examples/burgers.py

nelems=20 Number of elements along a single dimension.
ndims=1 Number of spatial dimensions.
degree=1 Polynomial degree for discontinuous basis functions.
timescale=.5 Fraction of timestep and element size: timestep=timescale/nelems.
newtontol=1e-5 Newton tolerance.
endtime=0.5 Stopping time.

optimize

topology 1/1

integrating 1+1+1 distinct blocks

solve

solving 40 dof system to machine precision using direct solver

refinement iteration 1

residual decreased to 1e-17

refinement iteration 2

residual decreased to 7e-18

refinement iteration 3

residual decreased to 7e-18

refinement iteration 4

residual increased to 1e-17 (discarding)

solver returned with residual 7e-18

optimum value 4.05e-06

timestep 1

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1.0

newton 44%

solve

solving 40 dof system to tolerance 3e-06 using direct solver

solver returned with residual 5e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.99959

newton 100%

converged in 2 steps to residual 1.7e-06

timestep 2

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1.0

newton 43%

solve

solving 40 dof system to tolerance 3e-06 using direct solver

solver returned with residual 6e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.99887

newton 100%

converged in 2 steps to residual 3.7e-06

timestep 3

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1.0

newton 42%

solve

solving 40 dof system to tolerance 3e-06 using direct solver

solver returned with residual 4e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.99814

newton 100%

converged in 2 steps to residual 6.9e-06

timestep 4

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1.0

newton 40%

solve

solving 40 dof system to tolerance 4e-06 using direct solver

solver returned with residual 8e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.99716

newton 98%

solve

solving 40 dof system to tolerance 1e-08 using direct solver

solver returned with residual 2e-21

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.9999

newton 100%

converged in 3 steps to residual 1.2e-09

timestep 5

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1.0

newton 39%

solve

solving 40 dof system to tolerance 5e-06 using direct solver

solver returned with residual 3e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 0.99636

newton 93%

solve

solving 40 dof system to tolerance 2e-08 using direct solver

solver returned with residual 2e-21

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 7.2e-11

timestep 6

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 37%

solve

solving 40 dof system to tolerance 6e-06 using direct solver

solver returned with residual 9e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.99406

newton 88%

solve

solving 40 dof system to tolerance 3e-08 using direct solver

solver returned with residual 4e-21

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.6e-10

timestep 7

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 32%

solve

solving 40 dof system to tolerance 9e-06 using direct solver

solver returned with residual 2e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.9908

newton 78%

solve

solving 40 dof system to tolerance 9e-08 using direct solver

solver returned with residual 2e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.0e-09

timestep 8

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 5e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 32%

solve

solving 40 dof system to tolerance 9e-06 using direct solver

solver returned with residual 1e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.99249

newton 79%

solve

solving 40 dof system to tolerance 8e-08 using direct solver

solver returned with residual 1e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.6e-09

timestep 9

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 33%

solve

solving 40 dof system to tolerance 8e-06 using direct solver

solver returned with residual 1e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.98816

newton 77%

solve

solving 40 dof system to tolerance 1e-07 using direct solver

solver returned with residual 1e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 2.4e-09

timestep 10

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 97% of update vector

update accepted at relaxation 1.0

newton 26%

solve

solving 40 dof system to tolerance 2e-05 using direct solver

solver returned with residual 2e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.97389

newton 62%

solve

solving 40 dof system to tolerance 4e-07 using direct solver

solver returned with residual 3e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.3e-08

timestep 11

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 5e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 98% of update vector

update accepted at relaxation 1.0

newton 24%

solve

solving 40 dof system to tolerance 2e-05 using direct solver

solver returned with residual 3e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.97584

newton 61%

solve

solving 40 dof system to tolerance 5e-07 using direct solver

solver returned with residual 6e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 4.3e-08

timestep 12

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 2e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 28%

solve

solving 40 dof system to tolerance 1e-05 using direct solver

solver returned with residual 2e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.99017

newton 71%

solve

solving 40 dof system to tolerance 2e-07 using direct solver

solver returned with residual 2e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 9.9e-09

timestep 13

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 5e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 97% of update vector

update accepted at relaxation 1.0

newton 29%

solve

solving 40 dof system to tolerance 1e-05 using direct solver

solver returned with residual 2e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.97415

newton 64%

solve

solving 40 dof system to tolerance 4e-07 using direct solver

solver returned with residual 6e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 2.3e-08

timestep 14

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 5e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 95% of update vector

update accepted at relaxation 1.0

newton 21%

solve

solving 40 dof system to tolerance 3e-05 using direct solver

solver returned with residual 4e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 106% of update vector

update accepted at relaxation 0.94768

newton 50%

solve

solving 40 dof system to tolerance 1e-06 using direct solver

solver returned with residual 1e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.7e-07

timestep 15

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 96% of update vector

update accepted at relaxation 1.0

newton 20%

solve

solving 40 dof system to tolerance 3e-05 using direct solver

solver returned with residual 6e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 105% of update vector

update accepted at relaxation 0.95568

newton 50%

solve

solving 40 dof system to tolerance 1e-06 using direct solver

solver returned with residual 2e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 3.0e-07

timestep 16

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 4e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 99% of update vector

update accepted at relaxation 1.0

newton 25%

solve

solving 40 dof system to tolerance 2e-05 using direct solver

solver returned with residual 4e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 101% of update vector

update accepted at relaxation 0.9885

newton 66%

solve

solving 40 dof system to tolerance 3e-07 using direct solver

solver returned with residual 8e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 2.7e-08

timestep 17

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 5e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 98% of update vector

update accepted at relaxation 1.0

newton 29%

solve

solving 40 dof system to tolerance 1e-05 using direct solver

solver returned with residual 3e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.97622

newton 65%

solve

solving 40 dof system to tolerance 3e-07 using direct solver

solver returned with residual 3e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 3.9e-08

timestep 18

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 1e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 94% of update vector

update accepted at relaxation 1.0

newton 21%

solve

solving 40 dof system to tolerance 3e-05 using direct solver

solver returned with residual 2e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 106% of update vector

update accepted at relaxation 0.94108

newton 49%

solve

solving 40 dof system to tolerance 2e-06 using direct solver

solver returned with residual 1e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 2.1e-07

timestep 19

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 94% of update vector

update accepted at relaxation 1.0

newton 18%

solve

solving 40 dof system to tolerance 4e-05 using direct solver

solver returned with residual 4e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 107% of update vector

update accepted at relaxation 0.9362

newton 45%

solve

solving 40 dof system to tolerance 2e-06 using direct solver

solver returned with residual 5e-19

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 6.6e-07

timestep 20

solution.png

newton

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

newton 0%

solve

solving 40 dof system to tolerance 2e-04 using direct solver

solver returned with residual 3e-17

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 98% of update vector

update accepted at relaxation 1.0

newton 21%

solve

solving 40 dof system to tolerance 3e-05 using direct solver

solver returned with residual 5e-18

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 103% of update vector

update accepted at relaxation 0.97585

newton 57%

solve

solving 40 dof system to tolerance 8e-07 using direct solver

solver returned with residual 5e-20

topology 1/2

integrating 1+1 distinct blocks

topology 2/2

integrating 2+4 distinct blocks

estimated residual minimum at 100% of update vector

update accepted at relaxation 1

newton 100%

converged in 3 steps to residual 1.3e-07

timestep 21

solution.png