Getting Started¤

tatva: Lego-like building blocks for differentiable FEM

tatva (तत्त्व) is a Sanskrit word meaning principle or elements of reality. True to its name, tatva provides fundamental Lego-like building blocks (elements) which can be used to construct complex finite element method (FEM) simulations as energy functionals. tatva is a pure Python library for FEM simulations and is built on top of JAX ecosystem, making it easy to use FEM in a differentiable way.

Hertzian Contact

Surface Advection Diffusion

Cohesive Fracture

Energy-Centric Solver

Energy-based formulation of FEM operators with automatic differentiation via JAX. Just write energy and differentiate it directly.

Versitality

Operator abstractions that map, integrate, differentiate on arbitrary meshes. Capability to handle mixed-dimension coupling, multi-point constaints, and more.

High Performance

Built-in sparse differentiation via coloring and matrix-free assembly tailored for mordern architecture such as GPUs.

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 .

Quick Example¤

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)