rustytorch/crates/specialized/rtx-cfd/tests/embedded3_composite_poisson.rs

//! 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");
        }
    }
}