High-contrast homogenization: Provider.Quenched.SmallContrastFusionIsotropy #
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
The isotropy one-step chain and recursion constant steps 2 and 3, under the doctrine rule. #
The mapping of the fusion chain shows that almost none of it needs a parallel
definition. weakDropConstant, weakBaseCoefficientSummed,
weakSourceGroupSummed, split_at_recursionAlpha_at_level, iterationDropSum,
per_generation_hrec_at_recursionAlpha_sharp_at_jb_src and the recursion-family
core body are already abstract in the metric factor M, the load scale L
and the
recursion constant A; they carry no aspect ratio and are reused unchanged.
Π enters the one-step chain at exactly one link:
the one-step-to-scalar conversion of
HCPoly.Provider.Quenched.SmallContrastHrecInstance, whose hone
carries rowValue2 Cd g mAl G s t kap and whose conclusion carries
quadCoefficient d Cpre (rowCoefficient Cd g mAl G s t kap). Its proof is the
row-value equation followed by one_step_scalar_shape, which
is itself abstract in the row coefficient.
So the parallel copies needed are exactly three, and they are the ones here:
one_step_to_scalar_step_isotropy, hrec_line_of_one_step_isotropy_sharp_at_jb_src and
fusionRecursionConstantIsotropySharp. The last differs from
fusionRecursionConstantIsotropySharp
only in taking L as a parameter instead of fixing
weakLoadScale Cd g mAl G kap in its body, and in using rowCoefficientIsotropy;
fixing it in the body is precisely what cannot be repaired by an inequality.
The one-step scalar shape at the isotropy row #
The parallel copy of the one-step-to-scalar conversion. Identical
proof: the
row value is converted to its coefficient by an equation, and
one_step_scalar_shape — abstract in the row coefficient — does the rest.