### 16.1.7. Directional Recursive Coordinate Bisection

The Recursive Coordinate Bisection method recursively splits the domain into two parts using the x-, y-, or the z-coordinate direction (the choice depends on the biggest extension). This will geometrically lead to “cubic” partitions, but does not take into account the different mesh resolution in the three possible coordinate directions. Only the vertex coordinates are required for the partitioning. The graph (vertex/element connectivity) is not required, which makes this method very efficient.

In order to further improve the Recursive Coordinate Bisection method, there is the Optimized Recursive Coordinate Bisection method. Unlike the Recursive Bisection method, this method uses a graph to decide which coordinate direction has to be used for the bisection at each recursion level. The Directional Recursive Coordinate Bisection method is similar to the Optimized Recursive Coordinate Bisection, but is not limited to the three coordinate directions.

With respect to efficiency and partition quality (overlap region minimization), the methods can be ordered as follows, showing decreasing efficiency (increased CPU time and memory requirements) but better partitioning quality:

1. Recursive Coordinate Bisection

2. Optimized Recursive Coordinate Bisection

3. Directional Recursive Coordinate Bisection.

The best (but most expensive) partitioning method (Directional Recursive Coordinate Bisection) is still cheaper than Multilevel Graph Partitioning Software - MeTiS, but generates partitions of similar quality.

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