Reduced memory footprint of spectral discretizations via block-diagonal sparse operators

[brownbaerchen]

The spectral discretizations require a few block-diagonal matrices among all degrees of freedom. Constructing them as such actually reduces the memory requirements quite a bit compared to constructing general block matrices with only the diagonal blocks.
This is independent of the larger refactor, which is why I did a separate PR.
I added a test that the resulting operators are the same and that indeed memory is reduced.

[pancetta]

How large are these matrices in general?

[brownbaerchen]

The matrix size is number of degrees of freedom squared. For instance, in 3D RBC, you have $(5 \times N^3)^2$ for 5 solution components and $N^3$ grid points, which is very large. But a block diagonal matrix (diagonal in the components) has only $5\timesN^3^2$ entries, so a fifth. Now, since the matrices are sparse, I don’t understand why you need less memory when using different scipy functions for generating the same sparse block diagonal matrix. But that is the case in my tests.On 5. Jul 2025, at 11:26, Robert Speck ***@***.***> wrote:pancetta left a comment (Parallel-in-Time/pySDC#565) How large are these matrices in general? —Reply to this email directly, view it on GitHub, or unsubscribe.You are receiving this because you authored the thread.Message ID: ***@***.***>

[pancetta]

Allocation of memory in Python is not straightforward (and not efficient if done manually). Relying on libraries like scipy is strongly recommended over lists (or so).