Tatva (टत्तव) : Lego-like building blocks for FEM

tatva (is a Sanskrit word which means principle or elements of reality). True to its name, tatva provide fundamental Lego-like building blocks (elements) which can be used to construct complex finite element method (FEM) simulations. tatva is purely written in Python library for FEM simulations and is built on top of JAX and Equinox, making it easy to use FEM in a differentiable way.

License

tatva is distributed under the GNU Lesser General Public License v3.0 or later. See COPYING and COPYING.LESSER for the complete terms. © 2025 ETH Zurich (Mohit Pundir).

Features

• Energy-based formulation of FEM operators with automatic differentiation via JAX.
• Capability to handle coupled-PDE systems with multi-field variables, KKT conditions, and constraints.
• Element library covering line, surface, and volume primitives (Line2, Tri3, Quad4, Tet4, Hex8) with consistent JAX-compatible APIs.
• Mesh and Operator abstractions that map, integrate, differentiate, and interpolate fields on arbitrary meshes.
• Automatic handling of stacked multi-field variables through the tatva.compound utilities while preserving sparsity patterns.

Installation

Install the current release from PyPI:

pip install tatva

For development work, clone the repository and install it in editable mode (use your preferred virtual environment tool such as uv or venv):

git clone https://github.com/smec-ethz/tatva.git
cd tatva
pip install -e .

Usage

Create a mesh, pick an element type, and let Operator perform the heavy lifting with JAX arrays:

import jax.numpy as jnp
from tatva.element import Tri3
from tatva.mesh import Mesh
from tatva.operator import Operator

coords = jnp.array([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 1.0]])
elements = jnp.array([[0, 1, 2], [0, 2, 3]])

mesh = Mesh(coords, elements)

op = Operator(mesh, Tri3())
nodal_values = jnp.arange(coords.shape[0], dtype=jnp.float64)

# Integrate a nodal field over the mesh
total = op.integrate(nodal_values)

# Evaluate gradients at all quadrature points
gradients = op.grad(nodal_values)

Examples for various applications will be added very soon. They showcase patterns such as mapping custom kernels, working with compound fields, and sparse assembly helpers.

Dense vs Sparse

A unique aspect of tatva is that it can handle both dense and sparse matrices. This is achieved by using the library sparsejac that allows automatic differentiation of a functional based on a sparsity pattern. This significantly reduces the memory consumption. For more details on how the automatic differentiation can be done using sparsity pattern, please check the link below:

• 
• 
• 

👉 Where to contribute

If you have a suggestion that would make this better, please fork the repo and create a pull request on github.com/smec-ethz/tatva. Please use that repository to open issues or submit merge requests. You can also simply open an issue with the tag "enhancement". Don't forget to give the project a star! Thanks again!

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
3. Commit your Changes (git commit -m 'Add some AmazingFeature')
4. Push to the Branch (git push origin feature/AmazingFeature)
5. Open a Pull Request