Mesh Partitioning

Code parallelization requires the distribution of data over several processors. In the CVFE scheme, we distribute the nodal, volumetric and cohesive data and connectivities. The data includes such information as nodal displacements, velocities and accelerations, material properties of the elements as well as various other flags. The connectivity information includes the lists of all nodes connected to each element of a chunk. A simple representation of a CVFE mesh is presented in Figure 2.25 with the corresponding connectivity information in Table 2.2.

Figure 2.25: Simple CVFE mesh.

Table 2.2: Simple CVFE mesh connectivities.

Element	Node List
Volumetric - V1	1, 2, 3
Volumetric - V2	2, 3, 5
Volumetric - V3	4, 6, 8
Volumetric - V4	7, 9, 10
Volumetric - V5	9, 10, 11
Cohesive - C1	3, 4, 5, 6
Cohesive - C2	6, 7, 8, 9

Partitioning of the simple mesh into two chunks, A and B, is performed along the boundary line. All of the boundary elements, volumetric or cohesive, are partitioned along their edges so that they are fully defined in only a single chunk. Previous partitioning methods would partition a cohesive mesh by splitting the cohesive elements across two chunks. Once partitioned, each element and node must be renumbered locally so that the loop boundaries in the code will not have to be adjusted. The global numbering is also maintained so that the mesh can be reassembled at any time into its original form. Table 2.3 shows the result of partitioning the simple mesh into the two chunks. Note that nodes $A5$ and $B1$ were node $4$ of the original mesh - likewise nodes $A6$ and $B2$ were node $6$. These nodes are now shared between the two chunks.

Figure 2.26: Partitioned CVFE mesh.

Table 2.3: Partitioned CVFE mesh connectivities.

Chunk A
Element	Node List
Volumetric - AV1	1, 2, 3
Volumetric - AV2	2, 3, 4
Cohesive - AC1	3, 4, 5, 6

Chunk B
Element	Node List
Volumetric - BV1	1, 2, 4
Volumetric - BV2	3, 5, 6
Volumetric - BV3	5, 6, 7
Cohesive - BC1	2, 3, 4, 5