InitiateNodeToNodes

Inheritence

This method is inherited from the AbstractMesh class.

InitiateNodeToNodes

The obj_InitiateNodetoNodes method builds the node-to-node connectivity mapping in an AbstractMesh object. This mapping represents the topological relationship between nodes in the mesh, creating a graph structure where each node knows which other nodes it's connected to through mesh elements.

• In other words, it generates info of node-numbers in mesh surrounding a node number
• This mapping is stored inside obj%nodeData%globalNodeNum
• For a local node number i, obj%nodeData(i)%globalNodeNum denotes the global node data surrounding the local node number.
• This list does not include self node.
• The method needs node-to-elements data, therefore if this data is not initiated, then this method calls InitiateNodeToElements().

Purpose

This method establishes a critical data structure that identifies all adjacent nodes for each node in the mesh. The node-to-node connectivity map is essential for:

• Implementing finite element and finite volume methods
• Supporting mesh smoothing algorithms
• Applying boundary conditions along interfaces
• Facilitating graph-based operations on the mesh
• Implementing node-based solvers
• Supporting domain decomposition
• Implementing jump-based stabilization techniques

Interface

INTERFACE
  MODULE SUBROUTINE InitiateNodetoNodes(obj)
    CLASS(AbstractMesh_), INTENT(INOUT) :: obj
  END SUBROUTINE InitiateNodetoNodes
END INTERFACE

• obj (INTENT(INOUT)) - The AbstractMesh_ object for which to create the node-to-node connectivity map

Algorithm

1. If the mapping is already initialized (obj%isNodeToNodesInitiated is true), the method returns immediately
2. If node-to-element mapping isn't initialized, it calls obj%InitiateNodeToElements() first
3. Sets the initialization flag to true
4. For each node in the mesh:
   • Initializes a boolean array to track which nodes have been found
   • Gets all elements that contain this node
   • For each connected element:
     • Retrieves all nodes in this element
     • Adds each node to the current node's list of connections (except self)
     • Marks nodes as found to avoid duplicates
   • Finalizes the node's connection list

Implementation Details

• Uses a chunk-based allocation strategy for efficient list building
• The chunk_size parameter (set to 64) controls memory allocation growth
• Uses a boolean array found to prevent duplicate entries
• Performance timing is available when obj%showTime is enabled
• Debug information is provided when compiled with debug flags

Data Structures Modified

• obj%nodeData(inode)%ptr%globalNodes - For each node, stores the list of global node numbers connected to this node
• obj%isNodeToNodesInitiated - Flag indicating the node-to-node mapping has been built

Performance Considerations

• Time complexity is O(n × e × m) where n is the number of nodes, e is the average number of elements per node, and m is the average number of nodes per element
• Memory usage scales with the total number of node-node connections in the mesh
• For densely connected meshes, this operation can be memory-intensive
• The chunk-based allocation strategy helps reduce memory reallocation overhead

Usage Example

TYPE(Mesh_) :: mesh
! ... Initialize mesh ...

! Build node-to-node connectivity
CALL mesh%InitiateNodeToNodes()

! Now we can easily find all nodes connected to a specific node
connectedNodes = mesh%GetNodeToNodes(globalNode=nodeNum, includeSelf=.FALSE.)

Dependencies

This method depends on:

• Node-to-element connectivity (must be initialized first)
• NodeData_ExpandGlobalNodes for growing the node lists
• NodeData_GetTotalGlobalElements for querying element list sizes
• NodeData_GetPointerToGlobalElements for accessing element lists

Notes

• The node-to-node mapping does not include self-connections (a node is not considered connected to itself)
• The connectivity map represents the topological connectivity through mesh elements, not geometric proximity