solver: ties by dual mortar constraints

Each secondary node follows the main surface under it as the weighted average
u_A = sum_J (M_AJ / sum_K M_AK) u_J with M_AJ = int psi_A N_J over the reference overlaps and
psi the secondary faces' dual shape functions (Wohlmuth 2000), so the secondary mortar
matrix is diagonal; the rows join the couplings' constraint elimination in every implicit
analysis. Uncovered secondary nodes stay free with a warning; heat transfer and explicit
dynamics refuse ties by name. Tested by the tie patch test on non-matching hex8/tet4 meshes.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/solver/src/heat.rs

@@ -414,15 +414,25 @@ pub(crate) fn temperatures(model: &Model, resolved: &Resolved, step: &Step, limi
     Ok((s.mesh.labels, t))
 }
 
+/// Heat transfer does not tie temperatures across a tie yet.
+fn refuse_ties(model: &Model) -> Result<()> {
+    match model.ties().keys().next() {
+        Some(name) => Err(crate::Error::NotSupported(format!("ties (tie `{name}`) in heat transfer"))),
+        None => Ok(()),
+    }
+}
+
 /// The steady temperatures of a step's thermal conditions at the nodes `labels` (sorted), `None`
 /// at the nodes conduction does not reach.
 pub(crate) fn temperatures_at(model: &Model, resolved: &Resolved, step: &Step, limits: &Limits, labels: &[u32]) -> Result<Vec<Option<f64>>> {
+    refuse_ties(model)?;
     let (solved, t) = temperatures(model, resolved, step, limits)?;
     Ok(labels.iter().map(|l| solved.binary_search(l).ok().and_then(|i| t.get(i)).copied()).collect())
 }
 
 /// Solve a heat transfer step: the step named `step`, or the model's only one.
 pub fn solve_heat(model: &Model, step: Option<&str>, limits: &Limits) -> Result<HeatResult> {
+    refuse_ties(model)?;
     let resolved = model.resolve()?;
     let step = model.select_step(step, |p| matches!(p, Procedure::HeatTransfer { .. }), "heat transfer")?;
     let mut warnings: Vec<String> = resolved.warnings.iter().map(ToString::to_string).collect();