hyper.deal: An efficient, matrix-free finite-element library for high-dimensional partial differential equations

02/19/2020 ∙ by Peter Munch, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 10

page 29

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.