> I am currently looking into designing a new 3D finite element
> geo-electric code. I have come across deal.II and libmesh. Both
> libraries look quite promising, each having their
> advantages/disadvantages. On the plus side deal.II supports Nedelec
> elements which I am quite interested in using. However, libmesh allows
> to distribute the degrees of freedom (in addition to parallelising the
> linear algebra). A major design factor is memory requirements. This also
> seems to be one of the main distinguishing factors of the two libraries.
> Do you have estimates for the memory requirements for the stiffness
> matrix and load vector?
That depends on the problem you solve. For the Laplace equation in 2d with
Q1 elements you have 9 entries per row of the matrix, so you are talking
about 108 bytes in the matrix per degree of freedom. Plus storage for
solution vector, right hand side, and temporary vectors in the CG method.
For the Laplace equation in 2d, the linear system is not the largest
memory consumer of a finite element program, deal.II needs several hundred
(but less than 1000) bytes per degree of freedom.
That changes if you go to 3d and systems of equations because there you
have many more entries per row of the matrix (for example for an equation
like 'curl curl B = f' you would have 81 entries per row of the matrix
already for the lowest order elements. So you would already consume ~1000
bytes per degree of freedom for the linear system. This is independent of
the library you use, unless you go to schemes where the matrix is not
stored. Higher order elements would use even more memory, of course. In
these cases, the memory footprint of the linear system is larger than
grid, DoF handler, and the rest together.
> What size problems can be reasonably run?
On a machine with 16GB, using deal.II, you can solve linear systems with a
few million degrees of freedom (in 2d) or about a million (in 3d) without
too much trouble. On clusters we have solved problems with >20 million
unknowns.
Now let's see what our friends from the competition have to say ;-)
Cheers
W.
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