This article presents a systematic quantitative performance study for large finite element
computations on extreme scale computing systems. Three parallel iterative solvers for the …

This text presents contributions to efficient high-order finite element solvers in the context of
the project ExaDG, part of the DFG priority program 1648 Software for Exascale Computing …

This work is based on the seminar titled 'Resiliency in Numerical Algorithm Design for
Extreme Scale Simulations' held March 1–6, 2020, at Schloss Dagstuhl, that was attended …

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin
discretizations of elliptic problems, which are, for example, a key ingredient of …

In this article, a new generic higher-order finite-element framework for massively parallel
simulations is presented. The modular software architecture is carefully designed to exploit …

The computational complexity of naive, sampling-based uncertainty quantification for 3D
partial differential equations is extremely high. Multilevel approaches, such as multilevel …

In this paper, we report on a two-scale approach for efficient matrix-free finite element
simulations. It is an extended version of our previous conference publication [1]. The …

We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes
for saddle point problems. A unified framework to analyze the smoothing properties is …

Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of
physical processes relevant to science and engineering. Multilevel preconditioners …

Extreme scale simulation requires fast and scalable algorithms, such as multigrid methods.
To achieve asymptotically optimal complexity, it is essential to employ a hierarchy of grids …