ice_dyn_vp: allow for bit-for-bit reproducibility under `bfbflag` #774

The "Table of namelist options" in the user guide lists 'maxits_nonlin' as having a default value of 1000, whereas its actual default is 4, both in the namelist and in 'ice_init.F90'. This has been the case since the original implementation of the implicit solver in f7fd063 (dynamics: add implicit VP solver (CICE-Consortium#491), 2020-09-22). Fix the documentation.

When the implicit VP solver was added in f7fd063 (dynamics: add implicit VP solver (CICE-Consortium#491), 2020-09-22), it had not yet been tested with OpenMP enabled. The OpenMP implementation was carefully reviewed and then fixed in d1e972a (Update OMP (CICE-Consortium#680), 2022-02-18), which lead to all runs of the 'decomp' suite completing and all restart tests passing. The 'bfbcomp' tests are still failing, but this is due to the code not using the CICE global sum implementation correctly, which will be fixed in the next commits. Update the documentation accordingly.

When the OpenMP implementation was reviewed and fixed in d1e972a (Update OMP (CICE-Consortium#680), 2022-02-18), the 'PRIVATE' clause of the OpenMP directive for the loop where 'dyn_prep2' is called in 'implicit_solver' was corrected in line with what was done in 'ice_dyn_evp', but OpenMP was left unactivated for this loop (the 'TCXOMP' was not changed to a real 'OMP' directive). Activate OpenMP for this loop. All runs and restart tests of the 'decomp_suite' still pass with this change.

The system installation of OpenMPI at /usr/mpi/gcc/openmpi-4.1.2a1/ is not compiled with support for PBS. This leads to failures as the MPI runtime does not have the same view of the number of available processors as the job scheduler. Use our own build of OpenMPI, compiled with PBS support, for the 'ppp6_gnu' environment, which uses OpenMPI.

Intel MPI 2021.5.1, which comes with oneAPI 2022.1.2, seems to have an intermittent bug where a call to 'MPI_Waitall' fails with: Abort(17) on node 0 (rank 0 in comm 0): Fatal error in PMPI_Waitall: See the MPI_ERROR field in MPI_Status for the error code and no core dump is produced. This affects at least these cases of the 'decomp' suite: - *_*_restart_gx3_16x2x1x1x800_droundrobin - *_*_restart_gx3_16x2x2x2x200_droundrobin This was reported to Intel and they suggested setting the variable 'I_MPI_FABRICS' to 'ofi' (the default being 'shm:ofi' [1]). This disables shared memory transport and indeeds fixes the failures. Set this variable for all ECCC machine files using Intel MPI. [1] https://www.intel.com/content/www/us/en/develop/documentation/mpi-developer-reference-linux/top/environment-variable-reference/environment-variables-for-fabrics-control/communication-fabrics-control.html

Intel MPI, in contrast to OpenMPI (as far as I was able to test, and see [1], [2]), does not (by default) guarantee that repeated runs of the same code on the same machine with the same number of MPI ranks yield the same results when collective operations (e.g. 'MPI_ALLREDUCE') are used. Since the VP solver uses MPI_ALLREDUCE in its algorithm, this leads to repeated runs of the code giving different answers, and baseline comparing runs with code built from the same commit failing. When generating a baseline or comparing against an existing baseline, set the environment variable 'I_MPI_CBWR' to 1 for ECCC machine files using Intel MPI [3], so that (processor) topology-aware collective algorithms are not used and results are reproducible. Note that we do not need to set this variable on robert or underhill, on which jobs have exclusive node access and thus job placement (on processors) is guaranteed to be reproducible. [1] https://stackoverflow.com/a/45916859/ [2] https://scicomp.stackexchange.com/a/2386/ [3] https://www.intel.com/content/www/us/en/develop/documentation/mpi-developer-reference-linux/top/environment-variable-reference/i-mpi-adjust-family-environment-variables.html#i-mpi-adjust-family-environment-variables_GUID-A5119508-5588-4CF5-9979-8D60831D1411

If starting a run with with "ice_ic='none'" (no ice), the linearized problem for the ice velocity A x = b will have b = 0, since all terms in the right hand side vector will be zero: - strint[xy] is zero because the velocity is zero - tau[xy] is zero because the ocean velocity is also zero - [uv]vel_init is zero - strair[xy] is zero because the concentration is zero - strtlt[xy] is zero because the ocean velocity is zero We thus have a linear system A x = b with b=0, so we must have x=0. In the FGMRES linear solver, this special case is not taken into account, and so we end up with an all-zero initial residual since workspace_[xy] is also zero because of the all-zero initial guess 'sol[xy]', which corresponds to the initial ice velocity. This then leads to a division by zero when normalizing the first Arnoldi vector. Fix this special case by computing the norm of the right-hand-side vector before starting the iterations, and exiting early if it is zero. This is in line with the GMRES implementation in SciPy [1]. [1] https://github.com/scipy/scipy/blob/651a9b717deb68adde9416072c1e1d5aa14a58a1/scipy/sparse/linalg/_isolve/iterative.py#L620-L628 Close: #42

The VP solver uses a linear solver, FGMRES, as part of the non-linear iteration. The FGMRES algorithm involves computing the norm of a distributed vector field, thus performing global sums. These norms are computed by first summing the squared X and Y components of a vector field in subroutine 'calc_L2norm_squared', summing these over the local blocks, and then doing a global (MPI) sum using 'global_sum'. This approach does not lead to reproducible results when the MPI distribution, or the number of local blocks, is changed, for reasons explained in the "Reproducible sums" section of the Developer Guide (mostly, floating point addition is not associative). This was partly pointed out in [1] but I failed to realize it at the time. Introduce a new function, 'global_dot_product', to encapsulate the computation of the dot product of two grid vectors, each split into two arrays (for the X and Y components). Compute the reduction locally as is done in 'calc_L2norm_squared', but throw away the result and use the existing 'global_sum' function when 'bfbflag' is active, passing it the temporary array used to compute the element-by-element product. This approach avoids a performance regression from the added work done in 'global_sum', such that non-bfbflag runs are as fast as before. Note that since 'global_sum' loops on the whole array (and not just ice points as 'global_dot_product'), make sure to zero-initialize the 'prod' local array. Also add a 'global_norm' function implemented using 'global_dot_product'. Both functions will be used in subsequent commits to ensure bit-for-bit reproducibility.

…oducibility Make the results of the VP solver reproducible if desired by refactoring the code to use the subroutines 'global_norm' and 'global_dot_product' added in the previous commit. The same pattern appears in the FGMRES solver (subroutine 'fgmres'), the preconditioner 'pgmres' which uses the same algorithm, and the Classical and Modified Gram-Schmidt algorithms in 'orthogonalize'. These modifications do not change the number of global sums in the fgmres, pgmres and the MGS algorithm. For the CGS algorithm, there is (in theory) a slight performance impact as 'global_dot_product' is called inside the loop, whereas previously we called 'global_allreduce_sum' after the loop to compute all 'initer' sums at the same time. To keep that optimization, we would have to implement a new interface 'global_allreduce_sum' which would take an array of shape (nx_block,ny_block,max_blocks,k) and sum over their first three dimensions before performing the global reduction over the k dimension. We choose to not go that route for now mostly because anyway the CGS algorithm is (by default) only used for the PGMRES preconditioner, and so the cost should be relatively low as 'initer' corresponds to 'dim_pgmres' in the namelist, which should be kept low for efficiency (default 5). These changes lead to bit-for-bit reproducibility (the decomp_suite passes) when using 'precond=ident' and 'precond=diag' along with 'bfbflag=reprosum'. 'precond=pgmres' is still not bit-for-bit because some halo updates are skipped for efficiency. This will be addressed in a following commit. [1] CICE-Consortium#491 (comment)

The 'pgmres' subroutine implements a separate GMRES solver and is used as a preconditioner for the FGMRES linear solver. Since it is only a preconditioner, it was decided to skip the halo updates after computing the matrix-vector product (in 'matvec'), for efficiency. This leads to non-reproducibility since the content of the non-updated halos depend on the block / MPI distribution. Add the required halo updates, but only perform them when we are explicitely asking for bit-for-bit global sums, i.e. when 'bfbflag' is set to something else than 'not'. Adjust the interfaces of 'pgmres' and 'precondition' (from which 'pgmres' is called) to accept 'halo_info_mask', since it is needed for masked updates. Closes CICE-Consortium#518

…cibility In the previous commits we ensured bit-for-bit reproducibility of the outputs when using the VP solver. Some global norms computed during the nonlinear iteration still use the same non-reproducible pattern of summing over blocks locally before performing the reduction. However, these norms are used only to monitor the convergence in the log file, as well as to exit the iteration when the required convergence level is reached ('nlres_norm'). Only 'nlres_norm' could (in theory) influence the output, but it is unlikely that a difference due to floating point errors would influence the 'if (nlres_norm < tol_nl)' condition used to exist the nonlinear iteration. Change these remaining cases to also use 'global_norm', leading to bit-for-bit log reproducibility.

The previous commit removed the last caller of 'calc_L2norm_squared'. Remove the subroutine. Also, do not compute 'sum_squared' in 'residual_vec', since the variable 'L2norm' which receives this value is also unused in 'anderson_solver' since the previous commit. Remove that variable, and adjust the interface of 'residual_vec' accordingly.

In a previous commit, we removed the sole caller of 'global_allreduce_sum' (in ice_dyn_vp::orthogonalize). We do not anticipate that function to be ued elsewhere in the code, so remove it from ice_global_reductions. Update the 'sumchk' unit test accordingly.

The previous commits made sure that the model outputs as well as the log file output are bit-for-bit reproducible when using the VP solver by refactoring the code to use the existing 'global_sum' subroutine. Add a note in the documentation mentioning that 'bfbflag' is required to get bit-for-bit reproducible results under different decompositions / MPI counts when using the VP solver. Also, adjust the doc about 'bfbflag=lsum8' being the same as 'bfbflag=off' since this is not the case for the VP solver: in the first case we use the scalar version of 'global_sum', in the second case we use the array version.

During QC testing of the previous commit, the 5 years QC test with the updated VP solver failed twice with "bad departure points" after a few years of simulation. Simply bumping the number of nonlinear iterations (maxits_nonlin) from 4 to 5 makes these failures disappear and allow the simulations to run to completion, suggesting the solution is not converged enough with 4 iterations. We also noticed that in these failing cases, the relative tolerance for the linear solver (reltol_fmgres = 1E-2) is too small to be reached in less than 50 iterations (maxits_fgmres), and that's the case at each nonlinear iteration. Other papers mention a relative tolerance of 1E-1 for the linear solver, and using this value also allows both cases to run to completion (even without changing maxits_nonlin). Let's set the default tolerance for the linear solver to 1E-1, and let's be conservative and bump the number of nonlinear iterations to 10. This should give us a more converged solution and add robustness to the default settings.

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ice_dyn_vp: allow for bit-for-bit reproducibility under `bfbflag` #774

ice_dyn_vp: allow for bit-for-bit reproducibility under `bfbflag` #774

Commits on Oct 17, 2022

ice_dyn_vp: allow for bit-for-bit reproducibility under bfbflag #774

ice_dyn_vp: allow for bit-for-bit reproducibility under bfbflag #774

Commits on Oct 17, 2022

ice_dyn_vp: allow for bit-for-bit reproducibility under `bfbflag` #774

ice_dyn_vp: allow for bit-for-bit reproducibility under `bfbflag` #774