On the Quality of Partitions Based on Space-Filling Curves
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
A Cache-Aware Algorithm for PDEs on Hierarchical Data Structures Based on Space-Filling Curves
SIAM Journal on Scientific Computing
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
Dendro: parallel algorithms for multigrid and AMR methods on 2:1 balanced octrees
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
DaStGen--A Data Structure Generator for Parallel C++ HPC Software
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part III
A Parallel Geometric Multigrid Method for Finite Elements on Octree Meshes
SIAM Journal on Scientific Computing
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Cluster optimization and parallelization of simulations with dynamically adaptive grids
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
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In this paper, we present a parallel multigrid PDE solver working on adaptive hierarchical cartesian grids. The presentation is restricted to the linear elliptic operator of second order, but extensions are possible and have already been realised as prototypes. Within the solver the handling of the vertices and the degrees of freedom associated to them is implemented solely using stacks and iterates of a Peano space–filling curve. Thus, due to the structuredness of the grid, two administrative bits per vertex are sufficient to store both geometry and grid refinement information. The implementation and parallel extension, using a space–filling curve to obtain a load balanced domain decomposition, will be formalised. In view of the fact that we are using a multigrid solver of linear complexity $\mathcal{O}(n)$, it has to be ensured that communication cost and, hence, the parallel algorithm's overall complexity do not exceed this linear behaviour.