Fluid dynamics: Partitioning a mesh for parallel computing.



complex physics simulations, like in Computational Fluid Dynamics, require huge computational resources. A speed-up in the simulation times can be obtained by parallel computing. The original space of the simulation is covered by a discrete mesh, and the mesh is partitioned into a set of disjoint domains. Each domain is associated to a different computer. The mesh partitioning problem has multiple objectives: one aims at a well-balanced partition (sub-domains containing a similar number of nodes) and at a cut of minimum size (the number of edges which are cut is proportional to the number of messages that must flow between different processors, i.e., to the cost of communication).

Objectives of data mining and visualization:

  1. To couple visualization with an iterative mesh-partitioning (graph-partitioning) technique, so that one starts by a partition into two domains, and then iteratively splits each domain into two.
  2. To visualize the tree of solutions. The root of the tree corresponds to the entire mesh. The children of a node correspond to different ways of splitting each domain of the partition corresponding to the parent node.
  3. To identify a proper tradeoff between balance and cut of the partitions.

LIONoso sample visualization(s): Layered navigation

The navigation mode can visualize the multiple levels of the partitioning. By starting from the root and by double-clicking on a node one visualizes the nodes' children. By double-clicking on the background one visualizes the entire set of solutions. Tradeoffs can be studies by the parallel coordinate display or through the scatterplot visualization.




LIONoso 2.1 visualization a data mining image


LIONoso 2.1 visualization a data mining image

Download the LIONoso-ready data file: parallel-computing-mesh-partitioning.lion

References: Image derived from: Strategies for Parallel and Numerical Scalability of CFD Codes Ralf Winkelmann, Jochem Hauser and Roy Williams, Computational Methods in Applied Mechanical Engineering. 174 (3-4): 433-456 (1999).
Download the LIONoso-ready data file:parallel-computing-mesh-partitioning.lion