Algorithms and Bicycles

I was studying “FFTSVD: A Fast Multiscale Boundary-Element Method Solver Suitable for Bio-MEMS and Biomolecule simulation” by Altman et. al .

There are a few things that bother me about this paper. First, it is essentially a combination of ideas from  Kapur & Long’s SVD approach, the precorrected FFT, and a variation of the generalized FMM.  They use a low-rank approximation to construct what they call as the “dominant”  sources and responses. This uses a rank-revealing QR decomposition with re-orthogonalization for every box/node in the hierarchical oct-tree structure. Then, in order to integrate the pFFT ideas,  a set of equivalent grid-sources need to be constructed. This needs the evaluation of the potentials at pre-selected observation points and sub-sequently a Moore-Penrose inverse. Again, this needs to be done for every box/node. Essentially, the algorithm requires the setup operations of both pFFT and the SVD approaches. Unless, of course, I have missed something obvious and being dumb.

If my understanding is correct, then this algorithm must be terribly expensive to setup. Curiously enough, the authors do not report any  results on the setup times. Nothing. Zero.

They do, however, report  matrix-vector product timings, which show moderate improvement over existing techniques. Nothing breath-taking there either (less than a factor of 2 at best).

From a user’s perspective, it does not matter if we can get 10 times or 100 times speed-up for matrix-vector timings. What matters is if the over-all time is significantly reduced. Again, there is no report on those timings either.

My question is to the editor and the anonymous reviewers: how could you possibly accept this work without asking the most obvious and most important question? What were you doing?

Oh, well.