Macchiato.jl

A Julia framework for solving partial differential equations using radial basis function (RBF) meshless methods. Instead of generating and managing a mesh, Macchiato.jl operates directly on scattered point clouds — simplifying geometry handling, avoiding mesh quality issues, and enabling straightforward refinement by simply adding points.

The JuliaMeshless Ecosystem

Macchiato.jl is part of the JuliaMeshless organization, which provides three composable packages:

Package	Role
WhatsThePoint.jl	Point cloud generation — boundary discretization, surface splitting, interior fill algorithms
RadialBasisFunctions.jl	RBF interpolation and differential operators — Laplacian, gradient, partial derivatives, custom operators
Macchiato.jl	Physics simulation framework — models, boundary conditions, solvers, and post-processing

WhatsThePoint.jl creates the geometry, RadialBasisFunctions.jl provides the numerical building blocks, and Macchiato.jl ties them together into complete simulations.

Quick Example

Steady-state heat conduction on a unit square with prescribed temperatures:

using WhatsThePoint, Macchiato, Unitful: m, °

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

# Physics + BCs
model = SolidEnergy(k=1.0, ρ=1.0, cₚ=1.0)
bcs = Dict(
    :surface1 => Temperature(0.0),    # bottom
    :surface2 => Temperature(0.0),    # right
    :surface3 => Temperature(100.0),  # top
    :surface4 => Temperature(0.0)     # left
)
domain = Domain(cloud, bcs, model)

# Solve and extract results
sim = Simulation(domain)
run!(sim)
T = temperature(sim)

Supported Physics

• Heat Transfer — SolidEnergy: steady-state and transient conduction with optional source terms, Dirichlet (Temperature), Neumann (HeatFlux, Adiabatic), and Robin (Convection) boundary conditions
• Linear Elasticity — LinearElasticity: 2D plane stress with Displacement and Traction boundary conditions, body force support
• Incompressible Fluids (in development) — IncompressibleNavierStokes with Newtonian and Carreau-Yasuda viscosity models

Boundary Condition System

BCs are organized by mathematical type and physics domain:

Math Type	Generic Type	Energy	Mechanics	Fluids
Dirichlet	PrescribedValue	Temperature	Displacement	VelocityInlet / PressureOutlet
Neumann	PrescribedFlux / ZeroFlux	HeatFlux / Adiabatic	Traction / TractionFree	VelocityOutlet
Robin	—	Convection	—	—

All BCs accept constant values or functions (x, t) -> value for spatially/temporally varying conditions.

Installation

using Pkg
Pkg.add(url="https://github.com/JuliaMeshless/Macchiato.jl")

Or for development:

Pkg.develop(url="https://github.com/JuliaMeshless/Macchiato.jl")

Documentation

Full documentation is available at juliameshless.github.io/Macchiato.jl.

Contributing

Contributions are welcome! The package uses a dispatch-based design that makes it straightforward to add new physics domains. See the Package Design section of the docs for the architecture overview and extension guide.