GPEC outputs are unacceptably sensitive to small (<0.1%) numerical differences from RDCON that can occur with different compilers and architectures

[matt-pharr]

Delta_gw matrices having a small variation are seen to be the primary cause in huge differences between behavior at resonant surfaces across different code execution environments. See below:

Delta_gw matrices:

Terminal output comparison, left to right [flux (PPPL, gfortran on amd64), feynman (columbia, ifort on amd64), M1 MacBook (local, gfortran on arm64)]

When delta_gw is shared before rmatch is run:

When all rdcon outputs are shared before rmatch is run:

[matt-pharr]

I have heard you all have been compiling gpec with gfortran @AaronFroese. Any thoughts?

[matt-pharr]

These plots of the coupling demonstrate the dramatic variability in the dominant mode, pay attention to the half-wavelength as well as the overlaps calculated in the upper plots:

And the variability in the scales in these total control surface field plots shows ~10% differences in the total perturbed fields in some places:

[aglasser17]

It might be worth trying to replicate this sensitivity with STRIDE, which uses a very different integration method than RDCON, but ultimately solves the same equations. If STRIDE shares the same sensitivity, then either (1) both have numerical features that are unacceptably sensitive to compiler, or (2) it reflects the sensitivity of the underlying Newcomb equations themselves. But if STRIDE is robust to the compiler, at least (2) is ruled out.

[matt-pharr]

Hi Alan, I am unsure how to get a direct comparison here -- this is RDCON's delta matrix from delta_gw.dat, which is the following:

      OPEN(UNIT=gal_bin_unit,FILE=TRIM(name)//".dat",STATUS="UNKNOWN",
     $     FORM="UNFORMATTED")
      nsol=SIZE(delta,1)
      WRITE(gal_bin_unit)msing,nsol,coil%rpec_flag
      WRITE(gal_bin_unit)delta
      DO ising=1,msing
         singp => sing(ising)
         WRITE(gal_bin_unit)
     $        singp%restype%e,singp%restype%f,
     $        singp%restype%h,singp%restype%m,
     $        singp%restype%g,singp%restype%k,
     $        singp%restype%eta,singp%restype%rho,
     $        singp%restype%taua,singp%restype%taur,
     $        singp%restype%v1
      ENDDO      
      CLOSE(UNIT=gal_bin_unit)

delta contains gal%sol for all the resonant cells, I am assuming are the $\Delta_{in}$/ $\Delta_{out}$ from page 4 of your 2020 paper with Zhirui. STRIDE produces a $\Delta'$ matrix, is this matrix able to be compared with the matching $\Delta$ s from RDCON?

[matt-pharr]

Hi @aglasser17,

Just wanted to let you know we worked out the relation between the Deltas in stride and RDCON. Thanks for the input. This will help in diagnosing the problem.

[matt-pharr]

Furthermore, for documentation purposes, here is a comparison of the matched eigenfunctions for m=2,3,4 across compilers/platforms:

Will produce a similar plot with the ideal equivalent.