As a fellow I’ve worked on two main topics.
One is modeling ice-sheet dynamics. I model the flow of ice sheets with an emphasis on accurate discretization: using higher-order, mixed finite elements with adaptive refinement to resolve important flow features. I have developed a scalable solver framework for the nonlinear Stokes equations that govern the flow of ice sheets. The solver demonstrates robust convergence for multiple orders of approximation on highly distorted nonconforming meshes, and for varying material parameters. Good convergence has been demonstrated on a mesh of the Antarctic ice sheet, on problems scaling to 16,000 cores of the Texas Advanced Computing Center’s Stampede supercomputer.
The other is the development of algorithms for adaptive mesh refinement (AMR). I contribute to the p4est library, a library of algorithms for AMR designed to be highly scalable and suitable for a wide variety of applications. The main concept behind p4est, the octree, is quite simple: starting with a single cube, we recursively split each cube that is too large into eight smaller cubes until the desired mesh is achieved. I will give an example of how algorithms for octrees can have surprisingly complex subproblems with surprising solutions.
