solver: a tie row nearly repeated on a held secondary node is dropped

Where a tie's secondary surface meets a boundary condition or an
axis-aligned symmetry plane (a crosspoint), the secondary node's motion
is already prescribed and its mortar row can only constrain main
degrees of freedom. Its weights on main nodes off the boundary do not
vanish (the dual basis spreads over the node's faces), so after the
substitutions a small but real constraint is left: 1.3e-6 of the
coefficients that cancelled to give it on the tied hex-tet bar with
the needle-aware tet mesh (round-off would be ~1e-14; the geometry is
exact). It was refused as a near repeat, which made the tied bar
depend on how the tet faces fell. It is now dropped (the tie is then
off by that fraction at the crosspoint), after checking it does not
contradict the prescribed values. A near repeat on a secondary degree
of freedom another constraint eliminated (a node secondary in two
ties) is still refused (#389). Dropping every held secondary node's
row instead fails the tie patch test, so only near repeats go.

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

crates/solver/src/constraints.rs

@@ -534,11 +534,34 @@ impl Reduction {
             });
             // A tie whose secondary node is held already: what is left of the row must be a
             // constraint of its own, not the difference of two near copies of one.
-            if row.source == Source::Tie
-                && intended.is_none()
-                && let Some(&(_, c)) = largest
-                && c.abs() < NEARLY_REPEATED * gross
-            {
+            let nearly_repeated = row.source == Source::Tie && intended.is_none() && largest.is_some_and(|t| t.1.abs() < NEARLY_REPEATED * gross);
+            // Held by a prescribed value (the secondary surface meeting a boundary condition or an
+            // axis-aligned symmetry plane: a crosspoint), the row can only constrain main degrees
+            // of freedom, and nearly repeated, what it adds is the mortar condition of a node
+            // whose motion is already given: its weights on main nodes off the boundary do not
+            // vanish (the dual basis spreads over the node's faces), so after the substitutions
+            // a small but real constraint is left, not round-off (1.3e-6 of the coefficients that
+            // cancelled to give it where a tet face meets a symmetry plane, #540; round-off would
+            // be ~1e-14 there). Eliminating it divides by that smallness; dropping it leaves the
+            // tie off by that fraction at the crosspoint, below the discretization error. So it
+            // is dropped, with the same threshold that calls it a near repeat. A secondary degree
+            // of freedom another constraint already eliminated (a node secondary in two ties, a
+            // tie and a coupling) is a real conflict and still refused (#389).
+            if nearly_repeated && state.get(row.pivot) == Some(&State::Fixed) {
+                // Still consistent with the prescribed values, or a contradiction.
+                let value = |t: &(usize, f64)| t.1 * values.get(t.0).copied().unwrap_or(0.0);
+                let residual: f64 = terms.iter().filter(|t| state.get(t.0) == Some(&State::Fixed)).map(value).sum();
+                let size: f64 = terms.iter().map(|t| value(t).abs()).sum();
+                if residual.abs() > 1e-9 * size.max(f64::MIN_POSITIVE) && residual.abs() > 0.0 {
+                    return Err(Error::Invalid(format!(
+                        "{} `{}` contradicts the prescribed values (boundary conditions or couplings hold its nodes in a way it cannot follow)",
+                        row.source.what(),
+                        row.coupling
+                    )));
+                }
+                continue;
+            }
+            if nearly_repeated {
                 let mut others: Vec<String> = row
                     .terms
                     .iter()
@@ -858,6 +881,48 @@ impl Reduction {
 mod tests {
     use super::*;
 
+    fn tie(terms: Vec<(usize, f64)>, pivot: usize) -> Row<'static> {
+        Row { terms, pivot, coupling: "glue", source: Source::Tie }
+    }
+
+    /// Dofs `held` prescribed, dof 1 at `one` and the others at 0.
+    fn reduce(rows: &[Row], held: &[usize], one: f64) -> Result<Reduction> {
+        let layout = DofLayout::uniform(0..2, DofSet::TRANSLATIONS);
+        let budget = Budget { max_bytes: usize::MAX, pattern_entries: 0, matrices: 1 };
+        Reduction::new(
+            &layout,
+            std::iter::empty(),
+            &[0, 1],
+            rows,
+            |active| Ok((0..active.len()).map(|d| held.contains(&d).then_some(if d == 1 { one } else { 0.0 })).collect()),
+            budget,
+        )
+    }
+
+    /// A tie row of a secondary degree of freedom held by a boundary condition (dof 1), which
+    /// after substituting an earlier tie row (dof 0 following dofs 2 and 3) nearly repeats it, is
+    /// dropped (a crosspoint); dof 3 stays free.
+    #[test]
+    fn a_tie_row_on_a_held_degree_of_freedom_is_dropped() {
+        let rows = [tie(vec![(0, 1.0), (2, -0.5), (3, -0.5)], 0), tie(vec![(1, 1.0), (0, -1.0), (2, 0.5), (3, 0.5 - 1e-7)], 1)];
+        let r = reduce(&rows, &[1, 2], 0.0).unwrap();
+        assert_eq!(r.neq(), 3, "dofs 3, 4, 5 free");
+    }
+
+    /// Nearly repeated but inconsistent: on a secondary degree of freedom another tie already
+    /// eliminated (a node secondary in two ties) it is refused (#389), and on a held one whose
+    /// prescribed values it contradicts too.
+    #[test]
+    fn a_near_repeat_on_an_eliminated_degree_of_freedom_is_refused() {
+        let rows = [tie(vec![(0, 1.0), (2, -0.5), (3, -0.5)], 0), tie(vec![(0, 1.0), (2, -0.5), (3, -0.5 - 1e-7)], 0)];
+        let e = reduce(&rows, &[2], 0.0).err().map(|e| e.to_string()).unwrap_or_default();
+        assert!(e.contains("almost alike"), "{e}");
+        // Dof 1 held at 1 and dof 2 at 0 while the row says dof 1 follows them.
+        let rows = [tie(vec![(0, 1.0), (2, -0.5), (3, -0.5)], 0), tie(vec![(1, 1.0), (0, -1.0), (2, 0.5), (3, 0.5 - 1e-7)], 1)];
+        let e = reduce(&rows, &[1, 2], 1.0).err().map(|e| e.to_string()).unwrap_or_default();
+        assert!(e.contains("contradicts"), "{e}");
+    }
+
     #[test]
     fn reduced_matrix_budget_refuses_byte_counts_that_overflow() {
         for matrices in [1, 2] {