Updated 23 Aug 24
Selecting an appropriate shape parameter for radial basis function mappings can be a bit tricky.
To simplify this task, you can find the script rbfShape.py in the preCICE repository.
Given the width of the mesh and the amount of vertices to cover by the support radius, this script calculates an appropriate shape parameter for Gaussian basis-functions. The script also allows to specify a custom decay.
This solves the following equation:
\[\text{shape} = \frac{\sqrt{-log(\text{decay})}}{\text{vertices} \cdot \text{meshwidth}}\]Find more information about tuning the parameters of the RBF radial basis functions in Radial Basis Function Interpolation for Black-Box Multi-Physics Simulations and in further papers (see literature guide).
Version:
Since preCICE v3, just use the default partition-of-unity mapping. This script is mainly relevant for earlier versions, when tuning the shape parameter was crucial.