High performance adaptive finite element methods

Niclas Jansson
Department of High Performance Computing and Visualization
School of Computer Science and Communication
KTH, Stockholm


The massive computational cost for resolving all turbulent scales makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations for complex geometries with error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph.We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than 12k cores.