[Users] Higher dimensions

[Erik Schnetter]

Robert

I want to add to Roland's description: Most people simulating gravity
in 4+1 dimensions or higher will assume some symmetry (e.g.
axisymmetry), so that only 3 spatial dimensions are actually
simulated. This is possible with the toolkit in principle, but you
will need a thorn that implements the correspondingly reduced Einstein
(or scalar/vector field) equations.

If you actually want to solve some PDEs in full 4+1 dimensions,
without assuming symmetry, then you will not only need support from
the driver (which exists in principle), but also respective initial
conditions, evolution, and analysis thorns, which do not yet exist.

-erik


On Mon, Aug 9, 2021 at 4:06 PM Roland Haas <rhaas at illinois.edu> wrote:
>
> Hello Robert,
>
> > Is it possible to run computations using the Einstein Toolkit in higher
> > dimensional spaces? Like 1+4.
> It is mostly geared towards 1+3. The Carpet driver itself does
> (or did at one point) support 4 spatial dimensions if one adds:
>
> -DCARPET_DIM=4
>
> to CXXFLAGS in the option list. The respective code is from 2009 so may
> no longer work as expected.
>
> Other EinsteinToolkit thorns probably will not work though, eg even
> CartGrid3D will not work and neither will the initial data thorns that
> expect use coordinates x,y,z.
>
> So you would have to decide what you want to use an most likely
> (easily) expand them.
>
> Yours,
> Roland
>
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-- 
Erik Schnetter <schnetter at cct.lsu.edu>
http://www.perimeterinstitute.ca/personal/eschnetter/