324 citations · 1.1k across the 33 of their papers we have counts for
9 papers · 1 filter
Hybrid multigrid methods for high-order discontinuous Galerkin discretizations
Niklas Fehn, Peter Munch, Wolfgang A. Wall +1
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor produc…
The deal.II finite element library: design, features, and insights
Daniel Arndt, Wolfgang Bangerth, Denis Davydov +7
deal.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. Herein, we outline its primary design…
Propagating geometry information to finite element computations
Luca Heltai, Wolfgang Bangerth, Martin Kronbichler +1
The traditional workflow in continuum mechanics simulations is that a geometry description -- for example obtained using Constructive Solid Geometry or Computer Aided Design tools…
A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators
Martin Kronbichler, Katharina Kormann, Niklas Fehn +2
This work proposes a basis for improved throughput of matrix-free evaluation of discontinuous Galerkin symmetric interior penalty discretizations on hexahedral elements. The basis…
Algorithms and data structures for matrix-free finite element operators with MPI-parallel sparse multi-vectors
Denis Davydov, Martin Kronbichler
Traditional solution approaches for problems in quantum mechanics scale as , where is the number of electrons. Various methods have been proposed to address th…
A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid
Denis Davydov, Jean-Paul Pelteret, Daniel Arndt +1
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix…
High-order DG solvers for under-resolved turbulent incompressible flows: A comparison of and (div) methods
Niklas Fehn, Martin Kronbichler, Christoph Lehrenfeld +2
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-res…
A hybridizable discontinuous Galerkin method for electromagnetics with a view on subsurface applications
Luca Berardocco, Martin Kronbichler, Volker Gravemeier
Two Hybridizable Discontinuous Galerkin (HDG) schemes for the solution of Maxwell's equations in the time domain are presented. The first method is based on an electromagnetic diff…
A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM
Thomas C. Clevenger, Timo Heister, Guido Kanschat +1
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing o…