2026-08-13 –, Room 4
Macchiato.jl is designed to eliminate the need for traditional meshes in physics simulations. Instead, it operates on unstructured point clouds, which define the boundary of the region of interest. The package aims to provide a user-friendly yet robust environment enabling scientists and engineers to conduct meaningful simulations with minimal pre-processing effort. By bypassing the complexities of mesh generation, users are free to focus on their research and applications.
Established numerical methods such as the Finite Element Method (FEM) and Finite Volume Method (FVM) are routinely used to solve complex partial differential equation (PDE) problems. However, they require significant effort in mesh generation for complex geometries. Mesh generation is a significant bottleneck in practical engineering analysis and design, often becoming the single most time-intensive part of the process for the user. While recent advancements in deep-learning-based methods aim to address these limitations, they are not yet considered a reliable alternative to traditional mesh-based simulations.
An alternative approach to solving spatio-temporal PDEs is offered by meshless methods, which do not require a mesh and simply rely on a collection of points. Neighboring points influence each other but no further geometrical construction is required and all of the complications attached to a traditional mesh are eradicated. These methods are well-suited to addressing common challenges of mesh-based approaches such as negative volumes, highly skewed elements, inefficiencies in discretization and moving boundaries undergoing large deformations. They are particularly advantageous for applications where the geometry was not produced using geometric modeling software. An example is patient-specific cardiovascular simulations, where the geometry is extracted from a medical image. Meshless methods are also well-suited for the integration of Graph Neural Networks (GNNs) within models, as the neighborhoods of influence are naturally represented as graphs. To this end, Macchiato.jl was created to fill a gap in the Julia PDE community of Eulerian meshless methods.
Macchiato.jl is being actively developed alongside two other Julia packages which are the core dependencies - WhatsThePoint.jl and RadialBasisFunctions.jl. Macchiato.jl exposes the APIs relevant to scientists and engineers, while the other two packages are meant to provide the required numerical machinery. WhatsThePoint.jl is responsible for the initial phase of node generation - it contains a set of useful APIs to generate the node clouds necessary for subsequent discretization. RadialBasisFunctions.jl is a general package implementing anything related to Radial Basis Functions (RBF), designed to provide all the functionality required for implementing the Radial Basis Function-Finite Difference (RBF-FD) method - the meshless discretization scheme upon which Macchiato.jl relies.
The scope of this presentation is to announce the package to the Julia community and look for collaboration. Our talk will focus on the high-level architecture of the ecosystem, showing examples, and discussing future directions of development and the challenges still ahead.
I am a scientific software engineer specializing in the development of multiscale and multiphysics models for cardiovascular medicine. My work focuses on creating computational tools to facilitate fundamental medical research and improving clinical outcomes.
PhD in mechanical engineering, quiet life in north-east Italy, mountains and great coffee factories nearby. I don't get to use Julia at work, but use it in my free time a lot for building a new solver with friends from around the world. It's a fresh take on numerical methods for PDEs that I find really exciting and I'd love to talk more about.