autopdex.geometry.transfinite_interpolation

autopdex.geometry.transfinite_interpolation(x, boundary_psdfs, boundary_conditions)

Transfinite interpolation using positive smooth distance functions (PSDFs) and boundary conditions.

Parameters:

• x (jnp.ndarray) – The point where the interpolation is evaluated.

• boundary_psdfs (list of callable) – List of PSDF functions, each defining a boundary.

• boundary_conditions (list of callable) – List of boundary condition functions corresponding to the PSDF functions.

Returns:

The interpolated value at point x based on the boundary PSDFs and boundary conditions.

Return type:

jnp.ndarray

Notes

This function uses an unstable version of transfinite interpolation at the boundary. Usually one can simply delete all integration points (and in case of collocation also nodes) on the boundary. A more stable but inefficient version (commented out) can be used if stability issues arise.