rustyverse/rustytorch
2
0
Fork 0
Code Issues Pull Requests Actions 1 Packages Projects Releases Wiki Activity

R7 phase 1: host prototype of the composite Poisson with one nested ratio-2 patch (embedded3::composite; three coarse-fine fluxes, FAC-preconditioned BiCGStab; P1/P1b/P2/P3 gates as ignored tests). Additive module, nothing calls it.

Browse Source 
Co-Authored-By: Claude Opus 5.5 (1M context) <[email protected]>
This commit is contained in:
Omar Sobh
2026-09-25 17:53:50 -05:00
co-authored by Claude Opus 5.5
parent d63806c0e6
commit e19cad03b2
5 changed files with 1458 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files
crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/composite/assemble.rs
+519
View File
@@ -0,0 +1,519 @@
//! The composite operator: coarse–coarse, fine–fine and coarse–fine faces,
//! the Dirichlet outer boundary, the cut apertures of an optional body on
//! the fine level, and the uniform coarse [`Problem`] the preconditioner's
//! coarse correction solves.
use super::Csr;
use crate::solvers::incompressible::embedded3::poisson::Problem;
use crate::solvers::incompressible::embedded3::{Body, CutGeometry, Grid};
/// The coarse–fine face flux (see the module docs).
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum Interface {
Direct,
Octree,
Quadratic,
}
/// What to build. The coarse grid must be cubic; the patch `lo ≤ (i, j, k)
/// < hi` (coarse indices) keeps two coarse cells from the domain boundary.
pub struct CompositeSpec<'a> {
pub coarse: Grid,
pub lo: [usize; 3],
pub hi: [usize; 3],
pub interface: Interface,
/// A body cutting the fine level (φ > 0 fluid), Neumann on its wall.
pub body: Option<Sdf>,
/// `f = −Δp` (integrated by the midpoint rule over the fluid volume).
pub source: &'a (dyn Fn(f64, f64, f64) -> f64 + Sync),
/// The Dirichlet value on the outer boundary.
pub dirichlet: &'a (dyn Fn(f64, f64, f64) -> f64 + Sync),
}
/// The assembled composite problem.
pub struct Composite {
pub coarse: Grid,
pub fine: Grid,
pub lo: [usize; 3],
pub hi: [usize; 3],
pub interface: Interface,
/// Per coarse cell: its unknown, or `usize::MAX` (covered / solid).
pub coarse_id: Vec<usize>,
/// Per fine cell: its unknown, or `usize::MAX` (solid).
pub fine_id: Vec<usize>,
/// Unknowns `0..n_coarse` are coarse, the rest fine.
pub n_coarse: usize,
/// Per unknown: the coarse cell holding it (itself, or the fine
/// cell's parent) — the restriction / prolongation map.
pub parent: Vec<usize>,
/// Per unknown: the cell centre and the fluid volume.
pub centre: Vec<[f64; 3]>,
pub volume: Vec<f64>,
/// Per unknown: the cell owns a coarse–fine face.
pub at_interface: Vec<bool>,
/// Per unknown: the cell is cut by the body (0 < fluid fraction < 1).
pub cut: Vec<bool>,
pub a: Csr,
pub rhs: Vec<f64>,
/// The uniform coarse operator (coarse apertures under the patch too).
pub coarse_problem: Problem,
}
const NONE: usize = usize::MAX;
/// (axis, sign) of the six faces: −x, +x, −y, +y, −z, +z.
const DIRS: [(usize, isize); 6] = [(0, -1), (0, 1), (1, -1), (1, 1), (2, -1), (2, 1)];
/// A signed distance (φ > 0 fluid) shared by the coarse and fine builds.
pub type Sdf = std::sync::Arc<dyn Fn(f64, f64, f64) -> f64 + Send + Sync>;
/// The body of `phi` on a grid starting at `origin`.
fn body_at(phi: &Sdf, origin: [f64; 3]) -> Body {
let phi = phi.clone();
Body::from_sdf(move |x, y, z, _t| phi(x + origin[0], y + origin[1], z + origin[2]))
}
/// The fluid aperture of face `dir` of cell `c = (i, j, k)` of `cut`.
fn aperture(cut: Option<&CutGeometry>, g: Grid, c: [usize; 3], dir: usize) -> f64 {
let Some(cut) = cut else { return 1.0 };
let [i, j, k] = c;
match dir {
0 => cut.a_u[g.uface(k, j, i)],
1 => cut.a_u[g.uface(k, j, i + 1)],
2 => cut.a_v[g.vface(k, j, i)],
3 => cut.a_v[g.vface(k, j + 1, i)],
4 => cut.a_w[g.wface(k, j, i)],
_ => cut.a_w[g.wface(k + 1, j, i)],
}
}
fn fraction(cut: Option<&CutGeometry>, g: Grid, c: [usize; 3]) -> f64 {
cut.map_or(1.0, |cut| cut.vol[g.cell(c[2], c[1], c[0])])
}
fn active(cut: Option<&CutGeometry>, g: Grid, c: [usize; 3]) -> bool {
fraction(cut, g, c) > 0.0 && (0..6).any(|d| aperture(cut, g, c, d) > 0.0)
}
impl Composite {
#[must_use]
pub fn build(spec: &CompositeSpec<'_>) -> Self {
let cg = spec.coarse;
let (lo, hi) = (spec.lo, spec.hi);
let hc = cg.dx;
assert!(
(cg.dy - hc).abs() < 1e-14 * hc && (cg.dz - hc).abs() < 1e-14 * hc,
"cubic cells"
);
let dims = [cg.nx, cg.ny, cg.nz];
for d in 0..3 {
assert!(
lo[d] >= 2 && hi[d] + 2 <= dims[d] && hi[d] > lo[d],
"patch margin"
);
}
let hf = 0.5 * hc;
let fg = Grid::cubic(
2 * (hi[0] - lo[0]),
2 * (hi[1] - lo[1]),
2 * (hi[2] - lo[2]),
hf,
);
let fdims = [fg.nx, fg.ny, fg.nz];
let origin = [lo[0] as f64 * hc, lo[1] as f64 * hc, lo[2] as f64 * hc];
let fine_cut = spec
.body
.as_ref()
.map(|b| CutGeometry::build(&body_at(b, origin), fg, 0.0));
let coarse_cut = spec
.body
.as_ref()
.map(|b| CutGeometry::build(&body_at(b, [0.0; 3]), cg, 0.0));
let (fcut, ccut) = (fine_cut.as_ref(), coarse_cut.as_ref());
let covered = |c: [usize; 3]| (0..3).all(|d| c[d] >= lo[d] && c[d] < hi[d]);
// Unknowns.
let mut coarse_id = vec![NONE; cg.cells()];
let mut fine_id = vec![NONE; fg.cells()];
let (mut parent, mut centre, mut volume, mut cut_flag) =
(Vec::new(), Vec::new(), Vec::new(), Vec::new());
for k in 0..cg.nz {
for j in 0..cg.ny {
for i in 0..cg.nx {
let c = [i, j, k];
if covered(c) {
continue;
}
assert!(
fraction(ccut, cg, c) > 1.0 - 1e-12,
"the body must stay inside the patch"
);
coarse_id[cg.cell(k, j, i)] = centre.len();
parent.push(cg.cell(k, j, i));
centre.push([
(i as f64 + 0.5) * hc,
(j as f64 + 0.5) * hc,
(k as f64 + 0.5) * hc,
]);
volume.push(hc * hc * hc);
cut_flag.push(false);
}
}
}
let n_coarse = centre.len();
for k in 0..fg.nz {
for j in 0..fg.ny {
for i in 0..fg.nx {
let c = [i, j, k];
if !active(fcut, fg, c) {
continue;
}
let frac = fraction(fcut, fg, c);
fine_id[fg.cell(k, j, i)] = centre.len();
parent.push(cg.cell(lo[2] + k / 2, lo[1] + j / 2, lo[0] + i / 2));
centre.push([
origin[0] + (i as f64 + 0.5) * hf,
origin[1] + (j as f64 + 0.5) * hf,
origin[2] + (k as f64 + 0.5) * hf,
]);
volume.push(frac * hf * hf * hf);
cut_flag.push(frac < 1.0);
}
}
}
let n = centre.len();
let mut rows: Vec<Vec<(usize, f64)>> = vec![Vec::new(); n];
let mut rhs = vec![0.0; n];
let mut at_interface = vec![false; n];
let step = |c: [usize; 3], d: usize, s: isize| -> [isize; 3] {
let mut o = [c[0] as isize, c[1] as isize, c[2] as isize];
o[d] += s;
o
};
let cid = |c: [isize; 3]| coarse_id[cg.cell(c[2] as usize, c[1] as usize, c[0] as usize)];
let fid = |c: [usize; 3]| fine_id[fg.cell(c[2], c[1], c[0])];
// The fine children of covered coarse cell `k` (coarse coords).
let children = |kc: [usize; 3]| -> Vec<[usize; 3]> {
let b = [
2 * (kc[0] - lo[0]),
2 * (kc[1] - lo[1]),
2 * (kc[2] - lo[2]),
];
let mut v = Vec::with_capacity(8);
for dk in 0..2 {
for dj in 0..2 {
for di in 0..2 {
v.push([b[0] + di, b[1] + dj, b[2] + dk]);
}
}
}
v
};
// The quadratic ghost of fine cell `f` across its face (d, s): the
// weights on unknowns.
let ghost = |f: [usize; 3], d: usize, s: isize| -> Vec<(usize, f64)> {
let mut w = Vec::with_capacity(12);
let mut fin = f;
fin[d] = (f[d] as isize - s) as usize;
w.push((fid(fin), -0.2));
w.push((fid(f), 2.0 / 3.0));
// The coarse cell holding the ghost point.
let gf = [
(2 * lo[0] + f[0]) as isize,
(2 * lo[1] + f[1]) as isize,
(2 * lo[2] + f[2]) as isize,
];
let mut gc = gf;
gc[d] += s;
let cc = [
gc[0].div_euclid(2),
gc[1].div_euclid(2),
gc[2].div_euclid(2),
];
let (t1, t2) = match d {
0 => (1, 2),
1 => (0, 2),
_ => (0, 1),
};
let off = |t: usize| if gf[t] % 2 == 0 { -0.25 } else { 0.25 };
let (a, b) = (off(t1), off(t2));
let wn = 8.0 / 15.0;
let at = |dt1: isize, dt2: isize| {
let mut c = cc;
c[t1] += dt1;
c[t2] += dt2;
let id = cid(c);
assert!(
id != NONE,
"interpolation stencil on a covered/solid coarse cell"
);
id
};
w.push((at(0, 0), wn * (1.0 - a * a - b * b)));
w.push((at(-1, 0), wn * (0.5 * a * a - 0.5 * a)));
w.push((at(1, 0), wn * (0.5 * a * a + 0.5 * a)));
w.push((at(0, -1), wn * (0.5 * b * b - 0.5 * b)));
w.push((at(0, 1), wn * (0.5 * b * b + 0.5 * b)));
let x = wn * 0.25 * a * b;
w.push((at(1, 1), x));
w.push((at(-1, -1), x));
w.push((at(1, -1), -x));
w.push((at(-1, 1), -x));
w
};
// Coarse rows.
for k in 0..cg.nz {
for j in 0..cg.ny {
for i in 0..cg.nx {
let row = coarse_id[cg.cell(k, j, i)];
if row == NONE {
continue;
}
let c = [i, j, k];
let x = centre[row];
rhs[row] += volume[row] * (spec.source)(x[0], x[1], x[2]);
for &(d, s) in &DIRS {
let nb = step(c, d, s);
if nb[d] < 0 || nb[d] >= dims[d] as isize {
let coef = 2.0 * hc;
let mut fx = x;
fx[d] += s as f64 * 0.5 * hc;
rows[row].push((row, coef));
rhs[row] += coef * (spec.dirichlet)(fx[0], fx[1], fx[2]);
continue;
}
let nbu = [nb[0] as usize, nb[1] as usize, nb[2] as usize];
if !covered(nbu) {
let other = cid(nb);
if other != NONE {
rows[row].push((row, hc));
rows[row].push((other, -hc));
}
continue;
}
at_interface[row] = true;
let kids = children(nbu);
// The four children on the face (normal index nearest C).
let near: Vec<[usize; 3]> = kids
.iter()
.copied()
.filter(|f| {
let want = 2 * (nbu[d] - lo[d]) + usize::from(s < 0);
f[d] == want
})
.collect();
match spec.interface {
Interface::Direct => {
let coef = hf / 1.5;
for f in near {
rows[row].push((row, coef));
rows[row].push((fid(f), -coef));
}
}
Interface::Octree => {
rows[row].push((row, hc));
for f in kids {
rows[row].push((fid(f), -hc / 8.0));
}
}
Interface::Quadratic => {
for f in near {
// Out of the fine cell through its face −s.
rows[row].push((fid(f), -hf));
for (u, w) in ghost(f, d, -s) {
rows[row].push((u, hf * w));
}
}
}
}
}
}
}
}
// Fine rows.
for k in 0..fg.nz {
for j in 0..fg.ny {
for i in 0..fg.nx {
let row = fine_id[fg.cell(k, j, i)];
if row == NONE {
continue;
}
let f = [i, j, k];
let x = centre[row];
rhs[row] += volume[row] * (spec.source)(x[0], x[1], x[2]);
for (dir, &(d, s)) in DIRS.iter().enumerate() {
let nb = step(f, d, s);
if nb[d] >= 0 && nb[d] < fdims[d] as isize {
let nbu = [nb[0] as usize, nb[1] as usize, nb[2] as usize];
let a = aperture(fcut, fg, f, dir);
let other = fid(nbu);
if a > 0.0 && other != NONE {
rows[row].push((row, a * hf));
rows[row].push((other, -a * hf));
}
continue;
}
at_interface[row] = true;
assert!(
aperture(fcut, fg, f, dir) > 1.0 - 1e-12,
"the body must not reach the interface"
);
let mut gc = [
(2 * lo[0] + f[0]) as isize,
(2 * lo[1] + f[1]) as isize,
(2 * lo[2] + f[2]) as isize,
];
gc[d] += s;
let cc = [
gc[0].div_euclid(2),
gc[1].div_euclid(2),
gc[2].div_euclid(2),
];
let c_row = cid(cc);
match spec.interface {
Interface::Direct => {
let coef = hf / 1.5;
rows[row].push((row, coef));
rows[row].push((c_row, -coef));
}
Interface::Octree => {
let coef = hf * hf / hc;
let kc = [lo[0] + i / 2, lo[1] + j / 2, lo[2] + k / 2];
for sib in children(kc) {
rows[row].push((fid(sib), coef / 8.0));
}
rows[row].push((c_row, -coef));
}
Interface::Quadratic => {
rows[row].push((row, hf));
for (u, w) in ghost(f, d, s) {
rows[row].push((u, -hf * w));
}
}
}
}
}
}
}
let a = Csr::from_rows(rows);
let coarse_problem = Self::coarse_operator(cg, ccut);
Self {
coarse: cg,
fine: fg,
lo,
hi,
interface: spec.interface,
coarse_id,
fine_id,
n_coarse,
parent,
centre,
volume,
at_interface,
cut: cut_flag,
a,
rhs,
coarse_problem,
}
}
/// The uniform coarse operator of the same problem (the coarse cut
/// under the patch), Dirichlet outside: the FAC coarse correction.
fn coarse_operator(cg: Grid, ccut: Option<&CutGeometry>) -> Problem {
let h = cg.dx;
let mut p = Problem::new(cg.nx, cg.ny, cg.nz);
let dims = [cg.nx, cg.ny, cg.nz];
for k in 0..cg.nz {
for j in 0..cg.ny {
for i in 0..cg.nx {
let idx = cg.cell(k, j, i);
p.active[idx] = active(ccut, cg, [i, j, k]);
}
}
}
for k in 0..cg.nz {
for j in 0..cg.ny {
for i in 0..cg.nx {
let idx = cg.cell(k, j, i);
if !p.active[idx] {
continue;
}
let c = [i, j, k];
for (dir, &(d, s)) in DIRS.iter().enumerate() {
let mut nb = [i as isize, j as isize, k as isize];
nb[d] += s;
if nb[d] < 0 || nb[d] >= dims[d] as isize {
p.extra_diag[idx] += 2.0 * h;
continue;
}
let other = cg.cell(nb[2] as usize, nb[1] as usize, nb[0] as usize);
let coef = if p.active[other] {
aperture(ccut, cg, c, dir) * h
} else {
0.0
};
match dir {
0 => p.aw[idx] = coef,
1 => p.ae[idx] = coef,
2 => p.as_[idx] = coef,
3 => p.an[idx] = coef,
4 => p.ab[idx] = coef,
_ => p.at[idx] = coef,
}
}
}
}
}
p
}
#[must_use]
pub fn unknowns(&self) -> usize {
self.centre.len()
}
}
/// A uniform grid's operator and right-hand side in the same form (the
/// reference / cost comparator), optionally cut by `body`; Dirichlet
/// outside. Returns the problem and the per-cell fluid fraction.
#[must_use]
pub fn uniform_problem(
g: Grid,
body: Option<&Sdf>,
source: &(dyn Fn(f64, f64, f64) -> f64 + Sync),
dirichlet: &(dyn Fn(f64, f64, f64) -> f64 + Sync),
) -> (Problem, Vec<f64>) {
let cut = body.map(|b| CutGeometry::build(&body_at(b, [0.0; 3]), g, 0.0));
let mut p = Composite::coarse_operator(g, cut.as_ref());
let h = g.dx;
let dims = [g.nx, g.ny, g.nz];
let mut frac = vec![0.0; g.cells()];
for k in 0..g.nz {
for j in 0..g.ny {
for i in 0..g.nx {
let idx = g.cell(k, j, i);
if !p.active[idx] {
continue;
}
let fr = fraction(cut.as_ref(), g, [i, j, k]);
frac[idx] = fr;
let x = [
(i as f64 + 0.5) * h,
(j as f64 + 0.5) * h,
(k as f64 + 0.5) * h,
];
p.rhs[idx] = fr * h * h * h * source(x[0], x[1], x[2]);
for &(d, s) in &DIRS {
let c = [i, j, k][d] as isize + s;
if c < 0 || c >= dims[d] as isize {
let mut fx = x;
fx[d] += s as f64 * 0.5 * h;
p.rhs[idx] += 2.0 * h * dirichlet(fx[0], fx[1], fx[2]);
}
}
}
}
}
(p, frac)
}
crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/composite/mod.rs
+103
View File
@@ -0,0 +1,103 @@
//! R7 phase 1 (omni-cortex roadmap R7, A3-ii): the composite pressure
//! Poisson problem on a uniform coarse grid with ONE nested ratio-2 box
//! patch, cell-centred, in the integrated (finite-volume) form of
//! [`super::poisson::Problem`]: `Σ_faces c_f (p_i − p_nb) = rhs_i`.
//!
//! A host prototype, not wired into the solver (nothing in the step calls
//! it): it exists to measure what the coarse–fine interface costs in order
//! and in work before the patch is carried into the predictor and onto the
//! device. Three interface fluxes are built so the choice is a measurement:
//!
//! - [`Interface::Direct`]: each fine sub-face couples its fine cell to the
//! coarse cell by a two-point flux over the centre distance `1.5 h_f`
//! (symmetric, conservative, not consistent tangentially);
//! - [`Interface::Octree`]: 2604.18886 eq. 13 — the coarse face's flux
//! `(p_C − mean of the covered coarse cell's 8 children) / h_c`, shared
//! equally by the 4 fine sub-faces (conservative, non-symmetric);
//! - [`Interface::Quadratic`]: the fine ghost by quadratic interpolation
//! (tangential quadratic with the cross term on the coarse layer, then
//! quadratic in the normal direction through two fine cells), the coarse
//! face's flux = the sum of its four fine fluxes (refluxing; conservative,
//! non-symmetric) — the AMReX / Martin–Cartwright construction.
//!
//! Layout: coarse cells `(k, j, i)` of [`Grid`]; the patch covers the
//! coarse box `lo ≤ (i, j, k) < hi` and is refined by 2 in every direction.
//! Unknowns: the uncovered active coarse cells first, then the active fine
//! cells. A body (φ > 0 fluid) may cut the fine level; it must not reach
//! the interface or the coarse uncovered cells.
mod assemble;
mod solve;
pub use assemble::{Composite, CompositeSpec, Interface, Sdf, uniform_problem};
pub use solve::{CompositeSolve, SolveStats, solve_bicgstab};
/// Compressed sparse rows.
#[derive(Debug, Clone, Default)]
pub struct Csr {
pub start: Vec<usize>,
pub col: Vec<usize>,
pub val: Vec<f64>,
}
impl Csr {
/// Rows from per-row `(column, value)` lists; duplicates are summed in
/// the order they appear, zero entries dropped.
#[must_use]
pub fn from_rows(rows: Vec<Vec<(usize, f64)>>) -> Self {
let mut start = Vec::with_capacity(rows.len() + 1);
let mut col = Vec::new();
let mut val = Vec::new();
start.push(0);
for mut row in rows {
row.sort_by_key(|e| e.0);
let mut last: Option<usize> = None;
for (c, v) in row {
if last == Some(c) {
*val.last_mut().expect("entry") += v;
} else {
col.push(c);
val.push(v);
last = Some(c);
}
}
start.push(col.len());
}
Self { start, col, val }
}
#[must_use]
pub fn rows(&self) -> usize {
self.start.len() - 1
}
pub fn apply(&self, x: &[f64], y: &mut [f64]) {
use rayon::prelude::*;
y.par_iter_mut().enumerate().for_each(|(r, yr)| {
let mut s = 0.0;
for e in self.start[r]..self.start[r + 1] {
s += self.val[e] * x[self.col[e]];
}
*yr = s;
});
}
/// The largest `|a_ij − a_ji|` relative to the largest |a_ij|.
#[must_use]
pub fn asymmetry(&self) -> f64 {
let mut map = std::collections::HashMap::with_capacity(self.val.len());
let mut amax: f64 = 0.0;
for r in 0..self.rows() {
for e in self.start[r]..self.start[r + 1] {
map.insert((r, self.col[e]), self.val[e]);
amax = amax.max(self.val[e].abs());
}
}
let mut d: f64 = 0.0;
for (&(r, c), &v) in &map {
let t = map.get(&(c, r)).copied().unwrap_or(0.0);
d = d.max((v - t).abs());
}
d / amax.max(f64::MIN_POSITIVE)
}
}
crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/composite/solve.rs
+195
View File
@@ -0,0 +1,195 @@
//! The composite solve: BiCGStab (the Quadratic and Octree operators are
//! not symmetric) right-preconditioned by one FAC cycle (McCormick's fast
//! adaptive composite grid method in correction form):
//!
//! 1. `ν` forward Gauss–Seidel sweeps of the composite operator from zero;
//! 2. the composite residual, restricted to the whole coarse grid — an
//! uncovered coarse cell keeps its own, a covered coarse cell receives
//! the SUM of its children's (integrated form);
//! 3. one V-cycle of the uniform coarse operator (embedded3's aggregation
//! [`Hierarchy`], unchanged) on that residual;
//! 4. the correction added to the coarse unknowns and injected (piecewise
//! constant) into the fine ones;
//! 5. `ν` backward Gauss–Seidel sweeps.
//!
//! Correction form over the COMPOSITE residual is the linear counterpart of
//! 2604.18886's FAS right-hand side `b = β R r + A_c u*` (Algorithm 4): the
//! interface flux enters the coarse problem exactly once, through the
//! composite residual, so nothing is double-counted at the T-junctions.
use super::Composite;
use crate::solvers::incompressible::MultigridParameters;
use crate::solvers::incompressible::embedded3::poisson::Hierarchy;
/// The prepared preconditioner.
pub struct CompositeSolve {
hier: Hierarchy<f64>,
diag: Vec<f64>,
sweeps: usize,
rc: Vec<f64>,
ec: Vec<f64>,
res: Vec<f64>,
}
/// Outcome of [`solve_bicgstab`].
#[derive(Debug, Clone, Copy)]
pub struct SolveStats {
pub iterations: usize,
/// `‖b − A x‖₂ / ‖b‖₂` at exit (recomputed).
pub rel_residual: f64,
pub converged: bool,
pub setup_s: f64,
pub solve_s: f64,
}
impl CompositeSolve {
#[must_use]
pub fn new(c: &Composite, sweeps: usize) -> Self {
let params = MultigridParameters::default();
let hier = Hierarchy::<f64>::build(&c.coarse_problem, &params);
let n = c.unknowns();
let mut diag = vec![0.0; n];
for (r, d) in diag.iter_mut().enumerate() {
for e in c.a.start[r]..c.a.start[r + 1] {
if c.a.col[e] == r {
*d = c.a.val[e];
}
}
assert!(*d > 0.0, "row {r} has no positive diagonal");
}
let nc = c.coarse.cells();
Self {
hier,
diag,
sweeps: sweeps.max(1),
rc: vec![0.0; nc],
ec: vec![0.0; nc],
res: vec![0.0; n],
}
}
fn gs_row(&self, c: &Composite, b: &[f64], x: &mut [f64], r: usize) {
let mut s = b[r];
for e in c.a.start[r]..c.a.start[r + 1] {
let col = c.a.col[e];
if col != r {
s -= c.a.val[e] * x[col];
}
}
x[r] = s / self.diag[r];
}
/// `z = M⁻¹ r` (one FAC cycle from zero).
pub fn precondition(&mut self, c: &Composite, r: &[f64], z: &mut [f64]) {
let n = c.unknowns();
z.iter_mut().for_each(|v| *v = 0.0);
for _ in 0..self.sweeps {
for row in 0..n {
self.gs_row(c, r, z, row);
}
}
c.a.apply(z, &mut self.res);
self.rc.iter_mut().for_each(|v| *v = 0.0);
for u in 0..n {
self.rc[c.parent[u]] += r[u] - self.res[u];
}
for (idx, v) in self.rc.iter_mut().enumerate() {
if !c.coarse_problem.active[idx] {
*v = 0.0;
}
}
self.hier.apply_preconditioner(&self.rc, &mut self.ec);
for u in 0..n {
let p = c.parent[u];
if c.coarse_problem.active[p] {
z[u] += self.ec[p];
}
}
for _ in 0..self.sweeps {
for row in (0..n).rev() {
self.gs_row(c, r, z, row);
}
}
}
}
fn dot(a: &[f64], b: &[f64]) -> f64 {
a.iter().zip(b).map(|(x, y)| x * y).sum()
}
/// Solve `A x = rhs` to `‖r‖₂ ≤ tol ‖rhs‖₂` from the given `x`.
pub fn solve_bicgstab(
c: &Composite,
x: &mut [f64],
tol: f64,
max_it: usize,
sweeps: usize,
) -> SolveStats {
let t0 = std::time::Instant::now();
let mut pre = CompositeSolve::new(c, sweeps);
let setup_s = t0.elapsed().as_secs_f64();
let t1 = std::time::Instant::now();
let n = c.unknowns();
let b = &c.rhs;
let bn = dot(b, b).sqrt().max(f64::MIN_POSITIVE);
let mut r = vec![0.0; n];
c.a.apply(x, &mut r);
for i in 0..n {
r[i] = b[i] - r[i];
}
let rhat = r.clone();
let (mut rho, mut alpha, mut omega) = (1.0, 1.0, 1.0);
let mut v = vec![0.0; n];
let mut p = vec![0.0; n];
let mut ph = vec![0.0; n];
let mut sh = vec![0.0; n];
let mut s = vec![0.0; n];
let mut t = vec![0.0; n];
let mut it = 0;
let mut rel = dot(&r, &r).sqrt() / bn;
while rel > tol && it < max_it {
it += 1;
let rho_n = dot(&rhat, &r);
let beta = (rho_n / rho) * (alpha / omega);
for i in 0..n {
p[i] = r[i] + beta * (p[i] - omega * v[i]);
}
pre.precondition(c, &p, &mut ph);
c.a.apply(&ph, &mut v);
alpha = rho_n / dot(&rhat, &v);
for i in 0..n {
s[i] = r[i] - alpha * v[i];
}
if dot(&s, &s).sqrt() / bn <= tol {
for i in 0..n {
x[i] += alpha * ph[i];
}
r.copy_from_slice(&s);
break;
}
pre.precondition(c, &s, &mut sh);
c.a.apply(&sh, &mut t);
omega = dot(&t, &s) / dot(&t, &t);
for i in 0..n {
x[i] += alpha * ph[i] + omega * sh[i];
r[i] = s[i] - omega * t[i];
}
rho = rho_n;
rel = dot(&r, &r).sqrt() / bn;
}
// The true residual.
c.a.apply(x, &mut r);
let mut rr = 0.0;
for i in 0..n {
let d = b[i] - r[i];
rr += d * d;
}
let rel = rr.sqrt() / bn;
SolveStats {
iterations: it,
rel_residual: rel,
converged: rel <= 10.0 * tol,
setup_s,
solve_s: t1.elapsed().as_secs_f64(),
}
}
crates/specialized/rtx-cfd/src/solvers/incompressible/embedded3/mod.rs
+1
View File
@@ -8,6 +8,7 @@
pub mod body; pub mod body;
pub mod closure; pub mod closure;
pub mod composite;
pub mod cut; pub mod cut;
pub mod cutwall; pub mod cutwall;
pub mod exchange; pub mod exchange;
crates/specialized/rtx-cfd/tests/embedded3_composite_poisson.rs
+640
View File
@@ -0,0 +1,640 @@
//! R7 phase 1: the composite Poisson problem with one nested ratio-2 patch
//! (`embedded3::composite`, a host prototype nothing else calls).
//!
//! - P1 (`composite_mms_ladder`, ignored): manufactured solution on the unit
//! cube, patch = the middle half, n = 16/32/64 coarse; errors split into
//! the interface cells (owners of a coarse–fine face), the rest of the
//! patch, and the rest of the coarse grid, for the three interface fluxes
//! and the uniform coarse / fine grids;
//! - P2 (`composite_cut_sphere`, ignored): a Neumann sphere inside the patch
//! cut by embedded3's `CutGeometry` on the fine level, against the
//! uniformly fine grid with the same cut;
//! - P3 (`composite_cost`, ignored): unknowns and wall time against the
//! uniformly fine grid solved by embedded3's production PCG.
//!
//! Output CSVs go to `$R7_OUT` when set. The default (non-ignored) test is a
//! seconds-scale smoke of the assembly and the solve.
use rtx_cfd::solvers::incompressible::MultigridParameters;
use rtx_cfd::solvers::incompressible::embedded3::Grid;
use rtx_cfd::solvers::incompressible::embedded3::composite::{
Composite, CompositeSpec, Interface, Sdf, solve_bicgstab, uniform_problem,
};
use rtx_cfd::solvers::incompressible::embedded3::poisson::solve_pcg;
use std::f64::consts::PI;
use std::io::Write;
use std::sync::Arc;
fn mms_u(x: f64, y: f64, z: f64) -> f64 {
(1.3 * PI * x + 0.2).cos() * (1.1 * PI * y + 0.4).cos() * (0.9 * PI * z + 0.6).cos()
}
fn mms_f(x: f64, y: f64, z: f64) -> f64 {
PI * PI * (1.69 + 1.21 + 0.81) * mms_u(x, y, z)
}
/// A localized feature inside the patch on top of the smooth field: the
/// case local refinement is for (a Gaussian of width 0.06 at the centre).
const BUMP_S: f64 = 0.06;
fn bump_u(x: f64, y: f64, z: f64) -> f64 {
let r2 = (x - 0.5).powi(2) + (y - 0.5).powi(2) + (z - 0.5).powi(2);
mms_u(x, y, z) + (-r2 / (BUMP_S * BUMP_S)).exp()
}
fn bump_f(x: f64, y: f64, z: f64) -> f64 {
let r2 = (x - 0.5).powi(2) + (y - 0.5).powi(2) + (z - 0.5).powi(2);
let s2 = BUMP_S * BUMP_S;
mms_f(x, y, z) - (4.0 * r2 / (s2 * s2) - 6.0 / s2) * (-r2 / s2).exp()
}
const SPH_C: [f64; 3] = [0.52, 0.49, 0.51];
const SPH_R: f64 = 0.12;
const SPH_A: f64 = 2.0 * PI;
fn sph_r(x: f64, y: f64, z: f64) -> f64 {
((x - SPH_C[0]).powi(2) + (y - SPH_C[1]).powi(2) + (z - SPH_C[2]).powi(2)).sqrt()
}
/// `cos(a (r − R))`: zero normal derivative on the sphere.
fn sph_u(x: f64, y: f64, z: f64) -> f64 {
(SPH_A * (sph_r(x, y, z) - SPH_R)).cos()
}
fn sph_f(x: f64, y: f64, z: f64) -> f64 {
let r = sph_r(x, y, z);
let q = SPH_A * (r - SPH_R);
SPH_A * SPH_A * q.cos() + 2.0 * SPH_A * q.sin() / r
}
fn sphere() -> Sdf {
Arc::new(|x, y, z| sph_r(x, y, z) - SPH_R)
}
/// Volume-weighted RMS and max of the error over a subset.
#[derive(Default, Clone, Copy)]
struct Err {
s2: f64,
vol: f64,
max: f64,
count: usize,
}
impl Err {
fn add(&mut self, e: f64, v: f64) {
self.s2 += e * e * v;
self.vol += v;
self.max = self.max.max(e.abs());
self.count += 1;
}
fn l2(&self) -> f64 {
if self.vol > 0.0 {
(self.s2 / self.vol).sqrt()
} else {
f64::NAN
}
}
}
fn out_file(name: &str) -> Option<std::fs::File> {
let dir = std::env::var("R7_OUT").ok()?;
std::fs::create_dir_all(&dir).ok()?;
std::fs::File::create(format!("{dir}/{name}")).ok()
}
struct CompositeRun {
unknowns: usize,
fine_unknowns: usize,
iterations: usize,
rel: f64,
setup_s: f64,
solve_s: f64,
asym: f64,
/// interface, patch interior (fine, not interface), coarse (not
/// interface), cut cells, all.
err: [Err; 5],
}
fn run_composite(
n: usize,
lo: usize,
hi: usize,
iface: Interface,
body: Option<Sdf>,
exact: fn(f64, f64, f64) -> f64,
source: fn(f64, f64, f64) -> f64,
measure_asym: bool,
) -> CompositeRun {
let g = Grid::cubic(n, n, n, 1.0 / n as f64);
let spec = CompositeSpec {
coarse: g,
lo: [lo; 3],
hi: [hi; 3],
interface: iface,
body,
source: &source,
dirichlet: &exact,
};
let t = std::time::Instant::now();
let c = Composite::build(&spec);
let build_s = t.elapsed().as_secs_f64();
let mut x = vec![0.0; c.unknowns()];
let st = solve_bicgstab(&c, &mut x, 1e-11, 400, 2);
assert!(st.converged, "composite solve did not converge: {st:?}");
let mut err = [Err::default(); 5];
for u in 0..c.unknowns() {
let p = c.centre[u];
let e = x[u] - exact(p[0], p[1], p[2]);
let v = c.volume[u];
let fine = u >= c.n_coarse;
let class = if c.at_interface[u] {
0
} else if fine {
1
} else {
2
};
err[class].add(e, v);
if c.cut[u] {
err[3].add(e, v);
}
err[4].add(e, v);
}
CompositeRun {
unknowns: c.unknowns(),
fine_unknowns: c.unknowns() - c.n_coarse,
iterations: st.iterations,
rel: st.rel_residual,
setup_s: build_s + st.setup_s,
solve_s: st.solve_s,
asym: if measure_asym {
c.a.asymmetry()
} else {
f64::NAN
},
err,
}
}
struct UniformRun {
cells: usize,
iterations: usize,
setup_s: f64,
solve_s: f64,
/// inside the patch region [lo, hi)·h_c, outside it, cut cells, all.
err: [Err; 4],
}
fn run_uniform(
n: usize,
region: (f64, f64),
body: Option<&Sdf>,
exact: fn(f64, f64, f64) -> f64,
source: fn(f64, f64, f64) -> f64,
) -> UniformRun {
let g = Grid::cubic(n, n, n, 1.0 / n as f64);
let t = std::time::Instant::now();
let (prob, frac) = uniform_problem(g, body, &source, &exact);
let build_s = t.elapsed().as_secs_f64();
let mut p = vec![0.0; g.cells()];
let l1: f64 = prob.rhs.iter().map(|v| v.abs()).sum();
let params = MultigridParameters {
max_iterations: 2000,
..MultigridParameters::default()
};
let sol = solve_pcg(&prob, &mut p, &params, 1e-11 * l1, None);
assert!(sol.converged, "uniform solve did not converge");
let h = g.dx;
let mut err = [Err::default(); 4];
for k in 0..n {
for j in 0..n {
for i in 0..n {
let idx = g.cell(k, j, i);
if !prob.active[idx] {
continue;
}
let x = [
(i as f64 + 0.5) * h,
(j as f64 + 0.5) * h,
(k as f64 + 0.5) * h,
];
let e = p[idx] - exact(x[0], x[1], x[2]);
let v = frac[idx] * h * h * h;
let inside = x.iter().all(|&c| c > region.0 && c < region.1);
err[usize::from(!inside)].add(e, v);
if frac[idx] < 1.0 {
err[2].add(e, v);
}
err[3].add(e, v);
}
}
}
UniformRun {
cells: prob.active.iter().filter(|&&a| a).count(),
iterations: sol.iterations,
setup_s: build_s + sol.setup_ns as f64 * 1e-9,
solve_s: sol.iterate_ns as f64 * 1e-9,
err,
}
}
fn order(a: f64, b: f64) -> f64 {
(a / b).log2()
}
#[test]
fn composite_smoke() {
for iface in [Interface::Direct, Interface::Octree, Interface::Quadratic] {
let r = run_composite(12, 3, 9, iface, None, mms_u, mms_f, true);
eprintln!(
"{iface:?}: {} unknowns, {} it, rel {:.2e}, asym {:.2e}, L2 iface {:.3e} all {:.3e}",
r.unknowns,
r.iterations,
r.rel,
r.asym,
r.err[0].l2(),
r.err[4].l2()
);
assert!(r.err[4].l2() < 5e-3);
if iface == Interface::Direct {
assert!(r.asym < 1e-14);
}
}
}
#[test]
#[ignore = "P1 ladder (minutes)"]
fn composite_mms_ladder() {
ladder("p1_mms.csv", mms_u, mms_f);
}
#[test]
#[ignore = "P1b ladder with a localized bump (minutes)"]
fn composite_bump_ladder() {
ladder("p1b_bump.csv", bump_u, bump_f);
}
fn ladder(name: &str, exact: fn(f64, f64, f64) -> f64, source: fn(f64, f64, f64) -> f64) {
let mut csv = out_file(name);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"scheme,n,unknowns,iters,rel,l2_iface,linf_iface,l2_patch,linf_patch,l2_coarse,linf_coarse,l2_all,linf_all,setup_s,solve_s"
)
.ok();
}
let ns = [16usize, 32, 64];
let mut table: Vec<(String, Vec<[f64; 8]>)> = Vec::new();
for iface in [Interface::Direct, Interface::Octree, Interface::Quadratic] {
let mut rows = Vec::new();
for &n in &ns {
let r = run_composite(n, n / 4, 3 * n / 4, iface, None, exact, source, false);
let e = r.err;
eprintln!(
"{iface:?} n {n}: {} unk, {} it, rel {:.1e}; iface L2 {:.3e} Linf {:.3e} | patch L2 {:.3e} Linf {:.3e} | coarse L2 {:.3e} Linf {:.3e} | all L2 {:.3e} | {:.2}+{:.2} s",
r.unknowns,
r.iterations,
r.rel,
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[2].l2(),
e[2].max,
e[4].l2(),
r.setup_s,
r.solve_s
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{iface:?},{n},{},{},{:.3e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.3},{:.3}",
r.unknowns,
r.iterations,
r.rel,
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[2].l2(),
e[2].max,
e[4].l2(),
e[4].max,
r.setup_s,
r.solve_s
)
.ok();
}
rows.push([
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[2].l2(),
e[2].max,
e[4].l2(),
e[4].max,
]);
}
table.push((format!("{iface:?}"), rows));
}
for (label, n_of) in [("uniform-coarse", 1usize), ("uniform-fine", 2)] {
for &n in &ns {
let r = run_uniform(n_of * n, (0.25, 0.75), None, exact, source);
let e = r.err;
eprintln!(
"{label} n {}: {} cells, {} it; patch-region L2 {:.3e} Linf {:.3e} | outside L2 {:.3e} Linf {:.3e} | all L2 {:.3e} | {:.2}+{:.2} s",
n_of * n,
r.cells,
r.iterations,
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[3].l2(),
r.setup_s,
r.solve_s
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{label},{},{},{},0,nan,nan,{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.3},{:.3}",
n_of * n,
r.cells,
r.iterations,
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[3].l2(),
e[3].max,
r.setup_s,
r.solve_s
)
.ok();
}
}
}
eprintln!("orders (16→32, 32→64): iface L2 / Linf | patch L2 | coarse L2 | all L2 / Linf");
for (label, rows) in &table {
let o = |c: usize| (order(rows[0][c], rows[1][c]), order(rows[1][c], rows[2][c]));
eprintln!(
"{label}: iface {:.2},{:.2} / {:.2},{:.2} | patch {:.2},{:.2} | coarse {:.2},{:.2} | all {:.2},{:.2} / {:.2},{:.2}",
o(0).0,
o(0).1,
o(1).0,
o(1).1,
o(2).0,
o(2).1,
o(4).0,
o(4).1,
o(6).0,
o(6).1,
o(7).0,
o(7).1
);
}
}
#[test]
#[ignore = "P2 cut sphere in the patch (minutes)"]
fn composite_cut_sphere() {
let mut csv = out_file("p2_sphere.csv");
if let Some(f) = csv.as_mut() {
writeln!(
f,
"scheme,n,unknowns,iters,l2_iface,linf_iface,l2_patch,linf_patch,l2_coarse,l2_cut,linf_cut,l2_all,linf_all"
)
.ok();
}
let body = sphere();
for &n in &[16usize, 32, 64] {
for iface in [Interface::Direct, Interface::Octree, Interface::Quadratic] {
let r = run_composite(
n,
n / 4,
3 * n / 4,
iface,
Some(body.clone()),
sph_u,
sph_f,
false,
);
let e = r.err;
eprintln!(
"{iface:?} n {n}: {} unk ({} fine), {} it; iface L2 {:.3e} | patch L2 {:.3e} Linf {:.3e} | coarse L2 {:.3e} | cut L2 {:.3e} Linf {:.3e} | all L2 {:.3e} Linf {:.3e}",
r.unknowns,
r.fine_unknowns,
r.iterations,
e[0].l2(),
e[1].l2(),
e[1].max,
e[2].l2(),
e[3].l2(),
e[3].max,
e[4].l2(),
e[4].max
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{iface:?},{n},{},{},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e}",
r.unknowns,
r.iterations,
e[0].l2(),
e[0].max,
e[1].l2(),
e[1].max,
e[2].l2(),
e[3].l2(),
e[3].max,
e[4].l2(),
e[4].max
)
.ok();
}
}
for (label, m) in [("uniform-coarse", n), ("uniform-fine", 2 * n)] {
let r = run_uniform(m, (0.25, 0.75), Some(&body), sph_u, sph_f);
let e = r.err;
eprintln!(
"{label} n {m}: {} cells, {} it; patch-region L2 {:.3e} Linf {:.3e} | outside L2 {:.3e} | cut L2 {:.3e} Linf {:.3e} | all L2 {:.3e} Linf {:.3e}",
r.cells,
r.iterations,
e[0].l2(),
e[0].max,
e[1].l2(),
e[2].l2(),
e[2].max,
e[3].l2(),
e[3].max
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{label},{m},{},{},nan,nan,{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e},{:.6e}",
r.cells,
r.iterations,
e[0].l2(),
e[0].max,
e[1].l2(),
e[2].l2(),
e[2].max,
e[3].l2(),
e[3].max
)
.ok();
}
}
}
}
#[test]
#[ignore = "P3 cost against the uniformly fine grid (minutes)"]
fn composite_cost() {
let mut csv = out_file("p3_cost.csv");
if let Some(f) = csv.as_mut() {
writeln!(
f,
"field,case,n,patch,unknowns,iters,setup_s,solve_s,l2_patch_region,linf_patch_region,l2_all"
)
.ok();
}
let n = 64usize;
let h = 1.0 / n as f64;
type Pair = (
&'static str,
fn(f64, f64, f64) -> f64,
fn(f64, f64, f64) -> f64,
);
let fields: [Pair; 2] = [("smooth", mms_u, mms_f), ("bump", bump_u, bump_f)];
for (field, exact, source) in fields {
for (label, lo, hi) in [("half", 16usize, 48usize), ("quarter", 24, 40)] {
let r = run_composite(n, lo, hi, Interface::Quadratic, None, exact, source, false);
// The patch region's error: interface fine cells + patch interior.
let mut e = Err::default();
let c = {
let g = Grid::cubic(n, n, n, h);
let spec = CompositeSpec {
coarse: g,
lo: [lo; 3],
hi: [hi; 3],
interface: Interface::Quadratic,
body: None,
source: &source,
dirichlet: &exact,
};
Composite::build(&spec)
};
let mut x = vec![0.0; c.unknowns()];
let _ = solve_bicgstab(&c, &mut x, 1e-11, 400, 2);
for u in c.n_coarse..c.unknowns() {
let p = c.centre[u];
e.add(x[u] - exact(p[0], p[1], p[2]), c.volume[u]);
}
eprintln!(
"{field} composite {label} (n {n}, patch {lo}..{hi}): {} unknowns, {} it, setup {:.2} s, solve {:.2} s, patch L2 {:.3e} Linf {:.3e}, all L2 {:.3e}",
r.unknowns,
r.iterations,
r.setup_s,
r.solve_s,
e.l2(),
e.max,
r.err[4].l2()
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{field},composite-{label},{n},{lo}..{hi},{},{},{:.3},{:.3},{:.6e},{:.6e},{:.6e}",
r.unknowns,
r.iterations,
r.setup_s,
r.solve_s,
e.l2(),
e.max,
r.err[4].l2()
)
.ok();
}
for (ulabel, m) in [("uniform-fine", 2 * n), ("uniform-coarse", n)] {
let r = run_uniform(m, (lo as f64 * h, hi as f64 * h), None, exact, source);
eprintln!(
"{field} {ulabel} n {m} (region {lo}..{hi}): {} cells, {} it, setup {:.2} s, solve {:.2} s, region L2 {:.3e} Linf {:.3e}, all L2 {:.3e}",
r.cells,
r.iterations,
r.setup_s,
r.solve_s,
r.err[0].l2(),
r.err[0].max,
r.err[3].l2()
);
if let Some(f) = csv.as_mut() {
writeln!(
f,
"{field},{ulabel},{m},{lo}..{hi},{},{},{:.3},{:.3},{:.6e},{:.6e},{:.6e}",
r.cells,
r.iterations,
r.setup_s,
r.solve_s,
r.err[0].l2(),
r.err[0].max,
r.err[3].l2()
)
.ok();
}
}
}
}
}
fn quad_u(x: f64, y: f64, z: f64) -> f64 {
x * x + 2.0 * y * y - 1.5 * z * z + 0.7 * x * y - 0.4 * y * z + 0.9 * x * z + 0.3 * x
}
fn quad_f(_x: f64, _y: f64, _z: f64) -> f64 {
-(2.0 + 4.0 - 3.0)
}
/// Local consistency: the exact quadratic's residual on the rows away from
/// the outer boundary, per interface flux (the Quadratic ghost is exact for
/// quadratics, so its interface rows must be at round-off).
#[test]
fn composite_quadratic_consistency() {
let n = 12;
let g = Grid::cubic(n, n, n, 1.0 / n as f64);
for iface in [Interface::Direct, Interface::Octree, Interface::Quadratic] {
let spec = CompositeSpec {
coarse: g,
lo: [3; 3],
hi: [9; 3],
interface: iface,
body: None,
source: &quad_f,
dirichlet: &quad_u,
};
let c = Composite::build(&spec);
let u: Vec<f64> = c.centre.iter().map(|p| quad_u(p[0], p[1], p[2])).collect();
let mut au = vec![0.0; u.len()];
c.a.apply(&u, &mut au);
let h = g.dx;
let (mut m_if, mut m_in) = (0.0f64, 0.0f64);
for r in 0..u.len() {
let p = c.centre[r];
if p.iter().any(|&x| x < h || x > 1.0 - h) {
continue;
}
// Relative to the row's volume source |f| V.
let res = (c.rhs[r] - au[r]).abs() / (3.0 * c.volume[r]);
if c.at_interface[r] {
m_if = m_if.max(res);
} else {
m_in = m_in.max(res);
}
}
eprintln!("{iface:?}: max |truncation| / |f V|: interface {m_if:.3e}, interior {m_in:.3e}");
assert!(m_in < 1e-10);
if iface == Interface::Quadratic {
assert!(m_if < 1e-10, "quadratic ghost not exact on a quadratic");
}
}
}