Tesserae.jl

A Julia-powered toolkit for material point method

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 interpolation types, including B-splines, GIMP, CPDI, and MLS-MPM
• Convenient macros for transferring data between grid and particles
• Multithreading support
• Exporting VTK files for visualization

Documentation

Examples

The following examples are taken from the tutorials.

Simulations using various transfers (PIC, FLIP, APIC, TPIC, and XPIC) 🔗

Jacobian-free Newton-Krylov method 🔗

Stabilized mixed MPM for incompressible fluid flow 🔗

Other MPM packages in Julia

• MaterialPointSolver.jl

Inspiration

Some functionalities are inspired from the following packages:

• Ferrite.jl
• taichi_mpm

Citation

If you find Tesserae.jl useful in your work, I kindly request that you cite it as below:

@software{NakamuraTesserae2024,
    title = {Tesserae.jl: a {J}ulia-powered toolkit for material point method},
   author = {Nakamura, Keita},
      doi = {10.5281/zenodo.13956709},
     year = {2024},
      url = {https://github.com/KeitaNakamura/Tesserae.jl}
  licence = {MIT},
}