Radial Basis Functions

For transfers of intensive variables between volumes, Radial Basis Functions (RBF) are used to generate target data for overlapping target locations.

The location of the source data determines the RBF algorithm used to map data to overlapping target mesh locations (either element centroids, mesh nodes, or point cloud nodes), as illustrated in the diagrams below.

  • When source points are on mesh nodes:

    • A node-based RBF algorithm maps the data to overlapping target locations.

    • Non-overlapping target locations receive values from the nearest source point value.

  • When source points are on element centroids:

    • An element-based RBF algorithm maps the data to overlapping target locations.

    • Non-overlapping target locations receive values from the centroid of the intersecting element.

Generation of target data on non-overlapping locations is not applicable for point cloud-to-point cloud mapping.


  • For volumes, the element-based RBF algorithm, which performs mapping directly on the element centroids, is used by default. A beta setting allows you to revert to the node-based RBF algorithm, which reconstructs elemental data on element nodes and then performs mapping on the reconstructed data.

  • For surfaces, the element-based RBF algorithm is available as a beta feature.

Note:  For details, see Activate System Coupling Hidden Features.


Figure 4: Example input and output for Radial Basis Function mapping

Example input and output for Radial Basis Function mapping

Mapping weights are generated using radial basis functions (RBFs) for the source nodes or centroids that define the associated source elements. Example weights are shown in the figure below.

Figure 5: Example mapping weights wi generated for a target node (T), based on the distance to nodes with the associated source elements Si via Radial Basis Function mapping

Example mapping weights wi generated for a target node (T), based on the distance to nodes with the associated source elements Si via Radial Basis Function mapping