In many applications involving incompressible fluid flow, the Stokes system plays an
important role. Complex flow problems may require extremely fine resolutions, easily …

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

In this work, we extend Achi Brandt's notion of textbook multigrid efficiency (TME) to
massively parallel algorithms. Using a finite element based geometric multigrid …

Multigrid solvers for semistructured meshes are developed. Such semistructured meshes
provide flexibility to address complex computational domains while still allowing most …

The adjoint method is a computationally efficient way to compute the gradient of a physical
observable or an associated objective function relative to its parameters. In geodynamics the …

Fault tolerant massively parallel multigrid methods for elliptic partial differential equations
are a step towards resilient solvers. Here, we combine domain partitioning with geometric …

Multigrid and related multilevel methods are the approaches of choice for solving linear
systems that result from discretization of a wide class of PDEs. A large gap, however, exists …

Biological structures are hierarchical and non-homogeneous objects. In particular, in each
type of the biological cell various organelles exist. Also, in the cell many nonlinear …

Stencil computations are widely used to simulate the change of state of physical systems
across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in …