When are materials evaluated?

[matthiasneuner]

Hello, I am trying to figuring out how and when materials are evaluated during a transient simulation using the classical NEWTON scheme.

Assume that I have a simple linear stress-strain material for the tensor mechanics module. Within computeQpProperties(), both the 1) current stress and 2) the derivative Jacobian_mult for assembling the Jacobian are computed simultaneously. Such a simultaneous computation is reasonable for e.g., plasticity models, where the jacobian is computed as a byproduct of the return mapping algorithm.

Considering a single element with a single quadrature point, a simple print statement gives me following output:

Time Step 0, time = 0                                                                                                                                                                    
                                                                                                                                                                                         
Time Step 1, time = 0.1, dt = 0.1                                                                                                                                                        
Material @ qp 0 evaluated                         # evaluation n.1 with zero strain                                                                                                                                                          
Material @ qp 0 evaluated                         # evaluation n.2  for computing the residual                                                                                                                                       
 0 Nonlinear |R| = 1.414214e-01                                                                                                                                                          
Material @ qp 0 evaluated                         # evaluation n.3 for computing the Jacobian                                                                                                                                      
      0 Linear |R| = 1.414214e-01                                                                                                                                                        
      1 Linear |R| = 2.220446e-17                                                                                                                                                        
  Linear solve converged due to CONVERGED_RTOL iterations 1                                                                                                                              
Material @ qp 0 evaluated                         # evaluation n.4 for checking convergence after solving                                                                                                                                       
 1 Nonlinear |R| = 3.925231e-17                                                                                                                                                            
Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1                                                                                                                        
 Solve Converged!                                                                                                                                                                        
                                                                                                                                                                                         
Outlier Variable Residual Norms:                                                                                                                                                         
  disp_x: 3.925231e-17

Time Step 2, time = 0.2, dt = 0.1
Material @ qp 0 evaluated 
Material @ qp 0 evaluated 
 0 Nonlinear |R| = 1.414214e-01
Material @ qp 0 evaluated 
      0 Linear |R| = 1.414214e-01
      1 Linear |R| = 2.220446e-17
  Linear solve converged due to CONVERGED_RTOL iterations 1
Material @ qp 0 evaluated 
 1 Nonlinear |R| = 0.000000e+00
Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 1
 Solve Converged!

So, within each time step, the material is evaluated 4 times (!), which seems a lot for a linear simulation.

• The first evaluation is unclear to me,
• the second one is for computing the residual,
• the third one is for computing the Jacobian,
• and the fourth one is for checking convergence (which is trivially satisfied after one iteration in this example).

My questions are:

• Why is the first evaluation performed in each time step with a zero strain increment?
• Why are evaluation 2 and evaluation 3 separated, although properties stress and Jacobian_mult are computed simultenously (which means that it is readily available after evaluation 2, evalation 3 is performed with the exact same solution and accordingly, produces the same result)?

Thank you in advance !

[GiudGiud]

@rwcarlsen might be able to help on this as I think he's looking into this now

[rwcarlsen]

Evaluations 2 and 3 (residual and jac) are indeed a (known) underoptimization in the framework with AD (automatic differentiation) at least. But it looks like you are using material objects that manually calculate a jacobian contribution along with every residual evaluation. In that case - the material object just needs to be smarter. Materials can ask the framework what operation (residual/jac) is triggering a given material evaluation - those materials could be updated to query that state and omit unnecessary calcs accordingly.

With respect to the redundant work when using AD - there are some subtleties about how the residual and jacobian calcs are integrated between MOOSE and PETSc that make it not quite as straight forward for us to combine them into one evaluation so instead we compute the residual during residual evaluation and then compute the residual and jacobian together during the jacobian evaluation (even though we don't need the residual again).

I honestly can't remember what the detail is around the 1st evaluation. Probably @lindsayad or @fdkong could clarify that one.

[lindsayad]

There are two residual evaluations done before the first jacobian evaluation. The first residual evaluation is done by MOOSE; the second is done by PETSc. This is another known place of under-optimization, at least pending some criteria regarding preset boundary conditions.

If you are running a real problem with PJFNK, then the extra residual evaluation in the beginning is not very impactful since you may be doing 10 to 30 residual evaluations per nonlinear iteration.

[fdkong]

Why is the first evaluation performed in each time step with a zero strain increment?

We knew this. It could be optimized out in the future for some cases

Why are evaluation 2 and evaluation 3 separated, although properties stress and Jacobian_mult are computed simultenously (which means that it is readily available after evaluation 2, evalation 3 is performed with the exact same solution and accordingly, produces the same result)?

Jacobian and Residual evaluations are involved from PETSc side via two different call-back functions. The Jacobian evaluation needs to compute material again because we do not store the materials from the earlier residual computation. Materials are expensive to store. That being said, storing materials might use a lot of memory when considering the values at each quadrature point are needed.

[matthiasneuner]

Thank you all for the elaborate answers!
I am dealing mostly with complex (expensive) plasticity models. As mentioned, for such models the (consistent algorithmic) Jacobian is computed as a byproduct along with the return mapping algorithm. A separate computing would require to completely repeat the return mapping algorithm. Accordingly, I believe the same concerns as for AD materials apply.

However, despite the expensive nature of those material models, I am currently surprised that for large scale simulations the overhead of the multiple material evaluation only has negligible influence (In my case: An accumulated Residual/Jacobian percentage of 25% compared to ~75% taken by the linear solve). So I agree that there is not very much potential for optimization.