Parallel Sparse Grids

Sparse grids provide an efficient representation of discrete solutions of partial differential equations with a competitive advantage especially for higher dimensional problems. They are mainly based on specific tensor products of one dimensional multi-resolution schemes and easily allow for adaptive grid refinement.

We present a key based addressing scheme for the nodes of the sparse grid. Along with a hash table storage this proves to be superior to conventional tree data structures. We propose a parallelization strategy for codes with adaptive grid refinement, which is based on space-filling curves. This results in a cheap, parallel partitioning and mapping algorithm, which can be executed whenever new workload is created due to local grid refinement.