An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains

We present a spectral element algorithm and open-source code for computing the fractional Laplacian defined by eigenfunction expansion on finite 2D/3D complex domains with both homogeneous nonhomogeneous boundaries. demonstrate scalability of large clusters constructing based computed eigenvalues eigenfunctions using up to thousands CPUs. To accuracy this eigen-based approach factional Laplacian, we approximate solutions diffusion equation 2D quadrilateral, 3D cubic cylindrical domain, compare results contrived fast convergence. Subsequently, simulation hand-shaped domain discretized hexahedra, as well constructed from Hanford site geometry corresponding nonzero Dirichlet boundary conditions. Finally, apply solve surface quasi-geostrophic (SQG) square periodic Simulation accuracy, efficiency, geometric flexibility our that can capture subtle dynamics anomalous modeled domains. The included is first its kind. Program title: Nektarpp_EigenMM CPC Library link program files: https://doi.org/10.17632/whtc75rj55.1 Developer’s repository link: https://github.com/paralab/Nektarpp_EigenMM Licensing provisions: MIT License Programming language: C/C++, MPI Nature problem: An parallel Solution method: A distributed, sparse, iterative developed an associated integer-order Laplace eigenvalue problem use in equation. Additional comments including restrictions unusual features: implemented CPUs super-linear efficiency at extreme scale.