Macchiato.jl

Solve partial differential equations on scattered point clouds — no mesh required.

Macchiato.jl is a general-purpose meshless PDE framework. Define any PDE by implementing a small model interface, and Macchiato handles operator assembly, boundary condition application, and time integration. The package ships with ready-to-use models for heat transfer, linear elasticity, and fluid dynamics — but these are convenience built-ins, not the whole story. See Custom PDEs to learn how to solve your own equations.

Quick Start

using WhatsThePoint, Macchiato
using Unitful: m, °

# 1. Geometry: 1m × 1m rectangle point cloud
part = PointBoundary(rectangle(1m, 1m)...)
split_surface!(part, 75°)
cloud = discretize(part, ConstantSpacing(1/33 * m), alg=VanDerSandeFornberg())

# 2. Boundary conditions
bcs = Dict(
    :surface1 => Temperature(0.0),    # bottom
    :surface2 => Temperature(0.0),    # right
    :surface3 => Temperature(100.0),  # top
    :surface4 => Temperature(0.0),    # left
)

# 3. Solve
domain = Domain(cloud, bcs, SolidEnergy(k=1.0, ρ=1.0, cₚ=1.0))
sim = Simulation(domain)
run!(sim)

# 4. Extract results
T = temperature(sim)

Gallery

Heat Conduction	Cantilever Beam
Steady-state temperature on a unit square	Displacement magnitude under end shear

See the Examples page for complete worked examples with visualization code.

Why Meshless Methods?

Meshless methods operate on scattered point clouds with no connectivity requirements:

• Simple geometry handling — drop points on the boundary and fill the interior; no element quality concerns
• Easy refinement — add more points where you need accuracy; no remeshing required
• Natural for moving boundaries — points move freely without topological constraints

Macchiato.jl uses radial basis function (RBF) collocation, where differential operators are approximated at each point using its local neighborhood of nearest neighbors.

The JuliaMeshless Ecosystem

Macchiato.jl is part of the JuliaMeshless organization — three composable packages that form a complete simulation pipeline:

┌─────────────────────┐     ┌──────────────────────────┐     ┌─────────────────────────────┐
│   WhatsThePoint.jl  │     │ RadialBasisFunctions.jl  │     │  Macchiato.jl               │
│                     │     │                          │     │                             │
│  Boundary creation  │────▶│  RBF interpolation       │────▶│  PDE model interface        │
│  Surface splitting  │     │  Differential operators  │     │  Boundary conditions        │
│  Interior fill      │     │  (∇², ∂/∂x, custom)      │     │  Simulation & time stepping │
│  Point repulsion    │     │  KNN stencil selection   │     │  Field extraction & VTK I/O │
└─────────────────────┘     └──────────────────────────┘     └─────────────────────────────┘
        Geometry                   Numerics                      PDE Framework

• WhatsThePoint.jl — Point cloud generation from geometric primitives, surface splitting, interior fill, and point repulsion.
• RadialBasisFunctions.jl — RBF interpolation and meshless differential operators (Laplacian, partial, gradient, custom) with automatic stencil selection.
• Macchiato.jl — General-purpose PDE framework: define custom models or use built-in physics (heat, elasticity, fluids), with boundary conditions, steady-state and transient solvers, field extraction, and VTK export.

Built-in Models

Macchiato ships with ready-to-use models for common physics. You can also define your own for any PDE.

Next Steps

• Getting Started — step-by-step tutorial from geometry to results
• Custom PDEs — define and solve your own equations
• Examples — complete worked examples with visualization
• Package Design — architecture and extension guide
• API Reference — full type and function documentation