From 7ed78e9f5e59c33c85577ee99583d7320ed58c32 Mon Sep 17 00:00:00 2001
From: Jukka Aho <ahojukka5@gmail.com>
Date: Sat, 9 May 2026 16:59:58 +0300
Subject: [PATCH] feat(geometry): add Piola push-forward helpers for curl/div
 fields

Implement covariant and contravariant Piola maps using Tensors.jl Jacobians.
---
 src/geometry/piola.jl | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 src/geometry/piola.jl

diff --git a/src/geometry/piola.jl b/src/geometry/piola.jl
new file mode 100644
index 0000000..4438f57
--- /dev/null
+++ b/src/geometry/piola.jl
@@ -0,0 +1,30 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+using Tensors
+
+"""
+    piola_covariant(J::Tensor{2,3}, u_ref::Vec{3}) -> Vec{3}
+
+Covariant Piola transform (push-forward for `H(curl)`-type fields):
+
+``u^{\\mathrm{phys}} = J^{-T} u^{\\mathrm{ref}}``,
+
+with `J = ∂x/∂ξ` the Jacobian of the reference-to-physical map.
+
+See also [`piola_contravariant`](@ref) for `H(\\mathrm{div})`.
+"""
+@inline function piola_covariant(J::Tensor{2, 3}, u_ref::Vec{3})
+    return inv(J)' ⋅ u_ref
+end
+
+"""
+    piola_contravariant(J::Tensor{2,3}, u_ref::Vec{3}) -> Vec{3}
+
+Contravariant Piola transform (push-forward for `H(\\mathrm{div})`-type fields):
+
+``u^{\\mathrm{phys}} = (\\det J)^{-1} J \\, u^{\\mathrm{ref}}``.
+"""
+@inline function piola_contravariant(J::Tensor{2, 3}, u_ref::Vec{3})
+    return (J ⋅ u_ref) / det(J)
+end