Coarse-graining support: #
Support.Sobolev.Foundations.CubeNeumannW22CZ.WeakInteriorDQ.PoissonTranslation
Imported from the Apache-2.0 CoarseGraining development at commit
c7ddd76c08ade64fed1b8d2ca51be14dfee8deb4.
noncomputable def
HCPolySupport.MeanZeroNeumannPoissonSolution.untranslateToOrigin
{d : ℕ}
(Q : TriadicCube d)
{F : Vec d → ℝ}
(W : MeanZeroNeumannPoissonSolution Q F)
:
MeanZeroNeumannPoissonSolution (originCube d Q.scale) fun (x : Vec d) => F (x + triadicCubeShift Q)
Pull a cube Neumann solution back to the centered cube of the same scale.
Equations
- One or more equations did not get rendered due to their size.
Instances For
theorem
HCPolySupport.MeanZeroNeumannPoissonSolution.untranslateToOrigin_translate_grad
{d : ℕ}
(Q : TriadicCube d)
{F : Vec d → ℝ}
(W : MeanZeroNeumannPoissonSolution Q F)
(x : Vec d)
:
((untranslateToOrigin Q W).w.toH1Function.translate (triadicCubeShift Q)).grad x = W.w.toH1Function.grad x