving PDEs.
With finite differences you have nodes at i-1, i, and i+1 (and possibly
in time or in multiple dimensions). You approximate the derivative with
differences in the values at those points. You can use Indexed to
represent these. As the mesh gets more fine, it's a closer
representation of the derivative as the formulas come from Taylor
series. I guess you could think of them as tensors, but it's not a
common thing. It's just that Indexed provides a useful way you can do
the representation.
The tensors are from continuum mechanics. The more sophisticated
analysis of material deformation all comes down to this, and tensors are
the usual way to represent things.
Have you used code generation with them? If you have and have some
example
code with them you could send my way that'd be great. It'd be really
useful
for me to understand exactly what the scope of support for them is, as
I
work around the implementation trying to get other things to work.
No, I haven't. Sorry.
For example, would you ever create an Indexed that did an operation
with a
Matrix? Or a Matrix with Indexed's as elements? What I'm trying to
see is
if there is any reason for them ever to coexist, or can the
implementations
assume that they're never used together? The tensor code makes
everything
really complicated as the loops introduce a scope of sorts (symbol
y[i]
isn't the same value at each point in a loop).
It's highly unlikely you'd create an Indexed that did an operation with
a Matrix, but a Matrix with Indexed elements, yes as this is what would
happen in a finite difference model.
Cheers,
Tim.
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