NUTILS 9.0 "Jook-Sing"
arguments
nelems=20
etype=square
btype=std
degree=1
poisson=0.25
angle=20
restol=1e-08
trim=True
start 2025-04-10 02:34:06
solve_constraints
optimizing for argument u (420,2) with drop tolerance 1e-15
solving 84 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
matrix is diagonally dominant, solving as SPD
peak memory use 166k
residual decreased by 16.0 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 1e-17
residual norm: 1.4e-17
optimal value: -1.1e-16
constrained 84 degrees of freedom of u
solve
optimizing for argument u (420,2) using direct method
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 15.0 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 3e-15
residual norm: 3.1e-15
optimal value: 1.2e-01
linear.png
solve
optimizing for argument u (420,2) using minimize method
iter 0
residual norm: 4.1e-01
iter 1
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.5 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 6e-16
spectrum: 2.1e-01..6.3e+00 (positive definite)
energy -1.43e-02 / e+0.0 and decreasing
residual norm: 2.8e-01 (2%)
iter 2
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.4 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 6e-16
spectrum: 1.9e-01..3.9e+00 (positive definite)
energy -1.48e-02 / e+0.5 and decreasing
residual norm: 3.0e-01 (2%)
iter 3
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.5 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 6e-16
spectrum: 1.8e-01..1.8e+01 (positive definite)
energy -4.04e-03 / e+1.0 and decreasing
residual norm: 2.1e-01 (4%)
iter 4
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 5e-16
spectrum: 1.8e-01..1.3e+01 (positive definite)
energy -5.23e-03 / e+1.5 and decreasing
residual norm: 2.2e-01 (4%)
iter 5
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.4 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 5e-16
spectrum: 1.7e-01..2.1e+01 (positive definite)
energy -4.35e-03 / e+2.0 and decreasing
residual norm: 1.7e-01 (5%)
iter 6
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 5e-16
spectrum: 1.7e-01..1.4e+01 (positive definite)
energy -7.49e-03 / e+2.5 and decreasing
residual norm: 1.7e-01 (5%)
iter 7
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 4e-16
spectrum: 1.6e-01..2.2e+01 (positive definite)
energy -5.75e-03 / e+3.0 and decreasing
residual norm: 1.2e-01 (7%)
iter 8
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
residual decreased by 0.0 orders using 2 krylov vectors
solver returned with residual 3e-16
spectrum: 1.5e-01..1.5e+01 (positive definite)
energy -8.25e-03 / e+3.5 and decreasing
residual norm: 9.6e-02 (8%)
iter 9
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 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
solver returned with residual 3e-16
spectrum: 1.4e-01..2.2e+01 (positive definite)
energy -4.45e-03 / e+4.0 and decreasing
residual norm: 5.8e-02 (11%)
iter 10
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 2e-16
spectrum: 1.4e-01..1.5e+01 (positive definite)
energy -3.62e-03 / e+4.5 and decreasing
residual norm: 2.9e-02 (15%)
iter 11
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 9e-17
spectrum: 1.3e-01..2.2e+01 (positive definite)
energy -8.10e-04 / e+5.0 and decreasing
residual norm: 1.1e-02 (21%)
iter 12
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.1 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 4e-17
spectrum: 1.2e-01..1.5e+01 (positive definite)
energy -1.83e-04 / e+5.5 and decreasing
residual norm: 1.9e-03 (31%)
iter 13
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 6e-18
spectrum: 8.4e-02..1.9e+01 (positive definite)
energy -4.69e-06 / e+6.0 and decreasing
residual norm: 3.0e-04 (41%)
iter 14
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 9e-19
spectrum: 3.3e-02..1.6e+01 (positive definite)
energy -1.39e-07 / e+6.5 and decreasing
residual norm: 8.7e-05 (48%)
iter 15
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 3e-19
spectrum: 2.1e-02..2.1e+01 (positive definite)
energy -9.20e-09 / e+7.0 and decreasing
residual norm: 2.5e-05 (55%)
iter 16
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 8e-20
spectrum: 1.8e-02..1.6e+01 (positive definite)
energy -1.17e-09 / e+7.5 and decreasing
residual norm: 3.7e-06 (66%)
iter 17
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.3 orders using 0 krylov vectors
residual decreased by 0.2 orders using 1 krylov vectors
solver returned with residual 1e-20
spectrum: 1.6e-02..2.1e+01 (positive definite)
energy -2.12e-11 / e+8.0 and decreasing
residual norm: 3.4e-07 (80%)
iter 18
solving 756 dof system to machine precision using arnoldi solver
constructing symmetric direct preconditioner
peak memory use 780k
residual decreased by 14.2 orders using 0 krylov vectors
residual decreased by 0.3 orders using 1 krylov vectors
solver returned with residual 1e-21
spectrum: 1.5e-02..1.7e+01 (positive definite)
energy -2.32e-13 / e+8.5 and decreasing
residual norm: 3.7e-09 (100%)
optimal value: 2.8e-01
nonlinear.png
finish 2025-04-10 02:34:14, elapsed 0:08