Request for forming the full linear system so that the full system can be solved through linear algebra solvers

[zcgan]

We want to request the fully coupled linear system (say the 47N*47N dense matrix for l=3) to be solved (or at least get the linear system assembled and we can pass to an external solver) so that we can get desired accuracy.

Some comments from Aleks in a list of emails discussing with Ronojoy,

Note that even if mat-vec product is O(N^2) and you use an iterative method like Conjugate Gradient, there is no reason to believe it will converge in O(1) iterations and thus be O(N^2) overall (though the wall screens hydrodynamic interactions so it may be). We have had a lot of luck with block-diagonal preconditioners though as we have discussed in the past, and this should work here too and help a lot. So in principle if one can write a matrix-vector product (which sounds like you more or less have already) and just assemble the dense (47*N)^2 matrices for each particle (the block diagonal blocks), this should be good enough to get a full solve easily in python.

What we need is an accurate mobility solver, i.e., we know forces and torques and slip, and want to get motion. This may require perhaps slight massaging of the linear system.