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
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jyvikoandClaude Opus 5.5 authored and Irakli Kourtis committed 2026-10-14 15:28:02 -04:00
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@@ -215,6 +215,9 @@ impl System {
if let Some(name) = model.couplings().keys().next() {
return Err(Error::NotSupported(format!("couplings (coupling `{name}`) in explicit dynamics")));
}
if let Some(name) = model.ties().keys().next() {
return Err(Error::NotSupported(format!("ties (tie `{name}`) in explicit dynamics")));
}
// Elements by label, with their section's material.
let mut materials: Vec<Material> = Vec::new();