Inexact GMRES: Stokes equation

Figures 10–14 of the paper: "Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method"

Submitted for peer review.

Fig. 10: (StokesConvergence.pdf)

Convergence of the boundary-integral solution for Stokes flow around a sphere, using a  first-kind equation; p=16, linear system solved to 10^-5 tolerance. The relative error is with respect to the analytical solution for drag on a sphere.

Fig. 11: (StokesResidualHistory.pdf)

Residual history solving for surface traction on the surface of a sphere (first-kind integral problem), with a 10^-5 solver tolerance, 8,192 panels, and p=16 in the multipole expansions.

Fig. 12: (StokesSolveBreakdown.pdf)

Time breakdown between P2P and M2L when using a relaxation strategy for solving surface traction on the surface of a sphere, 10^-5 solver tolerance, 8,192 panels, p=16.

Fig. 13: (StokesSpeedupRelaxation.pdf)

Speed-up for solving first-kind Stokes equation on the surface of a sphere, varying N. 10^-5 solver tolerance, p=16.

Fig. 14: (StokesSpeedupTolerance.pdf)

Speed-ups for solving a 1st-kind Stokes problem on a sphere discretized with 8,192 panels, as the GMRES solver's tolerance increases; p=16 for all cases.