Slow nonlinear convergence in struct/LV_Holzapfel_passive

[mrp089]

Description

While adding missing results to test cases (#175), I noticed that the test struct/LV_Holzapfel_passive (using the Holzapfel material) has a very slow nonlinear convergence.

Reproduction

In tests, run pytest -vrx -k LV_Holzapfel

This is the output I get:

---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 ST 1-1  3.470e-01  [0 1.000e+00 1.000e+00 8.598e-13]  [187 -45 35]
 ST 1-2  7.030e-01  [-26 4.651e-02 4.651e-02 5.679e-12]  [181 -36 33]
 ST 1-3  1.044e+00  [-46 4.694e-03 4.694e-03 5.971e-11]  [156 -2 30]
 ST 1-4  1.376e+00  [-60 9.761e-04 9.761e-04 2.513e-10]  [144 -58 29]
 ST 1-5  1.700e+00  [-71 2.766e-04 2.766e-04 9.835e-10]  [133 -44 27]
 ST 1-6  2.017e+00  [-81 8.715e-05 8.715e-05 2.911e-09]  [125 -32 25]
 ST 1-7  2.332e+00  [-90 2.845e-05 2.845e-05 9.251e-09]  [117 -19 23]
 ST 1-8  2.642e+00  [-100 9.439e-06 9.439e-06 2.672e-08]  [110 -7 23]
 ST 1-9  2.947e+00  [-110 3.162e-06 3.162e-06 8.636e-08]  [98 -71 22]
 ST 1-10  3.251e+00  [-119 1.066e-06 1.066e-06 2.274e-07]  [92 -61 20]
 ST 1-11  3.543e+00  [-128 3.618e-07 3.618e-07 6.808e-07]  [86 -50 18]
 ST 1-12  3.828e+00  [-138 1.234e-07 1.234e-07 2.239e-06]  [79 -38 16]
 ST 1-13  4.111e+00  [-147 4.225e-08 4.225e-08 6.368e-06]  [73 -28 15]
 ST 1-14  4.391e+00  [-156 1.454e-08 1.454e-08 1.748e-05]  [67 -17 14]
 ST 1-15  4.671e+00  [-165 5.022e-09 5.022e-09 5.320e-05]  [58 -6 14]
 ST 1-16  4.939e+00  [-175 1.742e-09 1.742e-09 1.504e-04]  [48 -88 12]
 ST 1-17  5.198e+00  [-184 6.076e-10 6.076e-10 4.638e-04]  [39 -77 8]
 ST 1-18  5.458e+00  [-193 2.159e-10 2.159e-10 1.163e-03]  [34 -68 7]
 ST 1-19s 5.729e+00  [-201 8.659e-11 8.659e-11 3.055e-03]  [28 -58 5]

I increased Max_iterations and set Tolerance = 1e-10.

Expected behavior

Should converge to this tolerance in ~5 Newton iterations.

Additional context

@ktbolt, @aabrown100-git, have you used this material outside this test case? If this slow convergence also appears outside of this test case, the linearization is incorrect.

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

[aabrown100-git]

I checked my old results when I created this test case, and the convergence is much better

---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 ST 1-1  1.930e-01  [0 1.000e+00 1.000e+00 9.859e-07]  [113 -11 7]
 ST 1-2  3.680e-01  [-19 1.073e-01 1.073e-01 9.834e-07]  [98 -62 7]
 ST 1-3  5.670e-01  [-59 1.101e-03 1.101e-03 9.644e-07]  [97 -60 6]
 ST 1-4s 7.740e-01  [-154 1.977e-08 1.977e-08 1.332e-05]  [79 -34 5]

Perhaps something changed since I added this test? Maybe during material model restructuring here: #159

[aabrown100-git]

Found a tiny bug in mat_models_carray.h line 946

        for (int i = 0; i < N; i++) {
          for (int j = 0; j < N; j++) {
            for (int k = 0; k < N; k++) {
              for (int l = 0; l < N; l++) {
                CCb[i][j][k][l] += g1 * Hss_prod[i][j][k][l];
              }
            }
          }
        }
        //CCb = CCb + g2*ten_dyad_prod(Hss, Hss, nsd);

As shown in the commented line, it should be g2 instead of g1.

With this change, convergence is excellent

---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 ST 1-1  4.700e-02  [0 1.000e+00 1.000e+00 8.962e-07]  [84 -45 17]
 ST 1-2  9.500e-02  [-25 5.159e-02 5.159e-02 9.870e-07]  [92 -55 15]
 ST 1-3  1.440e-01  [-74 1.835e-04 1.835e-04 9.218e-07]  [89 -51 18]
 ST 1-4s 2.060e-01  [-194 1.800e-10 1.800e-10 1.448e-03]  [47 -65 5]

Will make a pull request

[aabrown100-git]

Raises an interesting question. Is it possible to make our testing detect poor convergence, not just incorrect results?

[mrp089]

Thank you for looking into it! That's a good point. I'm currently cranking up all tolerances (#175) to get more reproducible results. I could then set the max number of Newton iterations to the current one. If the tests are sensitive enough, they should fail if the solver takes way more iterations.