Stabilize high-order Maxwellian initialization#24
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July 13, 2026 10:10
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Summary
Root cause
compute_C_nmpformed2 ** n,factorial(n),alpha ** (n + 1), and(U - u) ** nindependently. At high Hermite order these intermediatesoverflow even when their combined coefficient is small, so
inf / infproduces NaNs in the initial state before integration. An Orszag--Tang state
with
Nn=112reproduced the failure.The replacement evaluates the mathematically equivalent one-dimensional
recurrence
for each velocity axis and multiplies the three broadcast coefficient tables.
This avoids large cancelling intermediates and reduces the amount of repeated
power/factorial work.
Validation
pytest -q: 4 passedflake8checks: 01e-13Nn=256, Nm=4, Np=4initialization is finite129x129,112x4x4Orszag--Tang initialization changed from non-finite to finite0.679/0.606 s for the previous non-finite expression
This PR is independent of the parallelization stack and targets
main.