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### What's the role of restart in PGMRES?

Posted: Tue Jun 02, 2015 1:14 pm
Hi,

I have been experimenting solving a linear system with PGMRES+Jacobi preconditioner. The solver diverges with default restart. When I set the restart at 400, it converges in ~700 iterations. The number of iterations increases if I increase or decrease the restart from 400. How should I decide what restart is needed? Does the restart parameter change from system to system?

Quantity in brackets after PGMRES is the restart value. E.g. PGMRES(30) is with restart=30.

%=============================================================%
% PGMRES(30) solver summary:
% initial residual: 2.000000e+02
% iterations: 1000
% exact final residual: 4.569463e+00
% runtime: 1.0274 sec
%=============================================================%

%=============================================================%
% PGMRES(100) solver summary:
% initial residual: 2.000000e+02
% iterations: 1000
% exact final residual: 9.811325e-03
% runtime: 2.7982 sec
%=============================================================%

%=============================================================%
% PGMRES(400) solver summary:
% initial residual: 2.000000e+02
% iterations: 697
% exact final residual: 1.183331e-09
% runtime: 6.5171 sec
%=============================================================%

%=============================================================%
% PGMRES(500) solver summary:
% initial residual: 2.000000e+02
% iterations: 761
% exact final residual: 1.037513e-09
% runtime: 8.2672 sec
%=============================================================%

%=============================================================%
% PGMRES(350) solver summary:
% initial residual: 2.000000e+02
% iterations: 871
% exact final residual: 8.002018e-10
% runtime: 7.2320 sec
%=============================================================%

Thanks,