multigrid.hpp

Go to the documentation of this file.

// core — device (Kokkos) geometric-multigrid V-cycle on a BlockOctree,
// with the *consistent* graded (cut-cell-ready) operator.
//
// The device compute path's capstone: a full MG V-cycle running entirely in device
// kernels over the leaf Views, on a genuinely graded octree. The hierarchy is the
// octree coarsened uniformly one level at a time (same as host AmrMultigrid); each
// level's operator is the conservative two-point FV Laplacian
//     (L u)_i = invVol_i · Σ_f w_f (u[nbr_f] − u_i),  w_f = openness·A_f/d_f,
// captured as a precomputed face CSR (built on the host from AmrPoisson's exact
// forEachFaceNeighbor enumeration, so the 2:1 sub-faces and coefficients match the
// host operator bit-for-bit). This replaces the earlier *plain* (u_j−u_i)/h0²
// operator, which ignored 2:1-interface geometry and so stalled the graded V-cycle.
//
// Every stage is deterministic / order-independent ⇒ bit-identical to the same
// Jacobi V-cycle on the host (validated in test_amr_device_multigrid_kokkos):
//   * smoother    — weighted Jacobi over the face CSR (reads only the prev iterate);
//   * restriction — each coarse cell sums its children in fixed CSR order (no atomics);
//   * prolongation— piecewise-constant, per fine cell.
//
// 2nd-order at 2:1 interfaces: solveQuad() wraps the V-cycle in deferred correction
// with the quadratic coarse-fine flux (AmrPoisson::coarseStar), evaluated on device
// as a second precomputed CSR (quadDelta). Openness (cut-cell) flows in for
// free: build with an AmrPoisson that has openness set and w_f carries it.
//
#ifndef PECLET_AMR_MULTIGRID_HPP
#define PECLET_AMR_MULTIGRID_HPP
 
#include <cmath>
#include <memory>
#include <string>
#include <utility>
#include <vector>
 
#include "peclet/amr/amg_bottom.hpp"  // the exact coarsest-level solve (docs/amr_mg_depth.md §6.6)
#include "peclet/amr/assembly.hpp"    // assembleFv (device per-level operator rebuild, D5)
#include "peclet/amr/block_octree.hpp"
#include "peclet/amr/common.hpp"
#include "peclet/amr/fv_op.hpp"
#include "peclet/amr/poisson.hpp"
#include "peclet/core/common/host_parallel.hpp"
#include "peclet/core/common/view.hpp"
 
namespace peclet::amr {
 
inline void restrictField(View<const Index> childStart, View<const Index> childIdx,
                          View<const double> fine, View<double> coarse, Index nCoarse) {
  Kokkos::parallel_for(
      "amr::device_restrict", nCoarse, KOKKOS_LAMBDA(const Index p) {
        const Index a = childStart(p), z = childStart(p + 1);
        double s = 0.0;
        for (Index k = a; k < z; ++k)
          s += fine(childIdx(k));
        coarse(p) = (z > a) ? s / static_cast<double>(z - a) : 0.0;
      });
}
 
inline void restrictKappa(View<const Index> childStart, View<const Index> childIdx,
                          View<const double> fine, View<const double> kappa, View<double> coarse,
                          Index nCoarse) {
  Kokkos::parallel_for(
      "amr::device_restrict_kappa", nCoarse, KOKKOS_LAMBDA(const Index p) {
        const Index a = childStart(p), z = childStart(p + 1);
        double sw = 0.0, swv = 0.0;
        for (Index k = a; k < z; ++k) {
          const Index ch = childIdx(k);
          const double w = kappa(ch);
          sw += w;
          swv += w * fine(ch);
        }
        coarse(p) = (sw > 0.0) ? swv / sw : 0.0;
      });
}
 
inline void prolongAdd(View<const Index> c2p, View<const double> coarse, View<double> fine,
                       Index nFine) {
  Kokkos::parallel_for(
      "amr::device_prolong", nFine, KOKKOS_LAMBDA(const Index i) {
        const Index p = c2p(i);
        if (p >= 0)
          fine(i) += coarse(p);
      });
}
 
inline void prolongAddMasked(View<const Index> c2p, View<const double> coarse,
                             View<const char> excl, View<double> fine, Index nFine) {
  Kokkos::parallel_for(
      "amr::device_prolong_masked", nFine, KOKKOS_LAMBDA(const Index i) {
        if (excl(i))
          return;
        const Index p = c2p(i);
        if (p >= 0)
          fine(i) += coarse(p);
      });
}
 
inline void zeroMasked(View<double> v, View<const char> excl, Index n) {
  Kokkos::parallel_for(
      "amr::device_zero_masked", n, KOKKOS_LAMBDA(const Index i) {
        if (excl(i))
          v(i) = 0.0;
      });
}
 
template <int Dim, unsigned Bits = (Dim == 2 ? 32u : (Dim == 3 ? 21u : 16u))>
class Multigrid {
 public:
  using Octree = BlockOctree<Dim, Bits>;
  using M = typename Octree::M;
  using Code = typename Octree::Code;
  using Poisson = AmrPoisson<Dim, Bits>;
 
  enum class Bottom { Auto, Smoother, Agglomerated };
 
  void build(const Octree& finest, double h0, bool liftRoot = true, Index bottomExtent = 4) {
    build(finest, detail::filledVec<Dim>(h0), liftRoot, bottomExtent);
  }
  void build(const Octree& finest, const Vec<Dim>& h0, bool liftRoot = true,
             Index bottomExtent = 4) {
    bottomExtent_ = bottomExtent;
    hmg_ = std::make_unique<AmrMultigrid<Dim, Bits>>();
    hmg_->build(finest, h0, liftRoot, bottomExtent);
    buildFromHostMg();
  }
 
  template <class OpenFn>
  void build(const Octree& finest, double h0, OpenFn&& openFn, bool periodic = true,
             bool immersedWall = false, bool liftRoot = true, Index bottomExtent = 4) {
    build(finest, detail::filledVec<Dim>(h0), std::forward<OpenFn>(openFn), periodic, immersedWall,
          liftRoot, bottomExtent);
  }
  template <class OpenFn>
  void build(const Octree& finest, const Vec<Dim>& h0, OpenFn&& openFn, bool periodic = true,
             bool immersedWall = false, bool liftRoot = true, Index bottomExtent = 4) {
    bottomExtent_ = bottomExtent;
    hmg_ = std::make_unique<AmrMultigrid<Dim, Bits>>();
    hmg_->build(finest, h0, liftRoot, bottomExtent);
    hmg_->setOpenness(std::forward<OpenFn>(openFn));
    hmg_->setPeriodic(periodic);          // non-periodic ⇒ homogeneous Dirichlet domain walls
    hmg_->setImmersedWall(immersedWall);  // true ⇒ velocity operator (solid faces = no-slip walls)
    buildFromHostMg();
  }
 
  void buildRaw(const Octree& finest, const Vec<Dim>& h0, std::vector<double> alphaRaw,
                bool periodic = true, bool liftRoot = true, Index bottomExtent = 4) {
    bottomExtent_ = bottomExtent;
    hmg_ = std::make_unique<AmrMultigrid<Dim, Bits>>();
    hmg_->build(finest, h0, liftRoot, bottomExtent);
    hmg_->setOpennessRaw(std::move(alphaRaw));
    hmg_->setPeriodic(periodic);
    buildFromHostMg();
  }
 
  void setKappaRestrict(bool on) { kappaRestrict_ = on; }
 
  void setRemoveMean(bool on) { removeMean_ = on; }
 
  void setHelmholtz(double c0, double cD) {
    for (auto& lv : levels_) {
      lv.op.c0 = c0;
      lv.op.cD = cD;
    }
    // The exact bottom assembles the pure FV Laplacian from the host AmrPoisson, which carries no
    // reaction term — so a Helmholtz hierarchy falls back to the Jacobi bottom rather than solving
    // the wrong operator. (docs/amr_mg_depth.md §6.6 scopes the exact bottom to the pressure.)
    if (c0 != 0.0 || cD != 1.0)
      amgOn_ = false;
  }
 
  void setBottom(Bottom b) {
    bottomKind_ = b;
    buildBottom();
  }
  Bottom bottom() const { return bottomKind_; }
  std::string bottomName() const { return amgOn_ ? "amg" : "jacobi"; }
  Index bottomExtent() const { return bottomExtent_; }
  Index bottomSize() const { return amg_ ? amg_->size() : 0; }
  Index bottomIdentityRows() const { return amg_ ? amg_->numIdentityRows() : 0; }
  int bottomComponents() const { return amg_ ? amg_->numComponents() : 0; }
  int bottomIters() const { return amg_ ? amg_->lastIters() : 0; }
  bool bottomOnDevice() const { return amg_ && amg_->onDevice(); }
 
  void setBottomCheck(bool on) { bottomCheck_ = on; }
  double bottomResidual() const { return bottomRel_; }
 
  std::size_t numLevels() const { return levels_.size(); }
  Index numLeaves(std::size_t L = 0) const { return levels_[L].n; }
  Code octreeCode(std::size_t L, Index i) const { return hmg_->op(L).octree().code(i); }
  View<double> x(std::size_t L = 0) { return levels_[L].x; }
  View<double> b(std::size_t L = 0) { return levels_[L].b; }
  const FvOp& op(std::size_t L = 0) const { return levels_[L].op; }
  View<Index> quadStart() const { return qStart_; }
  View<Index> quadSlot() const { return qSlot_; }
  View<double> quadCoef() const { return qCoef_; }
 
  void vcycle(int pre = 2, int post = 2, int bottom = 40, double omega = 0.8, std::size_t L = 0) {
    Level& lv = levels_[L];
    View<const double> bc(lv.b);
    if (L + 1 == levels_.size()) {
      if (amgOn_) {
        bottomSolveExact(lv);  // §6.6: the agglomerated GraphAMG-PCG solve
      } else {
        for (int s = 0; s < bottom; ++s)
          jacobiFv(lv.op, lv.x, bc, lv.tmp, omega);
      }
      if (removeMean_)
        removeMeanFv(lv.op, lv.x);
      return;
    }
    for (int s = 0; s < pre; ++s)
      jacobiFv(lv.op, lv.x, bc, lv.tmp, omega);
    residualFv(lv.op, View<const double>(lv.x), bc, lv.res);
    Level& cl = levels_[L + 1];
    if (kappaRestrict_)
      restrictKappa(lv.childStart, lv.childIdx, View<const double>(lv.res),
                    View<const double>(lv.kappa), cl.b, cl.n);
    else
      restrictField(lv.childStart, lv.childIdx, View<const double>(lv.res), cl.b, cl.n);
    Kokkos::deep_copy(cl.x, 0.0);
    vcycle(pre, post, bottom, omega, L + 1);
    prolongAdd(lv.c2p, View<const double>(cl.x), lv.x, lv.n);
    for (int s = 0; s < post; ++s)
      jacobiFv(lv.op, lv.x, bc, lv.tmp, omega);
    if (removeMean_)
      removeMeanFv(lv.op, lv.x);
  }
 
  double solveQuad(int outer = 20, int cyclesPerOuter = 1, int pre = 2, int post = 2,
                   int bottom = 40, double omega = 0.8) {
    Level& lv = levels_[0];
    Kokkos::deep_copy(b0true_, lv.b);  // true rhs
    auto dq = dq_;
    auto b0 = b0true_;
    auto bb = lv.b;
    double r = 0.0;
    for (int o = 0; o < outer; ++o) {
      quadDelta(View<const Index>(qStart_), View<const Index>(qSlot_), View<const double>(qCoef_),
                View<const double>(lv.x), dq_, lv.n);
      Kokkos::parallel_for(
          "amr::quad_rhsp", lv.n, KOKKOS_LAMBDA(const Index i) { bb(i) = b0(i) - dq(i); });
      for (int c = 0; c < cyclesPerOuter; ++c)
        vcycle(pre, post, bottom, omega, 0);
    }
    // r = || b0true − (L_std + quad) x ||
    residualFv(lv.op, View<const double>(lv.x), View<const double>(b0true_), lv.res);
    quadDelta(View<const Index>(qStart_), View<const Index>(qSlot_), View<const double>(qCoef_),
              View<const double>(lv.x), dq_, lv.n);
    auto res = lv.res;
    double s = 0.0;
    Kokkos::parallel_reduce(
        "amr::quad_resnorm", lv.n,
        KOKKOS_LAMBDA(const Index i, double& acc) {
          double rr = res(i) - dq(i);
          acc += rr * rr;
        },
        s);
    r = std::sqrt(s);
    Kokkos::deep_copy(lv.b, b0true_);  // restore rhs
    return r;
  }
 
 private:
  struct Level {
    FvOp op;
    Index n = 0;
    View<double> x, b, res, tmp;
    View<double> kappa;                     // per-cell fluid-fraction weight (κ restriction)
    View<Index> c2p, childStart, childIdx;  // describe L → L+1 (unused on coarsest)
  };
 
  // Upload the device hierarchy from the host AmrMultigrid hmg_ (which already holds
  // the uniform-coarsened octrees + per-level operators with coarsened openness). Each
  // level's face CSR is built from hmg_->op(L), so the device operator == that host
  // operator bit-for-bit on every level.
  void buildFromHostMg() {
    const std::size_t nl = hmg_->numLevels();
    levels_.clear();
    levels_.resize(nl);
    for (std::size_t L = 0; L < nl; ++L) {
      const Poisson& ap = hmg_->op(L);
      const Octree& oct = ap.octree();
      Level& lv = levels_[L];
      lv.n = oct.numLeaves();
      buildFaceCsr(ap, oct, lv);
      // Per-cell κ weight for the optional κ-weighted restriction = mean face aperture
      // (1 fully open ⇒ reduces to plain average; <1 near cuts).
      std::vector<double> kap(static_cast<std::size_t>(lv.n));
      hostParFor(lv.n, [&](Index i) {  // per-cell disjoint (rung 2); the 2·Dim sum stays in-row
        double s = 0.0;
        for (int axis = 0; axis < Dim; ++axis)
          for (int dir = -1; dir <= 1; dir += 2)
            s += ap.faceOpenness(i, axis, dir);
        kap[static_cast<std::size_t>(i)] = s / static_cast<double>(2 * Dim);
      });
      lv.kappa = toDevice(kap, "mg_kappa");
      lv.x = View<double>("mg_x", static_cast<std::size_t>(lv.n));
      lv.b = View<double>("mg_b", static_cast<std::size_t>(lv.n));
      lv.res = View<double>("mg_res", static_cast<std::size_t>(lv.n));
      lv.tmp = View<double>("mg_tmp", static_cast<std::size_t>(lv.n));
    }
    for (std::size_t L = 0; L + 1 < nl; ++L) {
      const Octree& f = hmg_->op(L).octree();
      const Octree& c = hmg_->op(L + 1).octree();
      const Index nf = f.numLeaves(), nc = c.numLeaves();
      std::vector<Index> c2p(static_cast<std::size_t>(nf));
      std::vector<Index> cnt(static_cast<std::size_t>(nc), 0);
      // Covering-leaf construction: identical to ancestor(level+1)+find for merged children,
      // and CORRECT (identity) for cells already at root level in mixed-depth ladders — the
      // ancestor form maps those to the 2^(lmax+1)-aligned corner root cell instead (measured:
      // 49/56 root rows mis-parented on a graded 16^3 ladder), and its alignment depends on
      // the block origin, which would break the distributed WORLD==SELF transfer contract.
      // Rung 2: the `find` (the expensive half) is per-fine-row disjoint and runs host-parallel;
      // the child HISTOGRAM is many-to-one, so it stays serial — integer counts, unchanged.
      hostParFor(nf, [&](Index i) { c2p[static_cast<std::size_t>(i)] = c.find(f.code(i)); });
      for (Index i = 0; i < nf; ++i) {
        const Index p = c2p[static_cast<std::size_t>(i)];
        if (p >= 0)
          ++cnt[static_cast<std::size_t>(p)];
      }
      std::vector<Index> start(static_cast<std::size_t>(nc) + 1, 0);
      for (Index p = 0; p < nc; ++p)
        start[static_cast<std::size_t>(p) + 1] =
            start[static_cast<std::size_t>(p)] + cnt[static_cast<std::size_t>(p)];
      std::vector<Index> idx(static_cast<std::size_t>(nf));
      std::vector<Index> cur(start.begin(), start.end() - 1);
      for (Index i = 0; i < nf; ++i) {
        Index p = c2p[static_cast<std::size_t>(i)];
        if (p >= 0)
          idx[static_cast<std::size_t>(cur[static_cast<std::size_t>(p)]++)] = i;
      }
      levels_[L].c2p = toDevice(c2p, "mg_c2p");
      levels_[L].childStart = toDevice(start, "mg_cstart");
      levels_[L].childIdx = toDevice(idx, "mg_cidx");
    }
    // Quadratic coarse-fine correction CSR on the finest level (for solveQuad);
    // openness (if any) flows in through hmg_->op(0)'s aperture + coarseStar gating.
    buildQuadCsr(hmg_->op(0), hmg_->op(0).octree());
    const Index n0 = levels_[0].n;
    dq_ = View<double>("mg_dq", static_cast<std::size_t>(n0));
    b0true_ = View<double>("mg_b0", static_cast<std::size_t>(n0));
    buildBottom();  // §6.6: the exact coarsest-level solve, if the ladder stopped short
  }
 
  // Build the consistent face CSR (+ invVol/bcDiag) for one level by assembling it ON THE DEVICE
  // (D5/D2): upload this level's leaf set, then assembleFv reproduces AmrPoisson's exact
  // forEachFaceNeighbor enumeration + openness·A_f/d_f weights — bit-for-bit identical to the host
  // walk on OpenMP (validated in test_amr_assembly), but with no host CSR build / no
  // re-upload. The Helmholtz c0/cD of this level are preserved (assembleFv returns the pure-L
  // defaults; setHelmholtz / a prior value is re-applied), so a reassemble after the geometry moves
  // keeps the momentum-preconditioner form.
  void buildBottom() {
    amgOn_ = false;
    amg_.reset();
    if (!hmg_ || levels_.empty())
      return;
    const std::size_t Lc = levels_.size() - 1;
    const Poisson& ap = hmg_->op(Lc);
    Index E = 0;
    for (int d = 0; d < Dim; ++d)
      E = std::max(E, ap.octree().brick()[d]);
    const bool want =
        (bottomKind_ == Bottom::Agglomerated) || (bottomKind_ == Bottom::Auto && E > bottomExtent_);
    if (!want)
      return;
    // Singular iff the operator carries no Dirichlet term anywhere — read from the assembly, so it
    // does not depend on whether setRemoveMean has been called yet.
    const auto A = ap.assembleFv();
    bool singular = true;
    for (double d : A.bcDiag)
      if (d != 0.0) {
        singular = false;
        break;
      }
    amg_ = std::make_unique<AmgBottom<Dim, Bits>>();
    amg_->build(ap, singular);
    amgOn_ = true;
  }
 
  void bottomSolveExact(Level& lv) {
    amg_->solve(View<const double>(lv.b), lv.x);
    if (!bottomCheck_)
      return;
    residualFv(lv.op, View<const double>(lv.x), View<const double>(lv.b), lv.res);
    auto res = lv.res;
    auto bb = lv.b;
    double rm = 0.0, bm = 0.0;
    Kokkos::parallel_reduce(
        "amr::bottom_check", lv.n,
        KOKKOS_LAMBDA(const Index i, double& a, double& c) {
          const double r = res(i) < 0.0 ? -res(i) : res(i);
          const double b = bb(i) < 0.0 ? -bb(i) : bb(i);
          if (r > a)
            a = r;
          if (b > c)
            c = b;
        },
        Kokkos::Max<double>(rm), Kokkos::Max<double>(bm));
    bottomRel_ = (bm > 0.0) ? rm / bm : 0.0;
  }
 
  void buildFaceCsr(const Poisson& ap, const Octree& t, Level& lv) {
    const double c0 = lv.op.c0, cD = lv.op.cD;
    BlockOctreeView<Dim, Bits> ov;
    ov.upload(t);
    lv.op = assembleFv<Dim, Bits>(ap, ov);
    lv.op.c0 = c0;
    lv.op.cD = cD;
  }
 
 public:
  void reassembleOperators() {
    const std::size_t nl = hmg_->numLevels();
    for (std::size_t L = 0; L < nl && L < levels_.size(); ++L)
      buildFaceCsr(hmg_->op(L), hmg_->op(L).octree(), levels_[L]);
    buildBottom();  // the exact bottom is assembled FROM that operator, so it is stale otherwise
  }
 
 private:
  // Build the quadratic coarse-fine correction CSR: dq_i = Σ coef·u[slot] equals
  // (L_quad − L_std)u (AmrPoisson::coarseStar, expressed as a linear stencil).
  void buildQuadCsr(const Poisson& ap, const Octree& t) {
    const Index n = t.numLeaves();
    std::vector<std::vector<std::pair<Index, double>>> per(static_cast<std::size_t>(n));
    const Vec<Dim>& h0 = ap.h0();  // Phase 3: per-axis
    hostParFor(n, [&](Index i) {   // per[i]-disjoint (rung 2)
      const unsigned Li = t.level(i);
      const double invV = 1.0 / ap.cellVolume(i);
      ap.forEachFaceNeighbor(i, [&](Index j, Real c, int axis, double a) {
        const unsigned Lj = t.level(j);
        if (Lj == Li)
          return;
        const Index coarse = (Lj > Li) ? j : i;
        const Index fine = (Lj > Li) ? i : j;
        const double scale = invV * (a * c) * ((Lj > Li) ? 1.0 : -1.0);
        addCoarseStarStencil(ap, t, per[static_cast<std::size_t>(i)], coarse, fine, axis, scale,
                             h0);
      });
    });
    std::vector<Index> qs(static_cast<std::size_t>(n) + 1, 0);
    for (Index i = 0; i < n; ++i)
      qs[static_cast<std::size_t>(i) + 1] =
          qs[static_cast<std::size_t>(i)] +
          static_cast<Index>(per[static_cast<std::size_t>(i)].size());
    const Index nq = qs[static_cast<std::size_t>(n)];
    std::vector<Index> slot(static_cast<std::size_t>(nq));
    std::vector<double> coef(static_cast<std::size_t>(nq));
    Index k = 0;
    for (Index i = 0; i < n; ++i)
      for (auto& e : per[static_cast<std::size_t>(i)]) {
        slot[static_cast<std::size_t>(k)] = e.first;
        coef[static_cast<std::size_t>(k)] = e.second;
        ++k;
      }
    qStart_ = toDevice(qs, "mg_qstart");
    qSlot_ = toDevice(slot, "mg_qslot");
    qCoef_ = toDevice(coef, "mg_qcoef");
  }
 
  // coarseStar(coarse,fine,axis) − u[coarse] as a linear stencil over the coarse
  // cell + its tangential coarse neighbours, scaled, appended to `out`. Mirrors
  // AmrPoisson::coarseStar exactly (same gating, same coefficients).
  static void addCoarseStarStencil(const Poisson& ap, const Octree& t,
                                   std::vector<std::pair<Index, double>>& out, Index coarse,
                                   Index fine, int axis, double scale, const Vec<Dim>& h0) {
    auto bc = t.bounds(coarse);
    auto bf = t.bounds(fine);
    const double sc = static_cast<double>(Index(1) << t.level(coarse));
    const double sf = static_cast<double>(Index(1) << t.level(fine));
    for (int tt = 0; tt < Dim; ++tt) {
      if (tt == axis)
        continue;
      // Phase 3: the tangential offset AND the differencing width belong to axis `tt` — they
      // were one `H` when the cells were cubes. Mirrors AmrPoisson::coarseStar exactly.
      const double H = ap.cellWidth(coarse, tt);
      const double dt = ((static_cast<double>(bf[0][tt]) + 0.5 * sf) -
                         (static_cast<double>(bc[0][tt]) + 0.5 * sc)) *
                        h0[tt];
      Index cp = ap.periodicNeighbor(coarse, tt, +1);
      Index cm = ap.periodicNeighbor(coarse, tt, -1);
      if (cp < 0 || cm < 0)
        continue;
      if (t.level(cp) != t.level(coarse) || t.level(cm) != t.level(coarse))
        continue;
      if (ap.faceOpenness(coarse, tt, +1) < 0.5 || ap.faceOpenness(coarse, tt, -1) < 0.5)
        continue;
      const double cUp = dt / (2.0 * H) + 0.5 * dt * dt / (H * H);
      const double cUm = -dt / (2.0 * H) + 0.5 * dt * dt / (H * H);
      const double cUc = -dt * dt / (H * H);
      out.emplace_back(coarse, scale * cUc);
      out.emplace_back(cp, scale * cUp);
      out.emplace_back(cm, scale * cUm);
    }
  }
 
  // Owns the host hierarchy + per-level operators (with coarsened openness). The
  // operators hold pointers into its octrees, so keep it stable (unique_ptr) for the
  // lifetime of this object.
  std::unique_ptr<AmrMultigrid<Dim, Bits>> hmg_;
  std::vector<Level> levels_;
  bool kappaRestrict_ = false;  // default: plain volume-average restriction
  bool removeMean_ = false;     // default off; per-level nullspace projection for singular MG-PCG
  Bottom bottomKind_ = Bottom::Auto;
  Index bottomExtent_ = 4;
  bool amgOn_ = false, bottomCheck_ = false;
  double bottomRel_ = 0.0;
  std::unique_ptr<AmgBottom<Dim, Bits>> amg_;
  View<Index> qStart_, qSlot_;  // finest-level quadratic correction CSR
  View<double> qCoef_;
  View<double> dq_, b0true_;  // finest-level deferred-correction scratch
};
 
}  // namespace peclet::amr
 
#endif  // PECLET_AMR_MULTIGRID_HPP