# LION COMMUNITY USAGE CASE

### Fluid dynamics: Partitioning a mesh for parallel computing.

### Data:

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:

- 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.
- 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.
- 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.

**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**