# Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion

@article{Vollmann2019ExploitingMT, title={Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion}, author={Christian Vollmann and Volker Schulz}, journal={Computing and Visualization in Science}, year={2019}, volume={20}, pages={29-46} }

We present a finite element implementation for the steady-state nonlocal Dirichlet problem with homogeneous volume constraints. Here, the nonlocal diffusion operator is defined as integral operator characterized by a certain kernel function. We assume that the domain is an arbitrary d-dimensional hyperrectangle and the kernel is translation and reflection invariant. Under these assumptions, we carefully analyze the structure of the stiffness matrix resulting from a continuous Galerkin method…

## 6 Citations

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