High-contrast homogenization: #
Provider.PolynomialHomogenization.Root.RowSupply.ResidualScaledCoeffTransport
Imported from the Apache-2.0 HighContrastHomogenization development at commit
7a13dbcd8d6609264a713373f5c69ceeac870472.
Residual scaling of the physical coefficient sample #
After extracting an exact triadic dilation, the remaining dilation acts on the physically restored coefficient sample. The two coefficient fields agree almost everywhere after the elementary scalar change of variables.
theorem
HCPolySupport.HighContrast.RowSupply.scaledCoeff_mul_pow_physicalScaleCoeff_ae
{d : โ}
{epsilon : โ}
(hepsilon : 0 < epsilon)
(N : โ)
(a : CoeffSpace d)
:
scaledCoeff (epsilon * 3 ^ N) (Quenched.physicalScaleCoefficient N a) =แต[MeasureTheory.volume] scaledCoeff epsilon a
Scaling the restored sample by epsilon * 3^N is the same almost
everywhere as scaling the original sample by epsilon.