Mantle convection is the fundamental physical process within earth's interior responsible for
the thermal and geological evolution of the planet, including plate tectonics. The mantle is …

This article presents matrix-free finite-element techniques for efficiently solving partial
differential equations on modern many-core processors, such as graphics cards. We …

This study presents a fair performance comparison of the continuous finite element method,
the symmetric interior penalty discontinuous Galerkin method, and the hybridized …

Algebraic Multigrid (AMG) is a widely used technique for solving large, sparse linear
systems arising in various scientific and engineering applications. While AMG has shown …

Algebraic Multigrid (AMG) is a widely used numerical technique for solving large-scale
linear systems in various fields of computer science, such as computer graphics …

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

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

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning
techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite …

Multigrid methods are popular solution algorithms for many discretized PDEs, either as
standalone iterative solvers or as preconditioners, due to their high efficiency. However, 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 …