High-contrast homogenization: Provider.PolynomialHomogenization.ConvexHardyRowFluctuation #
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
Fractional fluctuation control on one Whitney row #
Every identity-grid cell in a fixed Whitney row has the same side length. The fractional Poincare estimate on each cell therefore has one common coefficient: after weighting by the inverse fractional scale, the cell volume and diameter cancel exactly. Pairwise disjointness then lets the diagonal product energies sum into the energy of the containing domain.
noncomputable def
HCPolySupport.HighContrast.whitneyRowFractionalKernel
{d : ℕ}
(s : ℝ)
(F : Vec d → Vec d)
(z : Vec d × Vec d)
:
The fractional Gagliardo kernel used to aggregate diagonal cell energies.
Equations
- HCPolySupport.HighContrast.whitneyRowFractionalKernel s F z = ENNReal.ofReal (HCPolySupport.vecNormSq (F z.1 - F z.2) / √(HCPolySupport.vecNormSq (z.1 - z.2)) ^ (↑d + 2 * s))