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 ecosystem, making it easy to use FEM in a differentiable way.
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 (SMEC).
- 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.compoundutilities while preserving sparsity patterns.
Install the current release from PyPI:
pip install tatvaFor 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 .Available at smec-ethz.github.io/tatva-docs. The documentation includes API references, tutorials, and examples to help you get started with tatva.
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.
A unique aspect of tatva is that it can handle construct dense matrices, sparse matrices, and matrix-free operators. tatva uses matrix-coloring algorithm and sparse differentiation to construct a sparse matrix. We use our own coloring library to color a matrix based on sparsity pattern, one can use other coloring libraries such as
for more advanced coloring algorithms. This significantly reduces the memory consumption. For large problems, we can also use matrix-free operators which do not require storing the matrix in memory. Since we have a energy functional, we can make use of
jax.jvp ti compute the matrix-vector product without explicitly forming the matrix. This is particularly useful for large problems where storing the matrix is not feasible.
To know more about tatva and how it works please check: (arXiv link)
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!
- Fork the Project
- Create your Feature Branch (
git checkout -b feature/AmazingFeature) - Commit your Changes (
git commit -m 'Add some AmazingFeature') - Push to the Branch (
git push origin feature/AmazingFeature) - Open a Pull Request