peclet.voro

A Kokkos engine for dynamic Voronoi tessellation of moving particles in three dimensions, part of the peclet suite. The same sources run on CUDA / HIP / OpenMP (the backend is chosen by the bootstrapped Kokkos prefix the build is pointed at, not hard-coded), and the distributed path is built on the shared core MPI halo. Features:

• Periodic boundary conditions (cubic and Lees–Edwards shear boxes)
• Incremental cell updates under particle motion (persistent Verlet-skin worklist)
• Compressible and incompressible Euler / Navier–Stokes dynamics
• Multiphase interface-tension (surface-tension) forces
• GPU and multicore execution through Kokkos backends; MPI block decomposition via core

The compact ConvexCell dual-triangle tessellator is the engine. (The original header-only half-edge CPU engine has been retired and removed; the device path is the whole library.)

Repository layout

voro/
├── include/
│   └── peclet/voro/                 # the Kokkos tessellator engine (namespace peclet::voro)
│       ├── convex_cell.hpp          #   compact dual-triangle ConvexCell + per-vertex geometry
│       ├── tessellator.hpp          #   cold build: grid + worklist gather + clip + CSR publish
│       ├── repair.hpp               #   MovingTessellation: incremental two-pass repair update
│       ├── topology_store.hpp       #   resident compact topology (+ poke4 cert planes) between steps
│       ├── tess_grid.hpp            #   counting-sort grid + presorted worklist
│       ├── subset_gather.hpp        #   the cold-build kernel restricted to an index list (repair)
│       ├── dynamic_validate.hpp     #   geometric invariants + oracle diff (validators)
│       ├── verlet_skin.hpp          #   per-particle Verlet-skin (insertion) tracker
│       ├── sdf.hpp                  #   SDF half-space clipping (solid boundaries)
│       ├── plane_policy.hpp         #   Voronoi / Power / SDF plane-definition policies
│       ├── transpose.hpp            #   neighbour<->facet reciprocal map helpers
│       ├── physics/                 # simulation + forces over the published view
│       │   ├── simulation.hpp       #   Euler / Navier-Stokes facade (ExplicitEuler)
│       │   ├── euler_pressure.hpp   #   EOS pressure force
│       │   ├── viscous.hpp          #   viscous Navier-Stokes term
│       │   └── interface.hpp        #   multiphase interface-tension force
│       ├── mpi/
│       │   └── voronoi_halo.hpp     #   distributed halo glue over core
│       └── tessellation_view.hpp    # published read-only CSR device view (engine<->consumer seam)
├── src/voro_bindings.cpp     # nanobind Python module (`peclet.voro`)
├── python/test_voro.py       # Python smoke test (Tessellation + Simulation)
├── tests/kokkos/                # device unit tests + benchmarks
├── tests/kokkos_mpi/            # distributed benchmarks
├── docs/                        # design notes, performance_report.md, Doxygen config
└── CMakeLists.txt               # build system (Kokkos device path)

Requirements

The Kokkos/ArborX backend and target architecture come from the bootstrapped prefix ../extern/install/<backend> (built once by ../tools/bootstrap_deps.sh), exactly as in sdflow and dem. Put nvcc on PATH for the CUDA backend.

Building with CMake

Device (production) path

# Point at the bootstrapped Kokkos prefix; clone core and morton as siblings.
cmake -B build -DPECLET_VORO_KOKKOS=ON \
      -DCMAKE_PREFIX_PATH="$PWD/../extern/install/nvidia-cuda"
cmake --build build --parallel
ctest --test-dir build --output-on-failure        # device tests under tests/kokkos

Add -DPECLET_VORO_MPI=ON to link MPI + core for the distributed path.

CMake options

Python bindings (peclet.voro)

The device tessellator is exposed to Python through a nanobind module that uses the shared core zero-copy array bridge (numpy (N,3) / (N,) arrays alias the device-staged buffers — no per-call copies). This is the same drive-from-Python pattern as the rest of the suite (sdflow/pnm, dem). The module is not pybind11 and is not fetched automatically: nanobind is located via the active interpreter through the suite's cmake/SuiteNanobind.cmake. The built module is importable as peclet.voro (formerly vordyn).

cmake -B build -DPECLET_VORO_KOKKOS=ON -DPECLET_VORO_BUILD_PYTHON=ON \
      -DCMAKE_PREFIX_PATH="$PWD/../extern/install/nvidia-cuda"
cmake --build build --target voro -j
PYTHONPATH=build python3 -c "import peclet.voro; print(peclet.voro.execution_space)"

The module exposes two surfaces — the bare Tessellation (cold build + incremental repair of a moving point set) and the Simulation fluid solver:

import numpy as np
import peclet.voro as voro

# bare moving-point Voronoi tessellation
t = voro.Tessellation()
t.set_box([1.0, 1.0, 1.0])
t.build(pos)                         # cold build, pos = (N,3) float64
vol = t.volumes()                    # (N,) cell volumes (sum ~= box volume)
nbr = t.neighbor_counts()            # (N,) Voronoi neighbours per cell
stats = t.step(pos_moved)            # incremental repair to new positions

# compressible-Euler / Navier-Stokes fluid on top of it
s = voro.Simulation()
s.set_box([6.0, 6.0, 6.0])
s.set_positions(pos)                 # (N,3) float64
s.set_velocities(vel)                # (N,3) float64
s.set_masses(masses)                 # (N,) float64
s.set_pressure(1.0)
s.set_viscosities(nu)                # (N,) float64 — enables the viscous Navier–Stokes term
s.init()                             # build the first tessellation + forces
s.step(num_steps=10, dt=1e-3)        # velocity-Verlet dynamics

pos  = s.get_positions()             # (N,3)
vol  = s.get_volumes()               # per-cell Voronoi volume (N,)
ke   = s.get_kinetic_energy()

Array shapes follow the suite convention (../docs/CONVENTIONS.md §6): positions/velocities (N,3) float64, masses/viscosities/volumes (N,). Call peclet.voro.finalize() for deterministic Kokkos teardown (also run from an atexit hook).

For the distributed (MPI) validation scripts see mpi/README.md and docs/distributed_voronoi.md.

Code quality

Formatting

The codebase follows the Google C++ Style Guide enforced by clang-format:

clang-format --dry-run --Werror include/peclet/voro/**/*.hpp tests/kokkos/*.cpp src/*.cpp

Static analysis

cmake -B build -DCMAKE_EXPORT_COMPILE_COMMANDS=ON
clang-tidy -p build include/peclet/voro/*.hpp

Documentation

cmake -B build -DPECLET_VORO_BUILD_DOCS=ON
cmake --build build --target docs
# HTML output: build/docs/html/index.html

Data structure overview

The production engine stores a Voronoi cell as a compact ConvexCell in the dual representation (include/peclet/voro/convex_cell.hpp). The cell is the intersection of half-spaces {x : n_k·x ≤ n_k·n_k} — one plane per neighbour (n_k is the foot-point normal: x = n_k is the foot of the perpendicular from the seed, so the connector to the neighbour is 2·n_k), plus the six bounding-box planes. Instead of explicit half-edge topology, each primal vertex is the intersection of three planes, stored as a triple of plane indices (one byte each):

unsigned char t0[MAXT], t1[MAXT], t2[MAXT];  // triangle = triple of plane indices
Real vx[MAXT], vy[MAXT], vz[MAXT];           // cached dual-vertex position

so the whole cell is a small triangle list (a few hundred bytes) that lives in registers / a tiny local frame — this is what lifts GPU occupancy far above the old ~32 KB half-edge frame. Clipping by a new plane (GEOGRAM / Ray-et-al. convex-cell clip) marks the triangles whose dual vertex falls outside the plane, finds the horizon, and adds one new triangle per horizon edge; there is no stored adjacency (the cell is tiny, so the triangle sharing an edge is found by a short scan). Cuts are applied closest-first with a security-radius early-out.

Per-cell geometry (volume, per-facet area and first moment, volume gradients) is computed by a sort-free, adjacency-free per-vertex scatter (volumePerVertex / geometryPerVertex and the facet*PerVertex family): each dual vertex scatters signed determinants into its three incident facets, so no facet polygon is ever assembled or ordered. Consumers (physics, microstructure analysis) read the results through the published read-only facetGeometry CSR in tessellation_view.hpp (TessellationView: a Kokkos View CSR of per-cell / per-facet quantities) rather than touching the cell internals.

See docs/mainpage.dox for the architecture overview and docs/performance_report.md for the cross-backend performance/memory/accuracy study.

License

See LICENSE for details.