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Tesserae.jl

A Julia toolkit for the material point method

Introduction

Tesserae is a toolkit for implementing the material point method in Julia. It is designed to maintain consistency between mathematical expressions and source code, enabling rapid development. Current features include:

  • Grid and particle generation
  • Various basis functions, including B-splines, GIMP, CPDI, and MLS–MPM
  • Convenient macros for transferring data between grid and particles
  • Multi-threading support
  • GPU support (CUDA and Metal)
  • Exporting VTK files for visualization
  • Unified framework for FEM and IGA (IGA support is experimental)

Why Tesserae.jl?

Tesserae is intended for users who want to implement MPM algorithms directly rather than operate a black-box solver. The core objects are deliberately small: a background mesh, grid fields, particles, and basis weights. Transfer macros such as @P2G and @G2P keep the implementation close to the equations, while the same code structure can be moved from CPU execution to multi-threaded or GPU execution.

Tensors are represented as tensors, using Tensorial.jl, so constitutive models and tangent operators can be written in notation that resembles the mathematical formulation.

Where to start

If you are new to Tesserae, start with the Getting started tutorial. It introduces the basic workflow:

  1. Define grid and particle properties.
  2. Generate a mesh, grid, particles, and basis weights.
  3. Transfer particle data to the grid with @P2G.
  4. Update grid quantities.
  5. Transfer grid data back to particles with @G2P.
  6. Update particle state and write or plot results.

After that, the Transfer schemes tutorial is a good next step for comparing FLIP, APIC, TPIC, and XPIC. The Manual overview connects the tutorial workflow to the individual API pages. For larger simulations, see Multi-threading and GPU computing.

Installation

You can add Tesserae using Julia's package manager, by typing ]add Tesserae in the Julia REPL:

pkg> add Tesserae