Slow nonlinear convergence in cmm/test_pipe_3d

[mrp089]

Description

While adding missing results to test cases (#175), I noticed that the test cmm/test_pipe_3d (steps 3a-inflate-cmm and 3b-prestress-cmm) have a very slow nonlinear convergence.

Reproduction

In tests, run pytest -vrx -k pipe_3d. The second simulation output corresponds to step 3a-inflate-cmm, the second to last to 3b-prestress-cmm.

This is the output I get for 3a-inflate-cmm:

---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 CM 1-1  8.150e-01  [0 1.000e+00 1.000e+00 1.331e-09]  !510 -19 88!
 CM 1-2  1.636e+00  [-24 5.971e-02 5.971e-02 7.006e-11]  !510 -20 88!
 CM 1-3  2.451e+00  [-48 3.758e-03 3.758e-03 1.125e-11]  !510 -19 88!
 CM 1-4  3.282e+00  [-70 3.053e-04 3.053e-04 1.497e-11]  !510 -19 88!
 CM 1-5  4.029e+00  [-90 2.876e-05 2.876e-05 1.255e-10]  [458 -21 86]
 CM 1-6  4.711e+00  [-109 3.288e-06 3.288e-06 1.112e-09]  [405 -17 85]
 CM 1-7  5.289e+00  [-129 3.506e-07 3.506e-07 1.056e-08]  [340 -11 83]
 CM 1-8  5.791e+00  [-146 4.982e-08 4.982e-08 7.380e-08]  [288 -11 80]
 CM 1-9  6.184e+00  [-163 6.346e-09 6.346e-09 5.752e-07]  [201 -18 74]
 CM 1-10  6.525e+00  [-179 1.076e-09 1.076e-09 3.337e-06]  [171 -7 70]
 CM 1-11  6.760e+00  [-195 1.622e-10 1.622e-10 2.272e-05]  [96 -18 57]
 CM 1-12  6.925e+00  [-211 2.647e-11 2.647e-11 1.336e-04]  [45 -89 39]
 CM 1-13  7.060e+00  [-227 4.230e-12 4.230e-12 8.472e-04]  [27 -71 23]
 CM 1-14  7.188e+00  [-243 6.915e-13 6.915e-13 5.041e-03]  [18 -53 14]
 CM 2-1  8.027e+00  [0 1.000e+00 1.530e+00 2.659e-10]  !510 -21 88!
 CM 2-2  8.863e+00  [-11 2.662e-01 4.073e-01 3.149e-11]  !510 -20 88!
 CM 2-3  9.717e+00  [-47 4.220e-03 6.458e-03 2.659e-11]  !510 -21 88!
 CM 2-4  1.056e+01  [-65 5.078e-04 7.771e-04 2.749e-11]  !510 -18 88!
 CM 2-5  1.131e+01  [-90 2.953e-05 4.519e-05 8.013e-11]  [450 -17 86]
 CM 2-6  1.203e+01  [-112 2.501e-06 3.827e-06 9.356e-10]  [400 -15 85]
 CM 2-7  1.267e+01  [-129 3.460e-07 5.295e-07 6.919e-09]  [356 -18 83]
 CM 2-8  1.321e+01  [-149 3.411e-08 5.220e-08 6.868e-08]  [289 -12 80]
 CM 2-9  1.361e+01  [-171 2.662e-09 4.074e-09 8.946e-07]  [198 -18 73]
 CM 2-10  1.395e+01  [-188 3.902e-10 5.971e-10 5.976e-06]  [164 -3 69]
 CM 2-11  1.421e+01  [-206 4.517e-11 6.912e-11 5.352e-05]  [112 -2 59]
 CM 2-12  1.437e+01  [-228 3.627e-12 5.550e-12 6.657e-04]  [41 -73 36]
 CM 2-13  1.452e+01  [-245 5.177e-13 7.922e-13 4.503e-03]  [25 -54 20]
 CM 3-1  1.539e+01  [0 1.000e+00 1.680e+00 3.004e-09]  !510 -16 88!
 CM 3-2  1.625e+01  [-6 4.626e-01 7.770e-01 4.546e-11]  !510 -20 88!
 CM 3-3  1.712e+01  [-31 2.542e-02 4.270e-02 5.074e-12]  !510 -19 88!
 CM 3-4  1.801e+01  [-57 1.321e-03 2.219e-03 1.362e-11]  !510 -18 88!
 CM 3-5  1.883e+01  [-81 8.104e-05 1.361e-04 2.709e-11]  [487 -10 87]
 CM 3-6  1.954e+01  [-103 6.546e-06 1.100e-05 3.227e-10]  [401 -16 85]
 CM 3-7  2.012e+01  [-123 6.924e-07 1.163e-06 3.183e-09]  [322 -6 82]
 CM 3-8  2.059e+01  [-142 7.723e-08 1.297e-07 2.786e-08]  [251 -16 79]
 CM 3-9  2.098e+01  [-161 8.801e-09 1.478e-08 2.454e-07]  [194 -16 73]
 CM 3-10  2.129e+01  [-179 1.016e-09 1.707e-09 2.092e-06]  [143 -16 66]
 CM 3-11  2.151e+01  [-198 1.187e-10 1.993e-10 1.852e-05]  [86 -14 53]
 CM 3-12  2.167e+01  [-217 1.396e-11 2.344e-11 1.537e-04]  [40 -88 34]
 CM 3-13  2.180e+01  [-235 1.650e-12 2.772e-12 1.271e-03]  [20 -67 17]
 CM 3-14  2.193e+01  [-254 1.962e-13 3.295e-13 9.565e-03]  [12 -46 11]
 CM 4-1  2.282e+01  [0 1.000e+00 1.131e+00 1.849e-10]  !510 -22 87!
 CM 4-2  2.369e+01  [-12 2.320e-01 2.624e-01 2.980e-11]  !510 -20 88!
 CM 4-3  2.456e+01  [-46 4.713e-03 5.330e-03 2.731e-11]  !510 -18 88!
 CM 4-4  2.543e+01  [-71 2.545e-04 2.879e-04 2.364e-11]  !510 -19 88!
 CM 4-5  2.616e+01  [-101 8.709e-06 9.850e-06 3.616e-10]  [431 -8 86]
 CM 4-6  2.677e+01  [-127 4.431e-07 5.011e-07 7.370e-09]  [342 -11 83]
 CM 4-7  2.727e+01  [-152 2.489e-08 2.815e-08 1.274e-07]  [268 -3 79]
 CM 4-8  2.764e+01  [-175 1.692e-09 1.914e-09 1.875e-06]  [185 -12 72]
 CM 4-9  2.793e+01  [-197 1.267e-10 1.433e-10 2.577e-05]  [126 -7 63]
 CM 4-10  2.811e+01  [-219 1.007e-11 1.138e-11 3.156e-04]  [47 -81 39]
 CM 4-11  2.824e+01  [-241 8.180e-13 9.251e-13 4.006e-03]  [18 -55 14]
 CM 5-1  2.911e+01  [0 1.000e+00 9.722e-01 4.469e-10]  !510 -19 88!
 CM 5-2  3.000e+01  [-15 1.729e-01 1.681e-01 2.508e-11]  !510 -20 88!
 CM 5-3  3.087e+01  [-45 5.518e-03 5.364e-03 2.346e-11]  !510 -19 88!
 CM 5-4  3.173e+01  [-75 1.775e-04 1.726e-04 2.040e-11]  [507 -18 88]
 CM 5-5  3.246e+01  [-105 5.504e-06 5.351e-06 6.746e-10]  [414 -1 85]
 CM 5-6  3.303e+01  [-136 1.484e-07 1.442e-07 2.530e-08]  [313 -2 82]
 CM 5-7  3.347e+01  [-166 4.901e-09 4.765e-09 7.565e-07]  [230 -9 76]
 CM 5-8  3.376e+01  [-194 1.918e-10 1.865e-10 1.981e-05]  [123 -7 63]
 CM 5-9  3.395e+01  [-221 8.059e-12 7.835e-12 4.644e-04]  [65 -3 46]
 CM 5-10s 3.411e+01  [-244 6.001e-13 5.834e-13 6.064e-03]  [15 -51 10]

I increased Max_iterations and set Tolerance = 1e-12.

Expected behavior

Should converge to this tolerance in ~5 Newton iterations.

Additional context

@ktbolt, @wgyang, I don't understand how CMM works. Is it normal to converge this slowly?

Before, we had a very coarse tolerance of 1e-4, which might explain why we got different results on different machines (#137).

Code of Conduct

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

[mrp089]

@wgyang, can you try running a "real-world" CMM and see if it converges similarly to FORTRAN svFSI?

[wgyang]

@wgyang, can you try running a "real-world" CMM and see if it converges similarly to FORTRAN svFSI?

Yes, will do.

[wgyang]

Pulsatile flow poses challenges for CMM simulations. The required number of iterations is influenced by instantaneous flow. Even under steady flow conditions, achieving convergence, defined by a threshold of 1e-12, typically necessitates approximately 55 to 100 time steps, with around 7 Newton iterations needed. Note that the solver advances to the next time step when either Ri/R1 or Ri/R0 becomes smaller than the threshold. The convergence order for the relative residual at each time step is approximately 1. Achieving quadratic convergence is unlikely for the solver. In patient-specific cases, I found convergence more difficult compared to a simple cylinder. The threshold of 1e-12 is too strict.

Here is the output for steady flow in a cylinder using cmm,

 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------

 CM 52-1  5.043e+01  [0 1.000e+00 1.812e-03 9.932e-05]  [142 -92 74]
 CM 52-2  5.057e+01  [-27 4.289e-02 7.773e-05 9.784e-05]  [124 -92 75]
 CM 52-3  5.069e+01  [-59 1.062e-03 1.925e-06 9.838e-05]  [107 -92 71]
 CM 52-4  5.082e+01  [-93 2.165e-05 3.924e-08 9.964e-05]  [111 -92 72]
 CM 52-5  5.094e+01  [-126 4.842e-07 8.777e-10 9.633e-05]  [109 -92 73]
 CM 52-6  5.105e+01  [-158 1.208e-08 2.190e-11 1.646e-04]  [98 -87 70]
 CM 52-7  5.110e+01  [-188 3.555e-10 6.443e-13 5.535e-03]  [20 -52 15]

Using the same input files (a cylinder with pulsatile flow), svFSI and svFSIplus have similar output.

svFSI
---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 New time step size: 5.000E-3
 CM     1-1  1.01E1  [   0 1.00000 1.00000 9.93E-5]  [ 236  -92  92]
 CM     1-2  1.91E1  [ -51 2.76E-3 2.76E-3 9.70E-5]  [ 222  -92  90]
 CM     1-3  2.30E1  [ -77 1.29E-4 1.29E-4 9.87E-5]  [ 126  -92  78]
 CM     1-4  2.71E1  [-104 5.63E-6 5.63E-6 9.77E-5]  [ 130  -92  79]
 CM     1-5  3.11E1  [-125 5.37E-7 5.37E-7 9.95E-5]  [ 128  -92  77]
 CM     1-6  3.57E1  [-151 2.71E-8 2.71E-8 9.80E-5]  [ 143  -92  81]
 CM     1-7  3.91E1  [-171 2.79E-9 2.79E-9 9.98E-5]  [ 116  -92  74]
 CM     1-8  4.33E1  [-195 1.5E-10 1.5E-10 9.71E-5]  [ 132  -92  79]
 CM     1-9  4.68E1  [-215 1.6E-11 1.6E-11 9.93E-5]  [ 119  -92  76]
 CM     1-10  4.90E1  [-239 1.0E-12 1.0E-12 4.83E-4]  [  74  -76  59]
 CM     2-1  5.70E1  [   0 1.00000 1.26583 9.92E-5]  [ 205  -92  89]
 CM     2-2  6.19E1  [ -28 3.75E-2 4.75E-2 9.88E-5]  [ 152  -92  83]
 CM     2-3  6.79E1  [ -68 3.81E-4 4.82E-4 9.98E-5]  [ 175  -92  85]
 CM     2-4  7.18E1  [ -91 2.64E-5 3.35E-5 9.81E-5]  [ 126  -92  77]
 CM     2-5  7.63E1  [-119 1.11E-6 1.40E-6 9.68E-5]  [ 143  -92  81]
 CM     2-6  8.07E1  [-144 6.24E-8 7.90E-8 9.83E-5]  [ 137  -92  79]
 CM     2-7  8.47E1  [-170 3.07E-9 3.88E-9 9.93E-5]  [ 132  -92  79]
 CM     2-8  8.91E1  [-195 1.7E-10 2.1E-10 9.79E-5]  [ 138  -92  80]
 CM     2-9  9.27E1  [-219 1.0E-11 1.2E-11 9.76E-5]  [ 119  -92  76]
 CM     2-10s 9.45E1  [-245 5.0E-13 6.4E-13 7.98E-4]  [  61  -71  51]

svFSIplus
---------------------------------------------------------------------
 Eq     N-i     T       dB  Ri/R1   Ri/R0    R/Ri     lsIt   dB  %t
---------------------------------------------------------------------
 CM 1-1  1.225e+01  [0 1.000e+00 1.000e+00 9.742e-05]  [237 -92 89]
 CM 1-2  2.316e+01  [-51 2.761e-03 2.761e-03 9.870e-05]  [221 -92 87]
 CM 1-3  2.812e+01  [-77 1.296e-04 1.296e-04 9.779e-05]  [127 -92 72]
 CM 1-4  3.322e+01  [-104 5.629e-06 5.629e-06 9.794e-05]  [131 -92 73]
 CM 1-5  3.832e+01  [-125 5.360e-07 5.360e-07 9.827e-05]  [131 -92 73]
 CM 1-6  4.409e+01  [-151 2.707e-08 2.707e-08 9.689e-05]  [143 -92 76]
 CM 1-7  4.861e+01  [-171 2.783e-09 2.783e-09 9.934e-05]  [117 -92 69]
 CM 1-8  5.395e+01  [-196 1.579e-10 1.579e-10 9.717e-05]  [135 -92 75]
 CM 1-9  5.848e+01  [-215 1.662e-11 1.662e-11 9.935e-05]  [118 -92 70]
 CM 1-10  6.128e+01  [-239 1.065e-12 1.065e-12 4.851e-04]  [73 -76 50]
 CM 2-1  7.095e+01  [0 1.000e+00 1.266e+00 9.920e-05]  [205 -92 86]
 CM 2-2  7.737e+01  [-28 3.756e-02 4.754e-02 9.885e-05]  [152 -92 79]
 CM 2-3  8.501e+01  [-68 3.815e-04 4.829e-04 9.987e-05]  [175 -92 82]
 CM 2-4  8.997e+01  [-91 2.649e-05 3.354e-05 9.817e-05]  [126 -92 73]
 CM 2-5  9.604e+01  [-119 1.112e-06 1.408e-06 9.685e-05]  [143 -92 74]
 CM 2-6  1.018e+02  [-144 6.248e-08 7.909e-08 9.831e-05]  [137 -92 75]
 CM 2-7  1.071e+02  [-170 3.072e-09 3.888e-09 9.944e-05]  [132 -92 75]
 CM 2-8  1.128e+02  [-195 1.706e-10 2.160e-10 9.796e-05]  [138 -92 76]
 CM 2-9  1.177e+02  [-219 1.005e-11 1.272e-11 9.769e-05]  [119 -92 71]
 CM 2-10s 1.202e+02  [-245 5.071e-13 6.419e-13 7.906e-04]  [61 -71 43]

[mrp089]

Thank you for looking into it, @wgyang!! We can close this issue. Even though the convergence is not great, it looks like it's "normal" for CMM. Maybe someone wants to dig that out in the future and check if the linearization is correct.