High-contrast homogenization: Provider.PolynomialHomogenization.ConvexHardyCellInitialAggregation

Imported from the Apache-2.0 HighContrastHomogenization development at commit 7a13dbcd8d6609264a713373f5c69ceeac870472.

Aggregating the initial cell-to-ball comparisons

The first link from a Whitney cell to its ball chain is charged through the cell coordinate of a disjoint family of product rectangles. Its scale weight cancels the inverse cell and ball volumes without any summation loss.

noncomputable def HCPolySupport.HighContrast.convexHardyCellInitialAggregationConstant (d : ℕ) (s rho Rad : ℝ) : ENNReal

The scale-free coefficient for all initial cell-to-ball comparisons.

Equations

• HCPolySupport.HighContrast.convexHardyCellInitialAggregationConstant d s rho Rad = ENNReal.ofReal (√↑d ^ d * (2 * (1 + √↑d * (1 + Rad / rho))).rpow (↑d + 2 * s))