Try to reduce roundoff error in LocalGeometry constructor #3706
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Purpose
This PR overwrites the constructor for
ClimaCore.Geometry.LocalGeometry
in an attempt to reduce the amount of roundoff error, which may be responsible for the lack of conservation @szy21 has observed in long Float32 simulations.To-do
If this change fixes the conservation issue, it should be moved into ClimaCore.
Content
gᵢⱼ = ∂x∂ξ' * ∂x∂ξ
withgᵢⱼ = (∂x∂ξ' * ∂x∂ξ + (∂x∂ξ' * ∂x∂ξ)') / 2
gⁱʲ = ∂ξ∂x' * ∂ξ∂x
withgⁱʲ = inv(gᵢⱼ)
J
andWJ
asJ = det(∂x∂ξ)
andWJ = W * J