hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations
Abstract
This work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal.II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results of the library hyper.deal are reported for high-dimensional advection problems and for the solution of the Vlasov--Poisson equation in up to 6D phase space.
Cite
@article{arxiv.2002.08110,
title = {hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations},
author = {Peter Munch and Katharina Kormann and Martin Kronbichler},
journal= {arXiv preprint arXiv:2002.08110},
year = {2020}
}
Comments
33 pages, 18 figures