## Research Projects

#### Scientific computing and applied mathematics

My main field of research is the discretization and numerical solution
of partial differential equations (PDEs). I develop finite element
and discontinuous Galerkin approaches for various elliptic and hyperbolic
systems of PDEs with a focus on non-conforming meshes and parallel solvers.

In cooperation with geophysicists I am working on science applications,
such as the simulation of thermal convection in the earth's mantle,
and global scale seismic wave propagation, where high performance
computing is essential to achieve the resolution necessary to capture
important physical phenomena.
A related field of interest are Newton-Krylov methods for ill-posed inverse
problems with applications in full waveform inversion for seismology and
uncertainty quantification in the simulation of ice sheets.

#### Scalable algorithms for adaptive mesh refinement

Many physical systems exhibit multiscale phenomena that lend themselves
to simulations using adaptive meshes. On large parallel computers however, and
in particular for problems that require frequent refinement, coarsening, and
repartitioning of the mesh, it is a challenge to perform such
mesh operations efficiently.
I have worked extensively on the forest-of-octrees approach and designed
scalable algorithms for parallel AMR.
These are implemented in the p4est
software library that is available under the GNU GPL version 2 (or later).
p4est has been used as parallel mesh infrastructure for a number of
large-scale simulation projects; see
my publications page for more details.
Another software project related to parallel adaptive mesh refinement that I am
working on is
ForestClaw.