PyNucleus

PyNucleus is a finite element code that specifically targets nonlocal operators of the form

$\int_{\mathbb{R}^d} [u(x)-u(y)] \gamma(x, y) dy $

for nonlocal kernels $\gamma$ with finite or infinite horizon and of integrable or fractional type. Specific examples of such operators include the integral and regional fractional Laplacians, their truncated and tempered variants, and operators arising from peridynamics.

The package aims to provide efficient discretization and assembly routines with $O(N \log N)$ quasi-optimal complexity. The resulting sets of equations can be solved using optimal linear solvers. The code is fully NumPy/SciPy compatible, allowing easy integration into application codes.