Inexact GMRES: Laplace equation

Figures and plotting scripts:<br>Figures 5–9 of the paper: <i>"Inexact Krylov iterations and relaxation strategies with fast-multipole boundary element method"</i><br>Submitted for peer review.<br>Fig. 5: (LaplaceConvergence.pdf)Convergence of 1st-kind (solid line) and 2nd-kind (dotted line) solvers for the Laplace equation on a sphere, using a GMRES with FMM-accelerated matrix-vecctor products.<br>Fig. 6: (LaplaceResidualIterations.pdf)In a test using a sphere discretized with 32,768 triangles, the residual (solid line, left axis) decreases with successive GMRES iterations while the necessary <i>p</i> (open circles, right axis) to achieve convergence drops quickly.<br>Fig. 7: (LaplaceSpeedupRelaxation.pdf)Speed-up using a relaxation strategy for three different triangulations of a sphere (<i>N</i> is the number of surface panels), using 1st-kind and 2nd-kind integral formulations. (Multi-threaded evaluator running on 6 CPU cores.)<br>Fig. 8: (LaplaceRelaxationP.pdf)Timings for solving a 1st-kind Laplace integral formulation on a sphere discretized with 32,768 panels, using a relaxed GMRES with different initial values of <i>p</i>, compared with a fixed-<i>p</i> solver. The iteration count was capped at 10 for all cases. (Multi-threaded evaluator running on 6 CPU cores.)<br>Fig. 9: (LaplaceSpeedupTolerance.pdf)Speed-ups for solving a 1st-kind Laplace integral problem on a sphere discretized with 8,192 panels, as the GMRES solver's tolerance increases; <i>p</i>=10 for all cases. (Multi-threaded evaluator running on 6 CPU cores.)<br>