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Figure [\[fig:domain_partitioning\]](#fig:domain_partitioning){reference-type="ref" reference="fig:domain_partitioning"} formally illustrates the aforementioned analogy. It shows a 3-D domain and the directions of the axes. The domain is divided in the X-direction _only_ among the MPI processes i.e. the 3-D domain is partitioned in a single dimension only (1-D domain partitioning - imagine slices of a bread). It is important to note that the direction of the axes of BioFVM-X/PhysiCell-X is different from the directions of the axes of MPI Cartesian Topology (An MPI Cartesian Topology is a _virtual_ arrangement of processes.). In this specific case, the whole 3-D domain is partitioned among 4 MPI processes (shown in gray, green, blue and red). This Cartesian Topology is $1 \\times 4 \\times 1$, indicating that we have 1 MPI process in the X-direction, 4 in the Y-direction and 1 in the Z-direction. Please note we have 4 processes in the Y-direction of the MPI Cartesian Topology because _the X-axis of BioFVM-X/PhysiCell-X is equivalent to the Y-axis of the MPI Topology_. Each of these sub-partitions (formally called sub-domains) can be located with the help of MPI Cartesian coordinates. Process 0 (formally called Rank 0) has coordinates $(0,0,0)$, process 1 (Rank 1) has $(0,1,0)$, process 2 (Rank 2) has $(0,2,0)$ and process 4 (Rank 3) has coordinates $(0,3,0)$. Within each sub-domain managed by a single MPI process, the wavy, dark, solid lines indicate OpenMP threads.
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Figure [\[fig:domain_partitioning\]](#fig:domain_partitioning){reference-type="ref" reference="fig:domain_partitioning"} formally illustrates the aforementioned analogy. It shows a 3-D domain and the directions of the axes. The domain is divided in the X-direction _only_ among the MPI processes i.e. the 3-D domain is partitioned in a single dimension only (1-D domain partitioning - imagine slices of a bread). It is important to note that the direction of the axes of BioFVM-X/PhysiCell-X is different from the directions of the axes of MPI Cartesian Topology (An MPI Cartesian Topology is a _virtual_ arrangement of processes.). In this specific case, the whole 3-D domain is partitioned among 4 MPI processes (shown in gray, green, blue and red). This Cartesian Topology is 1 x 4 x 1, indicating that we have 1 MPI process in the X-direction, 4 in the Y-direction and 1 in the Z-direction. Please note we have 4 processes in the Y-direction of the MPI Cartesian Topology because _the X-axis of BioFVM-X/PhysiCell-X is equivalent to the Y-axis of the MPI Topology_. Each of these sub-partitions (formally called sub-domains) can be located with the help of MPI Cartesian coordinates. Process 0 (formally called Rank 0) has coordinates (0,0,0), process 1 (Rank 1) has (0,1,0), process 2 (Rank 2) has (0,2,0) and process 4 (Rank 3) has coordinates (0,3,0). Within each sub-domain managed by a single MPI process, the wavy, dark, solid lines indicate OpenMP threads.
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