NUTILS 9.0 "Jook-Sing"
arguments
etype=square
btype=h-std
degree=2
nrefine=5
start 2025-04-09 21:29:02
level 1/6
solve_constraints
optimizing for argument u (21) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 5 degrees of freedom of u
solve_constraints
optimizing for argument u (21) with drop tolerance 1e-15
solving 11 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 145k
residual decreased by 16.1 orders using 0 krylov vectors
residual decreased by 0.5 orders using 1 krylov vectors
solver returned with residual 3e-17
residual norm: 2.8e-17
optimal value: 3.8e-07
constrained 11 degrees of freedom of u
solve
solving for argument u (21) using direct method
solving 5 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 143k
residual decreased by 15.9 orders using 0 krylov vectors
solver returned with residual 7e-17
residual norm: 6.5e-17
errors at 21 dofs: L2 5.22e-03, H1 8.79e-02
sol.png
err.png
level 2/6
solve_constraints
optimizing for argument u (65) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 9 degrees of freedom of u
solve_constraints
optimizing for argument u (65) with drop tolerance 1e-15
solving 23 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 150k
residual decreased by 15.9 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 6e-17
residual norm: 6.2e-17
optimal value: 1.1e-08
constrained 23 degrees of freedom of u
solve
solving for argument u (65) using direct method
solving 33 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 165k
residual decreased by 15.5 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.2 orders using 2 krylov vectors
solver returned with residual 1e-16
residual norm: 1.4e-16
errors at 65 dofs: L2 1.76e-03, H1 5.48e-02
error convergence rates: L2 -0.96 (optimal -1.5), H1 -0.42 (optimal -1.0)
sol.png
err.png
level 3/6
solve_constraints
optimizing for argument u (149) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 13 degrees of freedom of u
solve_constraints
optimizing for argument u (149) with drop tolerance 1e-15
solving 31 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 153k
residual decreased by 15.8 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
solver returned with residual 8e-17
residual norm: 8.8e-17
optimal value: 6.5e-09
constrained 31 degrees of freedom of u
solve
solving for argument u (149) using direct method
solving 105 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 248k
residual decreased by 15.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
residual decreased by 0.1 orders using 3 krylov vectors
solver returned with residual 3e-16
residual norm: 3.0e-16
errors at 149 dofs: L2 6.54e-04, H1 3.46e-02
error convergence rates: L2 -1.08 (optimal -1.5), H1 -0.49 (optimal -1.0)
sol.png
err.png
level 4/6
solve_constraints
optimizing for argument u (225) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 17 degrees of freedom of u
solve_constraints
optimizing for argument u (225) with drop tolerance 1e-15
solving 31 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 153k
residual decreased by 15.8 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
solver returned with residual 8e-17
residual norm: 8.8e-17
optimal value: 6.5e-09
constrained 31 degrees of freedom of u
solve
solving for argument u (225) using direct method
solving 177 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 363k
residual decreased by 15.0 orders using 0 krylov vectors
residual decreased by 0.5 orders using 1 krylov vectors
residual decreased by 0.2 orders using 2 krylov vectors
solver returned with residual 3e-16
residual norm: 3.1e-16
errors at 225 dofs: L2 2.67e-04, H1 2.20e-02
error convergence rates: L2 -1.33 (optimal -1.5), H1 -0.63 (optimal -1.0)
sol.png
err.png
level 5/6
solve_constraints
optimizing for argument u (301) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 21 degrees of freedom of u
solve_constraints
optimizing for argument u (301) with drop tolerance 1e-15
solving 31 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 153k
residual decreased by 15.8 orders using 0 krylov vectors
residual decreased by 0.0 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
solver returned with residual 8e-17
residual norm: 8.8e-17
optimal value: 6.5e-09
constrained 31 degrees of freedom of u
solve
solving for argument u (301) using direct method
solving 249 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 492k
residual decreased by 15.0 orders using 0 krylov vectors
residual decreased by 0.4 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
solver returned with residual 4e-16
residual norm: 3.8e-16
errors at 301 dofs: L2 1.42e-04, H1 1.42e-02
error convergence rates: L2 -1.52 (optimal -1.5), H1 -0.80 (optimal -1.0)
sol.png
err.png
level 6/6
solve_constraints
optimizing for argument u (453) with drop tolerance 1e-15
residual norm: 0.0e+00
optimal value: 0.0e+00
constrained 37 degrees of freedom of u
solve_constraints
optimizing for argument u (453) with drop tolerance 1e-15
solving 35 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 155k
residual decreased by 15.9 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
solver returned with residual 4e-17
residual norm: 5.5e-17
optimal value: 2.4e-09
constrained 35 degrees of freedom of u
solve
solving for argument u (453) using direct method
solving 381 dof system to machine precision using arnoldi solver
constructing direct preconditioner
peak memory use 672k
residual decreased by 14.9 orders using 0 krylov vectors
residual decreased by 0.5 orders using 1 krylov vectors
residual decreased by 0.1 orders using 2 krylov vectors
residual decreased by 0.0 orders using 3 krylov vectors
solver returned with residual 4e-16
residual norm: 4.2e-16
errors at 453 dofs: L2 7.16e-05, H1 8.98e-03
error convergence rates: L2 -1.62 (optimal -1.5), H1 -0.93 (optimal -1.0)
sol.png
err.png
finish 2025-04-09 21:29:18, elapsed 0:16