A notional example of geometry mesh parallel decomposition options available in MCATK. (a) Original 3 × 4 rectangular mesh geometry. The original mesh is shown with no decomposition applied. (b) Domain Replication: The mesh is replicated on four processes, resulting in each process holding an identical copy of the entire geometry. (c) Domain Decomposition: The mesh is decomposed into four segments, each containing a unique portion of the geometry. Each process holds one segment. (d) Hybrid Decomposition: A combination of domain decomposition and replication, where the mesh is divided into two segments, with each process holding two replicas of each segment.