I am looking into the suitability of Deal.ii for our problem. We
essentially have 5D problems (3 space and 2 additional independent
variables).
The 2 additional variables are handled by h-adaption and I am interested
in having Deal.ii deal with the spatial part (possibly by
hp-refinement). The implication of our h-refinement scheme for the
non-space coordinates is that we have a varying number of unknowns per
spatial element to deal with (may be highly variable from 8 to hundreds
of unbknowns). Can Deal.ii handle this situation? Note that I am mostly
interested in using the storage, mesh adaption and quadrature etc., not
so much in the matrix solvers…
In addition to the suggestion Markus has already given, here's another idea:
If you have cells where you want some variables to be active, and others
on which you do not need these variables [1], then you can use the
tricks of step-46 where we have the same number of variables in each
cell, but on some cells the variables we don't actually need there are
inactivated by using a finite element space that is constant zero for
these variables and, thus, does not need any degrees of freedom. I would
suggest taking a look at step-46 to see how this is done there and to
see if it could be used for your situation as well.
Best
W.
[1] I'm thinking for example of expanding a variable that depends, say,
on 3 space + 2 angular variables (e.g. in radiative transfer) into
spherical harmonics in the angles. Then you end up with a number of
spherical harmonics defined on each cell, but you want to keep around
more of these harmonics in places where radiation is highly anisotropic
and fewer of them in places where you have an optically dense material.
In other words, at every space point you have *up to a maximal number*
of harmonics, but you want to inactive some or most of them at some points.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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