NUTILS 9.0 "Jook-Sing"
arguments
nelems=32
etype=square
degree=3
reynolds=1000
compatible=False
strongbc=False
start 2025-04-10 02:33:03
solve_constraints
optimizing for argument u (9409,2) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 388 degrees of freedom of u
stokes
solve
solving for argument u (9409,2) and p (4225) using direct method
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 104,529k
residual decreased by 15.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 1e-17
residual norm: 1.5e-17
solve
optimizing for argument ψ (4225) using direct method
solving 4224 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 3,650k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 8e-16
residual norm: 8.1e-16
optimal value: 4.6e-05
velocity.png
vorticity.png
cross-hor.png
cross-ver.png
navier-stokes
solve
solving for argument u (9409,2) and p (4225) using linesearch-newton method
iter 0
residual norm: 6.3e-03
iter 1
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 104,567k
residual decreased by 3.0 orders using 0 krylov vectors
residual decreased by 2.5 orders using 1 krylov vectors
residual decreased by 3.6 orders using 2 krylov vectors
residual decreased by 3.1 orders using 3 krylov vectors
residual decreased by 2.3 orders using 4 krylov vectors
residual decreased by 0.0 orders using 5 krylov vectors
solver returned with residual 2e-17
estimated residual minimum at 44% of update vector
estimated residual minimum at 95% of update vector
update accepted at relaxation 0.44475
residual norm: 4.5e-03 (2%)
iter 2
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 104,790k
residual decreased by 7.6 orders using 0 krylov vectors
residual decreased by 6.9 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
solver returned with residual 1e-17
estimated residual minimum at 186% of update vector
update accepted at relaxation 0.42232
residual norm: 2.7e-03 (5%)
iter 3
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,032k
residual decreased by 6.4 orders using 0 krylov vectors
residual decreased by 4.9 orders using 1 krylov vectors
residual decreased by 3.3 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
solver returned with residual 6e-18
estimated residual minimum at 116% of update vector
update accepted at relaxation 0.78689
residual norm: 1.0e-03 (10%)
iter 4
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 104,706k
residual decreased by 3.5 orders using 0 krylov vectors
residual decreased by 3.5 orders using 1 krylov vectors
residual decreased by 4.2 orders using 2 krylov vectors
residual decreased by 2.8 orders using 3 krylov vectors
residual decreased by 0.0 orders using 4 krylov vectors
solver returned with residual 9e-18
estimated residual minimum at 37% of update vector
estimated residual minimum at 77% of update vector
update accepted at relaxation 0.33925
residual norm: 8.7e-04 (11%)
iter 5
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 104,831k
residual decreased by 2.5 orders using 0 krylov vectors
residual decreased by 1.7 orders using 1 krylov vectors
residual decreased by 2.0 orders using 2 krylov vectors
residual decreased by 2.2 orders using 3 krylov vectors
residual decreased by 2.3 orders using 4 krylov vectors
residual decreased by 2.7 orders using 5 krylov vectors
residual decreased by 0.7 orders using 6 krylov vectors
residual decreased by 0.0 orders using 7 krylov vectors
solver returned with residual 7e-18
estimated residual minimum at 137% of update vector
update accepted at relaxation 0.2615
residual norm: 6.9e-04 (12%)
iter 6
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,103k
residual decreased by 0.2 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.3 orders using 2 krylov vectors
residual decreased by 0.9 orders using 3 krylov vectors
residual decreased by 1.1 orders using 4 krylov vectors
residual decreased by 1.7 orders using 5 krylov vectors
residual decreased by 1.2 orders using 6 krylov vectors
residual decreased by 1.6 orders using 7 krylov vectors
residual decreased by 1.6 orders using 8 krylov vectors
residual decreased by 1.6 orders using 9 krylov vectors
residual decreased by 2.0 orders using 10 krylov vectors
residual decreased by 1.3 orders using 11 krylov vectors
residual decreased by 0.7 orders using 12 krylov vectors
solver returned with residual 3e-18
estimated residual minimum at 290% of update vector
update accepted at relaxation 0.35709
residual norm: 4.5e-04 (15%)
iter 7
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,250k
residual decreased by 0.3 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
residual decreased by 0.2 orders using 3 krylov vectors
residual decreased by 0.0 orders using 4 krylov vectors
residual decreased by 0.0 orders using 5 krylov vectors
residual decreased by 0.0 orders using 6 krylov vectors
residual decreased by 0.0 orders using 7 krylov vectors
residual decreased by 0.0 orders using 8 krylov vectors
residual decreased by 0.2 orders using 9 krylov vectors
residual decreased by 0.2 orders using 10 krylov vectors
residual decreased by 0.6 orders using 11 krylov vectors
residual decreased by 1.3 orders using 12 krylov vectors
residual decreased by 0.7 orders using 13 krylov vectors
residual decreased by 1.2 orders using 14 krylov vectors
residual decreased by 0.9 orders using 15 krylov vectors
residual decreased by 1.5 orders using 16 krylov vectors
residual decreased by 1.1 orders using 17 krylov vectors
residual decreased by 1.6 orders using 18 krylov vectors
residual decreased by 1.1 orders using 19 krylov vectors
residual decreased by 1.6 orders using 20 krylov vectors
residual decreased by 0.5 orders using 21 krylov vectors
residual decreased by 0.0 orders using 22 krylov vectors
solver returned with residual 3e-17
estimated residual minimum at 147% of update vector
update accepted at relaxation 0.71417
residual norm: 1.6e-04 (20%)
iter 8
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,195k
residual decreased by 0.0 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
residual decreased by 0.0 orders using 4 krylov vectors
residual decreased by 0.0 orders using 5 krylov vectors
residual decreased by 0.0 orders using 6 krylov vectors
residual decreased by 0.0 orders using 7 krylov vectors
residual decreased by 0.0 orders using 8 krylov vectors
residual decreased by 0.0 orders using 9 krylov vectors
residual decreased by 0.0 orders using 10 krylov vectors
residual decreased by 0.0 orders using 11 krylov vectors
residual decreased by 0.0 orders using 12 krylov vectors
residual decreased by 0.0 orders using 13 krylov vectors
residual decreased by 0.0 orders using 14 krylov vectors
residual decreased by 0.0 orders using 15 krylov vectors
residual decreased by 0.0 orders using 16 krylov vectors
residual decreased by 0.0 orders using 17 krylov vectors
residual decreased by 0.0 orders using 18 krylov vectors
residual decreased by 0.0 orders using 19 krylov vectors
residual decreased by 0.0 orders using 20 krylov vectors
residual decreased by 0.0 orders using 21 krylov vectors
residual decreased by 0.0 orders using 22 krylov vectors
residual decreased by 0.0 orders using 23 krylov vectors
residual decreased by 0.0 orders using 24 krylov vectors
residual decreased by 0.0 orders using 25 krylov vectors
residual decreased by 0.0 orders using 26 krylov vectors
residual decreased by 0.0 orders using 27 krylov vectors
residual decreased by 0.0 orders using 28 krylov vectors
residual decreased by 0.0 orders using 29 krylov vectors
residual decreased by 0.0 orders using 30 krylov vectors
residual decreased by 0.0 orders using 31 krylov vectors
residual decreased by 0.0 orders using 32 krylov vectors
residual decreased by 0.0 orders using 33 krylov vectors
residual decreased by 0.1 orders using 34 krylov vectors
residual decreased by 0.2 orders using 35 krylov vectors
residual decreased by 0.2 orders using 36 krylov vectors
residual decreased by 0.1 orders using 37 krylov vectors
residual decreased by 0.1 orders using 38 krylov vectors
residual decreased by 0.0 orders using 39 krylov vectors
residual decreased by 0.1 orders using 40 krylov vectors
residual decreased by 0.1 orders using 41 krylov vectors
residual decreased by 0.0 orders using 42 krylov vectors
residual decreased by 0.0 orders using 43 krylov vectors
residual decreased by 0.0 orders using 44 krylov vectors
residual decreased by 0.0 orders using 45 krylov vectors
residual decreased by 0.0 orders using 46 krylov vectors
residual decreased by 0.0 orders using 47 krylov vectors
residual decreased by 0.0 orders using 48 krylov vectors
residual decreased by 0.0 orders using 49 krylov vectors
residual decreased by 0.0 orders using 50 krylov vectors
residual decreased by 0.0 orders using 51 krylov vectors
residual decreased by 0.0 orders using 52 krylov vectors
residual decreased by 0.0 orders using 53 krylov vectors
residual decreased by 0.0 orders using 54 krylov vectors
residual decreased by 0.0 orders using 55 krylov vectors
residual decreased by 0.0 orders using 56 krylov vectors
residual decreased by 0.0 orders using 57 krylov vectors
residual decreased by 0.0 orders using 58 krylov vectors
residual decreased by 0.1 orders using 59 krylov vectors
residual decreased by 0.0 orders using 60 krylov vectors
residual decreased by 0.1 orders using 61 krylov vectors
residual decreased by 0.1 orders using 62 krylov vectors
residual decreased by 0.0 orders using 63 krylov vectors
residual decreased by 0.1 orders using 64 krylov vectors
residual decreased by 0.0 orders using 65 krylov vectors
residual decreased by 0.0 orders using 66 krylov vectors
residual decreased by 0.2 orders using 67 krylov vectors
residual decreased by 1.0 orders using 68 krylov vectors
residual decreased by 1.6 orders using 69 krylov vectors
residual decreased by 1.0 orders using 70 krylov vectors
residual decreased by 1.3 orders using 71 krylov vectors
residual decreased by 1.4 orders using 72 krylov vectors
residual decreased by 1.3 orders using 73 krylov vectors
residual decreased by 0.1 orders using 74 krylov vectors
residual decreased by 0.0 orders using 75 krylov vectors
residual decreased by 0.0 orders using 76 krylov vectors
residual decreased by 0.0 orders using 77 krylov vectors
residual decreased by 0.0 orders using 78 krylov vectors
residual decreased by 0.0 orders using 79 krylov vectors
residual decreased by 0.0 orders using 80 krylov vectors
solver returned with residual 8e-14
estimated residual minimum at 103% of update vector
update accepted at relaxation 1
residual norm: 7.5e-06 (37%)
iter 9
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,001k
residual decreased by 0.0 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
residual decreased by 0.0 orders using 4 krylov vectors
residual decreased by 0.0 orders using 5 krylov vectors
residual decreased by 0.0 orders using 6 krylov vectors
residual decreased by 0.0 orders using 7 krylov vectors
residual decreased by 0.0 orders using 8 krylov vectors
residual decreased by 0.0 orders using 9 krylov vectors
residual decreased by 0.0 orders using 10 krylov vectors
residual decreased by 0.0 orders using 11 krylov vectors
residual decreased by 0.0 orders using 12 krylov vectors
residual decreased by 0.0 orders using 13 krylov vectors
residual decreased by 0.0 orders using 14 krylov vectors
residual decreased by 0.0 orders using 15 krylov vectors
residual decreased by 0.0 orders using 16 krylov vectors
residual decreased by 0.0 orders using 17 krylov vectors
residual decreased by 0.0 orders using 18 krylov vectors
residual decreased by 0.0 orders using 19 krylov vectors
residual decreased by 0.0 orders using 20 krylov vectors
residual decreased by 0.0 orders using 21 krylov vectors
residual decreased by 0.0 orders using 22 krylov vectors
residual decreased by 0.0 orders using 23 krylov vectors
residual decreased by 0.0 orders using 24 krylov vectors
residual decreased by 0.0 orders using 25 krylov vectors
residual decreased by 0.0 orders using 26 krylov vectors
residual decreased by 0.0 orders using 27 krylov vectors
residual decreased by 0.0 orders using 28 krylov vectors
residual decreased by 0.0 orders using 29 krylov vectors
residual decreased by 0.0 orders using 30 krylov vectors
residual decreased by 0.0 orders using 31 krylov vectors
residual decreased by 0.0 orders using 32 krylov vectors
residual decreased by 0.0 orders using 33 krylov vectors
residual decreased by 0.1 orders using 34 krylov vectors
residual decreased by 0.1 orders using 35 krylov vectors
residual decreased by 0.0 orders using 36 krylov vectors
residual decreased by 0.0 orders using 37 krylov vectors
residual decreased by 0.0 orders using 38 krylov vectors
residual decreased by 0.3 orders using 39 krylov vectors
residual decreased by 0.3 orders using 40 krylov vectors
residual decreased by 0.3 orders using 41 krylov vectors
residual decreased by 0.1 orders using 42 krylov vectors
residual decreased by 0.1 orders using 43 krylov vectors
residual decreased by 0.0 orders using 44 krylov vectors
residual decreased by 0.0 orders using 45 krylov vectors
residual decreased by 0.0 orders using 46 krylov vectors
residual decreased by 0.0 orders using 47 krylov vectors
residual decreased by 0.0 orders using 48 krylov vectors
residual decreased by 0.0 orders using 49 krylov vectors
residual decreased by 0.0 orders using 50 krylov vectors
residual decreased by 0.1 orders using 51 krylov vectors
residual decreased by 0.0 orders using 52 krylov vectors
residual decreased by 0.2 orders using 53 krylov vectors
residual decreased by 0.1 orders using 54 krylov vectors
residual decreased by 0.1 orders using 55 krylov vectors
residual decreased by 0.1 orders using 56 krylov vectors
residual decreased by 0.5 orders using 57 krylov vectors
residual decreased by 0.7 orders using 58 krylov vectors
residual decreased by 0.6 orders using 59 krylov vectors
residual decreased by 0.2 orders using 60 krylov vectors
residual decreased by 0.0 orders using 61 krylov vectors
residual decreased by 0.0 orders using 62 krylov vectors
residual decreased by 0.4 orders using 63 krylov vectors
residual decreased by 1.1 orders using 64 krylov vectors
residual decreased by 1.2 orders using 65 krylov vectors
residual decreased by 1.0 orders using 66 krylov vectors
residual decreased by 1.1 orders using 67 krylov vectors
residual decreased by 0.9 orders using 68 krylov vectors
residual decreased by 0.3 orders using 69 krylov vectors
residual decreased by 0.0 orders using 70 krylov vectors
residual decreased by 0.0 orders using 71 krylov vectors
residual decreased by 0.0 orders using 72 krylov vectors
residual decreased by 0.0 orders using 73 krylov vectors
residual decreased by 0.0 orders using 74 krylov vectors
residual decreased by 0.0 orders using 75 krylov vectors
residual decreased by 0.0 orders using 76 krylov vectors
residual decreased by 0.0 orders using 77 krylov vectors
residual decreased by 0.0 orders using 78 krylov vectors
residual decreased by 0.0 orders using 79 krylov vectors
residual decreased by 0.0 orders using 80 krylov vectors
residual decreased by 0.0 orders using 81 krylov vectors
residual decreased by 0.0 orders using 82 krylov vectors
residual decreased by 0.0 orders using 83 krylov vectors
residual decreased by 0.0 orders using 84 krylov vectors
solver returned with residual 6e-16
estimated residual minimum at 100% of update vector
update accepted at relaxation 1
residual norm: 1.7e-09 (84%)
iter 10
solving 22654 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 105,334k
residual decreased by 0.0 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
residual decreased by 0.0 orders using 4 krylov vectors
residual decreased by 0.0 orders using 5 krylov vectors
residual decreased by 0.0 orders using 6 krylov vectors
residual decreased by 0.0 orders using 7 krylov vectors
residual decreased by 0.0 orders using 8 krylov vectors
residual decreased by 0.0 orders using 9 krylov vectors
residual decreased by 0.0 orders using 10 krylov vectors
residual decreased by 0.0 orders using 11 krylov vectors
residual decreased by 0.0 orders using 12 krylov vectors
residual decreased by 0.0 orders using 13 krylov vectors
residual decreased by 0.0 orders using 14 krylov vectors
residual decreased by 0.0 orders using 15 krylov vectors
residual decreased by 0.0 orders using 16 krylov vectors
residual decreased by 0.0 orders using 17 krylov vectors
residual decreased by 0.0 orders using 18 krylov vectors
residual decreased by 0.0 orders using 19 krylov vectors
residual decreased by 0.0 orders using 20 krylov vectors
residual decreased by 0.0 orders using 21 krylov vectors
residual decreased by 0.0 orders using 22 krylov vectors
residual decreased by 0.0 orders using 23 krylov vectors
residual decreased by 0.0 orders using 24 krylov vectors
residual decreased by 0.0 orders using 25 krylov vectors
residual decreased by 0.0 orders using 26 krylov vectors
residual decreased by 0.0 orders using 27 krylov vectors
residual decreased by 0.0 orders using 28 krylov vectors
residual decreased by 0.0 orders using 29 krylov vectors
residual decreased by 0.0 orders using 30 krylov vectors
residual decreased by 0.0 orders using 31 krylov vectors
residual decreased by 0.1 orders using 32 krylov vectors
residual decreased by 0.0 orders using 33 krylov vectors
residual decreased by 0.0 orders using 34 krylov vectors
residual decreased by 0.0 orders using 35 krylov vectors
residual decreased by 0.1 orders using 36 krylov vectors
residual decreased by 0.1 orders using 37 krylov vectors
residual decreased by 0.1 orders using 38 krylov vectors
residual decreased by 0.1 orders using 39 krylov vectors
residual decreased by 0.2 orders using 40 krylov vectors
residual decreased by 0.0 orders using 41 krylov vectors
residual decreased by 0.0 orders using 42 krylov vectors
residual decreased by 0.0 orders using 43 krylov vectors
residual decreased by 0.1 orders using 44 krylov vectors
residual decreased by 0.1 orders using 45 krylov vectors
residual decreased by 0.0 orders using 46 krylov vectors
residual decreased by 0.0 orders using 47 krylov vectors
residual decreased by 0.0 orders using 48 krylov vectors
residual decreased by 0.0 orders using 49 krylov vectors
residual decreased by 0.1 orders using 50 krylov vectors
residual decreased by 0.1 orders using 51 krylov vectors
residual decreased by 0.3 orders using 52 krylov vectors
residual decreased by 0.0 orders using 53 krylov vectors
residual decreased by 0.0 orders using 54 krylov vectors
residual decreased by 0.1 orders using 55 krylov vectors
residual decreased by 0.0 orders using 56 krylov vectors
residual decreased by 0.0 orders using 57 krylov vectors
residual decreased by 0.0 orders using 58 krylov vectors
residual decreased by 0.0 orders using 59 krylov vectors
residual decreased by 0.0 orders using 60 krylov vectors
residual decreased by 0.6 orders using 61 krylov vectors
residual decreased by 0.5 orders using 62 krylov vectors
residual decreased by 0.0 orders using 63 krylov vectors
residual decreased by 0.0 orders using 64 krylov vectors
residual decreased by 0.0 orders using 65 krylov vectors
residual decreased by 0.0 orders using 66 krylov vectors
residual decreased by 0.8 orders using 67 krylov vectors
residual decreased by 1.7 orders using 68 krylov vectors
residual decreased by 1.7 orders using 69 krylov vectors
residual decreased by 0.9 orders using 70 krylov vectors
residual decreased by 0.0 orders using 71 krylov vectors
residual decreased by 0.0 orders using 72 krylov vectors
residual decreased by 0.0 orders using 73 krylov vectors
residual decreased by 0.0 orders using 74 krylov vectors
residual decreased by 0.0 orders using 75 krylov vectors
residual decreased by 0.0 orders using 76 krylov vectors
residual decreased by 0.0 orders using 77 krylov vectors
residual decreased by 0.0 orders using 78 krylov vectors
residual decreased by 0.0 orders using 79 krylov vectors
residual decreased by 0.0 orders using 80 krylov vectors
residual decreased by 0.0 orders using 81 krylov vectors
solver returned with residual 3e-17
estimated residual minimum at 100% of update vector
update accepted at relaxation 1
residual norm: 1.9e-15 (100%)
solve
optimizing for argument ψ (4225) using direct method
solving 4224 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 3,650k
residual decreased by 14.1 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 1e-15
residual norm: 1.2e-15
optimal value: 1.1e-04
velocity.png
vorticity.png
cross-hor.png
cross-ver.png
locate
locate detected linear geometry: x = [0. 0.] + [0.03125 0.03125] xi ~[0. 0.]
center velocity: -0.062070497082069936, 0.02578743619581585
center vorticity: -2.066526156341388
upper-left (0,.95) vorticity: 10.008927533370018
finish 2025-04-10 02:33:46, elapsed 0:42