forked from 1b-agent/fieldcraft-upstream
jyvikoandClaude Opus 5.5
3a5a8213a1
A five-node pyramid, the conforming transition between a hexahedron's face and tetrahedra: Bedrosian's rational shape functions with a collapsed (Duffy) Gauss rule, a certified Jacobian on the base square with exact volume, a scaled Jacobian, C3D5 / CPYRAM / LS-DYNA degenerate solid, VTK_PYRAMID and the binary mesh code 13. A distorted hex8-pyramid5-tet4 transition mesh passes the patch test and uniaxial tension exactly. Co-Authored-By: Claude Opus 5.5 <[email protected]> Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo
258 lines
12 KiB
Rust
258 lines
12 KiB
Rust
//! Structured meshes generated in code for the analytic verification suite: a block of
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//! hexahedra (hex8, hex20), of wedges (two per cell) or of Kuhn-split tetrahedra (tet4, tet10) on [0, 1]³, mapped to the part
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//! by a function, and helpers to define the model on it.
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#![allow(dead_code)]
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use std::collections::BTreeMap;
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use fieldcraft_model::{
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BoundaryCondition, Coupling, CouplingKind, Dofs, Elastic, ElementFace, ElementKind, Formulation, Integration, Load, Material, Model, Procedure,
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ReferencePoint, Section, SectionKind, Set, Step, Symmetry, Target,
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};
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pub struct Grid {
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pub model: Model,
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/// Parametric coordinates of every node.
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pub param: BTreeMap<u32, [f64; 3]>,
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pub kind: ElementKind,
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}
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/// A structured mesh with `n` cells per direction. Nodes live on the doubled lattice
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/// (2n + 1 points per direction) so quadratic elements get their mid-side nodes from the map
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/// too (curved edges follow it).
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pub fn grid(n: [usize; 3], kind: ElementKind, map: impl Fn([f64; 3]) -> [f64; 3]) -> Grid {
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let size = n.map(|k| 2 * k + 1);
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let label = |i: [usize; 3]| (1 + i[0] + size[0] * (i[1] + size[1] * i[2])) as u32;
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let param_of = |i: [usize; 3]| [0, 1, 2].map(|k| i[k] as f64 / (2 * n[k]) as f64);
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let mut model = Model::default();
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let mut param = BTreeMap::new();
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let mut node = |model: &mut Model, i: [usize; 3]| -> u32 {
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let l = label(i);
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if let std::collections::btree_map::Entry::Vacant(slot) = param.entry(l) {
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let p = param_of(i);
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model.set_node(l, map(p)).unwrap();
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slot.insert(p);
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}
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l
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};
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let mut next = 1u32;
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for cz in 0..n[2] {
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for cy in 0..n[1] {
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for cx in 0..n[0] {
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let base = [2 * cx, 2 * cy, 2 * cz];
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let at = |d: [usize; 3]| [base[0] + d[0], base[1] + d[1], base[2] + d[2]];
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match kind {
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ElementKind::Hex8 | ElementKind::Hex20 => {
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let corners = [[0, 0, 0], [2, 0, 0], [2, 2, 0], [0, 2, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2], [0, 2, 2]];
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let mut nodes: Vec<u32> = corners.iter().map(|c| node(&mut model, at(*c))).collect();
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if kind == ElementKind::Hex20 {
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for e in kind.edges() {
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let (a, b) = (corners[e[0]], corners[e[1]]);
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nodes.push(node(&mut model, at([0, 1, 2].map(|k| (a[k] + b[k]) / 2))));
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}
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}
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model.set_element(next, kind, nodes).unwrap();
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next += 1;
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}
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ElementKind::Wedge6 => {
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// Two prisms along z, split by the cell's (x, y) diagonal, both counter-clockwise from above.
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for tri in [[[0, 0], [2, 0], [2, 2]], [[0, 0], [2, 2], [0, 2]]] {
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let nodes: Vec<u32> =
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[0, 2].iter().flat_map(|&z| tri.map(|t| [t[0], t[1], z])).map(|c| node(&mut model, at(c))).collect();
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model.set_element(next, kind, nodes).unwrap();
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next += 1;
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}
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}
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_ => {
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// Six tetrahedra around the cell's main diagonal (Kuhn), conforming across cells.
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for perm in [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]] {
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let mut v = [[0usize; 3]; 4];
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for s in 0..3 {
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v[s + 1] = v[s];
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v[s + 1][perm[s]] = 2;
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}
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// Orientation from the parametric volume.
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let p = v.map(|c| c.map(|x| x as f64));
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let e = |i: usize| [0, 1, 2].map(|k| p[i][k] - p[0][k]);
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let (a, b, c) = (e(1), e(2), e(3));
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let vol = a[0] * (b[1] * c[2] - b[2] * c[1]) - a[1] * (b[0] * c[2] - b[2] * c[0]) + a[2] * (b[0] * c[1] - b[1] * c[0]);
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if vol < 0.0 {
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v.swap(1, 2);
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}
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let mut nodes: Vec<u32> = v.iter().map(|c| node(&mut model, at(*c))).collect();
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if kind == ElementKind::Tet10 {
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for e in kind.edges() {
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let (a, b) = (v[e[0]], v[e[1]]);
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nodes.push(node(&mut model, at([0, 1, 2].map(|k| (a[k] + b[k]) / 2))));
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}
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}
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model.set_element(next, kind, nodes).unwrap();
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next += 1;
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}
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}
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}
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}
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}
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}
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Grid { model, param, kind }
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}
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/// A hex–tet transition mesh on [0, 1]³ with `n` cells per direction: the cells with x below
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/// one half are hex8, every other cell is split from its centre into six pyramids over its faces,
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/// and each pyramid whose face is not shared with a hex cell into two tetrahedra (split along
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/// the diagonal through the face's lowest node label, so neighbours agree). The mesh is
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/// conforming: hexahedra meet pyramids on whole quadrilaterals, everything else on triangles.
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pub fn transition_grid(n: [usize; 3], map: impl Fn([f64; 3]) -> [f64; 3]) -> Grid {
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let size = n.map(|k| 2 * k + 1);
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let label = |i: [usize; 3]| (1 + i[0] + size[0] * (i[1] + size[1] * i[2])) as u32;
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let param_of = |i: [usize; 3]| [0, 1, 2].map(|k| i[k] as f64 / (2 * n[k]) as f64);
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let mut model = Model::default();
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let mut param = BTreeMap::new();
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let mut node = |model: &mut Model, i: [usize; 3]| -> u32 {
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let l = label(i);
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if let std::collections::btree_map::Entry::Vacant(slot) = param.entry(l) {
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let p = param_of(i);
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model.set_node(l, map(p)).unwrap();
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slot.insert(p);
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}
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l
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};
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let is_hex = |c: [isize; 3]| (0..3).all(|k| c[k] >= 0 && (c[k] as usize) < n[k]) && 2 * c[0] < n[0] as isize;
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const CORNERS: [[usize; 3]; 8] = [[0, 0, 0], [2, 0, 0], [2, 2, 0], [0, 2, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2], [0, 2, 2]];
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// Hex8's faces (outward) and the cell across each.
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let across: [[isize; 3]; 6] = [[0, 0, -1], [0, 0, 1], [0, -1, 0], [1, 0, 0], [0, 1, 0], [-1, 0, 0]];
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let mut next = 1u32;
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for cz in 0..n[2] {
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for cy in 0..n[1] {
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for cx in 0..n[0] {
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let base = [2 * cx, 2 * cy, 2 * cz];
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let at = |d: [usize; 3]| [base[0] + d[0], base[1] + d[1], base[2] + d[2]];
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let cell = [cx as isize, cy as isize, cz as isize];
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let corners: Vec<u32> = CORNERS.iter().map(|c| node(&mut model, at(*c))).collect();
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if is_hex(cell) {
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model.set_element(next, ElementKind::Hex8, corners).unwrap();
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next += 1;
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continue;
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}
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let apex = node(&mut model, at([1, 1, 1]));
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for (face, d) in ElementKind::Hex8.faces().iter().zip(across) {
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// Reversed, the outward face's normal points into the cell, at the apex.
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let q: Vec<u32> = face.iter().rev().map(|&i| corners[i]).collect();
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if is_hex([cell[0] + d[0], cell[1] + d[1], cell[2] + d[2]]) {
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model.set_element(next, ElementKind::Pyramid5, vec![q[0], q[1], q[2], q[3], apex]).unwrap();
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next += 1;
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continue;
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}
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let lowest = (0..4).min_by_key(|&i| q[i]).unwrap();
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let (a, b, c, e) = if lowest % 2 == 0 { (q[0], q[1], q[2], q[3]) } else { (q[1], q[2], q[3], q[0]) };
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for tet in [[a, b, c, apex], [a, c, e, apex]] {
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model.set_element(next, ElementKind::Tet4, tet.to_vec()).unwrap();
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next += 1;
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}
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}
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}
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}
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}
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Grid { model, param, kind: ElementKind::Pyramid5 }
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}
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pub fn near(a: f64, b: f64) -> bool {
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(a - b).abs() < 1e-9
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}
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impl Grid {
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pub fn nodes_where(&self, f: impl Fn([f64; 3]) -> bool) -> Vec<u32> {
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self.param.iter().filter(|(_, p)| f(**p)).map(|(l, _)| *l).collect()
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}
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/// Element faces whose nodes all satisfy `f` (on parametric coordinates).
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pub fn faces_where(&self, f: impl Fn([f64; 3]) -> bool) -> Vec<ElementFace> {
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let mut out = Vec::new();
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for (label, e) in self.model.elements() {
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for (i, face) in e.kind.faces().iter().enumerate() {
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if face.iter().all(|k| f(self.param[&e.nodes[*k]])) {
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out.push(ElementFace { element: *label, face: i as u8 + 1 });
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}
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}
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}
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out
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}
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/// Material, section over every element and an empty step of the given procedure.
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pub fn define(&mut self, elastic: Elastic, density: Option<f64>, formulation: Formulation, procedure: Procedure) {
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let all: Vec<u32> = self.model.elements().keys().copied().collect();
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self.model.add_set("all", Set { elements: all, ..Set::default() }).unwrap();
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self.model.add_material("Mat", Material { elastic: Some(elastic), density, ..Material::default() }).unwrap();
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self.model.add_section("solid", Section { set: "all".into(), material: "Mat".into(), kind: SectionKind::Solid {}, formulation }).unwrap();
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self.model.add_step(Step::new("Step", procedure), None).unwrap();
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}
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pub fn node_set(&mut self, name: &str, f: impl Fn([f64; 3]) -> bool) {
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let nodes = self.nodes_where(f);
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self.model.add_set(name, Set { nodes, ..Set::default() }).unwrap();
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}
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pub fn face_set(&mut self, name: &str, f: impl Fn([f64; 3]) -> bool) {
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let faces = self.faces_where(f);
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self.model.add_set(name, Set { faces, ..Set::default() }).unwrap();
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}
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pub fn bc(&mut self, name: &str, bc: BoundaryCondition) {
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self.model.add_boundary_condition(name, bc).unwrap();
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self.model.set_boundary_condition_active("Step", name, true).unwrap();
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}
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pub fn load(&mut self, name: &str, load: Load) {
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self.model.add_load(name, load).unwrap();
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self.model.set_load_active("Step", name, true).unwrap();
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}
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pub fn symmetry(&mut self, name: &str, plane: Symmetry, f: impl Fn([f64; 3]) -> bool) {
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self.node_set(name, f);
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self.bc(name, BoundaryCondition::Symmetry { target: Target::Set(name.into()), plane });
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}
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/// A reference point `name` at `xyz`, coupled to the nodes where `f` holds.
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pub fn couple(&mut self, name: &str, xyz: [f64; 3], kind: CouplingKind, dofs: &[u8], f: impl Fn([f64; 3]) -> bool) {
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let set = format!("{name}_nodes");
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self.node_set(&set, f);
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self.model.add_reference_point(name, ReferencePoint { xyz, label: 0 }).unwrap();
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let dofs = Dofs::try_from(dofs.to_vec()).unwrap();
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self.model.add_coupling(&format!("{name}_coupling"), Coupling { reference_point: name.into(), set, kind, dofs }).unwrap();
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}
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pub fn fixed(&mut self, name: &str, f: impl Fn([f64; 3]) -> bool) {
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self.node_set(name, f);
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self.bc(name, BoundaryCondition::Fixed { target: Target::Set(name.into()) });
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}
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}
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pub fn iso(young: f64, poisson: f64) -> Elastic {
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Elastic::Isotropic { young, poisson }
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}
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pub fn full() -> Formulation {
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Formulation::default()
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}
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pub fn reduced() -> Formulation {
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Formulation { integration: Integration::Reduced, ..Formulation::default() }
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}
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pub fn incompatible() -> Formulation {
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Formulation { incompatible_modes: true, ..Formulation::default() }
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}
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/// The element kinds and formulations under test.
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pub fn variants() -> Vec<(ElementKind, Formulation, &'static str)> {
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vec![
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(ElementKind::Tet4, full(), "tet4"),
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(ElementKind::Tet10, full(), "tet10"),
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(ElementKind::Wedge6, full(), "wedge6"),
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(ElementKind::Hex8, full(), "hex8"),
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(ElementKind::Hex8, incompatible(), "hex8 incompatible"),
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(ElementKind::Hex20, full(), "hex20"),
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(ElementKind::Hex20, reduced(), "hex20 reduced"),
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]
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}
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