Precomputed operator files

For each combination of (kernel, multipole order m, Chebyshev degree q, precision), PVFMM precomputes translation operators (with symmetry compression). This happens automatically the first time such a combination is used and the result is written to a data file that is loaded on subsequent runs:

Precomp_<kernel-name>[_q<q>]_m<m>[_f].data

  • <kernel-name> — e.g. laplace, laplace_grad, stokes_vel, biot_savart, helmholtz;

  • _q<q> — present for volume-FMM operators (Chebyshev degree);

  • _f — single-precision variant (no suffix = double).

Search path

The directory for these files is resolved in this order:

  1. the compile-time default set with ./configure --with-precomp-dir=DIR;

  2. the PVFMM_DIR environment variable;

  3. the current working directory.

First-run cost

Particle-FMM operator construction takes seconds to minutes. Volume-FMM operators (which include singular near-field quadratures) can take minutes to hours and produce files from a few MB up to ~10 GB (e.g. Helmholtz with q=14). Plan accordingly:

  • set PVFMM_DIR to a persistent, shared location so every run and every user of a machine reuses the same cache;

  • do not delete the Precomp_*.data files casually — they are expensive to regenerate;

  • the cache is portable across runs but tied to precision and to the (kernel, m, q) triple, so parameter sweeps over m/q populate several files.

On load, rank 0 of the communicator reads the file and broadcasts its contents to the other ranks.