PERF-2: red-black symmetric Gauss–Seidel smoother behind a knob (MgSmoother::RedBlack; default lexicographic = the recorded regime, bit-identical) — red/black cell lists per level, the symmetric pair red,black,black,red, the operator cache keyed on the smoother; EmbeddedParameters::poisson_smoother, harness knobs RTX_FSI2O_MG_RB (overset) and RTX_FSI2_MG_RB (embedded, the noise probe); pin: solves the masked problem to the same stop, agrees with lexicographic to 2e-12, cached = uncached bit for bit

Co-Authored-By: Claude Fable 5.1 <[email protected]>
Claude-Session: https://claude.ai/code/session_01YJPeT6WA2e7YvAnS875AHL

crates/specialized/rtx-cfd/src/solvers/incompressible/poisson.rs

@@ -268,11 +268,27 @@ pub enum MgPrecision {
     F32,
 }
 
+/// The V-cycle's smoother ordering (PERF-2, `docs/perf2_campaign.md`).
+/// `Lexicographic` is the recorded regime (row-major symmetric
+/// Gauss–Seidel, a dependency chain through the division per cell);
+/// `RedBlack` updates the two colours of the five-point stencil in turn —
+/// each colour a map of independent cells (threads, vectors, the GPU) —
+/// and is a different preconditioner, gated by the noise probe and the
+/// anchor's band, never bit-identical.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
+pub enum MgSmoother {
+    #[default]
+    Lexicographic,
+    RedBlack,
+}
+
 /// Multigrid preconditioner parameters.
 #[derive(Debug, Clone)]
 pub struct MultigridParameters {
     /// Precision of the V-cycle (see [`MgPrecision`]).
     pub precision: MgPrecision,
+    /// Smoother ordering (see [`MgSmoother`]).
+    pub smoother: MgSmoother,
     /// Symmetric Gauss–Seidel sweeps before AND after the coarse correction
     /// (default 2; a value of 0 is treated as 1). One count for both on
     /// purpose: unequal pre/post counts make the V-cycle non-symmetric and
@@ -290,6 +306,7 @@ impl Default for MultigridParameters {
     fn default() -> Self {
         Self {
             precision: MgPrecision::F64,
+            smoother: MgSmoother::Lexicographic,
             smoother_sweeps: 2,
             coarsest_cells: 32,
             max_iterations: 500,
@@ -431,6 +448,10 @@ struct Level<T: MgScalar> {
     ap: Vec<T>,
     /// Row-major indices of the active cells.
     cells: Vec<usize>,
+    /// The active cells with `i + j` even / odd, each row-major (the
+    /// red-black smoother's two independent maps on the five-point stencil).
+    red: Vec<usize>,
+    black: Vec<usize>,
     /// Fine index → coarse index (empty on the coarsest level).
     coarse_of: Vec<usize>,
 }
@@ -491,6 +512,17 @@ impl<T: MgScalar> Level<T> {
             }
         }
         let cells: Vec<usize> = (0..n).filter(|&idx| active[idx]).collect();
+        let parity = |idx: usize| (idx % nx + idx / nx) % 2;
+        let red: Vec<usize> = cells
+            .iter()
+            .copied()
+            .filter(|&idx| parity(idx) == 0)
+            .collect();
+        let black: Vec<usize> = cells
+            .iter()
+            .copied()
+            .filter(|&idx| parity(idx) == 1)
+            .collect();
         let cast = |v: &[f64]| v.iter().map(|&x| T::from_f64(x)).collect::<Vec<T>>();
         Self {
             ae: cast(&problem.ae),
@@ -501,6 +533,8 @@ impl<T: MgScalar> Level<T> {
             problem,
             active,
             cells,
+            red,
+            black,
             coarse_of: Vec::new(),
         }
     }
@@ -559,6 +593,33 @@ impl<T: MgScalar> Level<T> {
         }
     }
 
+    /// One symmetric red-black Gauss–Seidel sweep: red, black, black, red —
+    /// within a colour every cell reads only the other colour, so each
+    /// half-sweep is a map (symmetric as a preconditioner, like the
+    /// lexicographic pair).
+    fn symmetric_gs_rb(&self, b: &[T], x: &mut [T]) {
+        for &idx in &self.red {
+            x[idx] = (b[idx] + self.neighbour_sum(x, idx)) / self.ap[idx];
+        }
+        for &idx in &self.black {
+            x[idx] = (b[idx] + self.neighbour_sum(x, idx)) / self.ap[idx];
+        }
+        for &idx in &self.black {
+            x[idx] = (b[idx] + self.neighbour_sum(x, idx)) / self.ap[idx];
+        }
+        for &idx in &self.red {
+            x[idx] = (b[idx] + self.neighbour_sum(x, idx)) / self.ap[idx];
+        }
+    }
+
+    /// One symmetric sweep in the chosen ordering.
+    fn smooth(&self, b: &[T], x: &mut [T], smoother: MgSmoother) {
+        match smoother {
+            MgSmoother::Lexicographic => self.symmetric_gs(b, x),
+            MgSmoother::RedBlack => self.symmetric_gs_rb(b, x),
+        }
+    }
+
     /// Galerkin coarsening: coarse face coefficient = sum of the fine
     /// coefficients across that coarse face, coarse `extra_diag` = sum of
     /// the children's. Returns the coarse problem and the parent map.
@@ -601,6 +662,7 @@ pub(crate) struct Hierarchy<T: MgScalar = f64> {
     levels: Vec<Level<T>>,
     work: Vec<Work<T>>,
     sweeps: usize,
+    smoother: MgSmoother,
 }
 
 impl<T: MgScalar> Hierarchy<T> {
@@ -630,6 +692,7 @@ impl<T: MgScalar> Hierarchy<T> {
             levels,
             work,
             sweeps: params.smoother_sweeps.max(1),
+            smoother: params.smoother,
         }
     }
 
@@ -672,7 +735,7 @@ impl<T: MgScalar> Hierarchy<T> {
                 wf.x[idx] = T::ZERO;
             }
             for _ in 0..self.sweeps {
-                fine.symmetric_gs(&wf.b, &mut wf.x);
+                fine.smooth(&wf.b, &mut wf.x, self.smoother);
             }
             fine.residual(&wf.b, &wf.x, &mut wf.r);
             for &idx in &coarse.cells {
@@ -695,7 +758,7 @@ impl<T: MgScalar> Hierarchy<T> {
                 wb.x[idx] = T::ZERO;
             }
             for _ in 0..COARSEST_SWEEPS {
-                bottom.symmetric_gs(&wb.b, &mut wb.x);
+                bottom.smooth(&wb.b, &mut wb.x, self.smoother);
             }
         }
         // Up: prolongate, smooth.
@@ -707,7 +770,7 @@ impl<T: MgScalar> Hierarchy<T> {
                 wf.x[idx] += T::from_f64(COARSE_CORRECTION) * wc.x[fine.coarse_of[idx]];
             }
             for _ in 0..self.sweeps {
-                fine.symmetric_gs(&wf.b, &mut wf.x);
+                fine.smooth(&wf.b, &mut wf.x, self.smoother);
             }
         }
         for &idx in &levels[0].cells {
@@ -762,6 +825,7 @@ struct OperatorKey {
     coefficients: Vec<u64>,
     smoother_sweeps: usize,
     coarsest_cells: usize,
+    smoother: MgSmoother,
 }
 
 impl OperatorKey {
@@ -782,6 +846,7 @@ impl OperatorKey {
             coefficients,
             smoother_sweeps: params.smoother_sweeps,
             coarsest_cells: params.coarsest_cells,
+            smoother: params.smoother,
         }
     }
 
@@ -790,6 +855,7 @@ impl OperatorKey {
             && self.ny == problem.ny
             && self.smoother_sweeps == params.smoother_sweeps
             && self.coarsest_cells == params.coarsest_cells
+            && self.smoother == params.smoother
             && self.active == problem.active
             && self.coefficients.iter().copied().eq(problem
                 .ae