Abstract

CHAPTER 2. TEMPORAL INTEGRATION 42
Table 2.2: Initialization Timings Newton-GMRES(800)
Nx Nk F 2 Final NLI Calls to F Avg. Kry/N Line Search Red.
32 32 2.689 e-05 400 280518 700 2752
32 64 1.560 e-06 66 107417 1626 125
64 64 8.302 e-14 19 25878 1361 8
64 128 7.725 e-14 31 108111 3486 7
86 72 8.045 e-14 27 87317 3232 12
Table 2.3: Initialization Timings Preconditioned Newton-GMRES(100)
Nx Nk F 2 Final NLI Calls to F Avg. Kry/N Line Search Red.
32 32 1.762 e-14 10 893 88 0
32 64 1.038 e-14 11 1065 96 0
64 64 1.351 e-15 11 690 62 0
64 128 1.268 e-14 10 669 66 0
86 72 4.558 e-15 11 572 50 0
On the two coarsest grids, the unpreconditioned Newton iteration fails to converge
to the solution. On the Nx = Nk = 32 grid, at the seventh newton iteration, the
function norm was 2.689e-05, which is the same as the terminating function norm. In
the remaining 300+ iterations, the method successfully calculates a Newton step, but
reduces this step a number of times until it gets a very small reduction in the function
norm, and then takes this step. On the Nx = 32,Nk = 64 grid, the Newton iteration
stops because an acceptable Newton step could not be found. For the remaining