Paper Info
Title
hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations
Abstract
AbstractThis work presents the efficient, matrix-free finite-element library hyper.deal for solving partial differential equations in two up 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 obtained with the library hyper.deal are reported for high-dimensional advection problems and for the solution of the Vlasov–Poisson equation in up to six-dimensional phase space.
Year
DOI
Venue
2021
10.1145/3469720
ACM Transactions on Mathematical Software
Keywords
DocType
Volume
Matrix-free operator evaluation, discontinuous Galerkin methods, high-dimensional, high-order, Vlasov-Poisson equation, MPI-3.0 shared memory
Journal
47
Issue
ISSN
Citations 
4
0098-3500
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Munch Peter100.34
Katharina Kormann2264.97
Martin Kronbichler332331.00