autopdex.models.heat_equation_fos

autopdex.models.heat_equation_fos(diffusivity_fun)[source]

Space-time heat equation with thermal diffusivity alpha as a first order system with curl-augmentation for more than 2 spatial dimensions

  • supports n_dim = 2 to n_dim = 3, i.e. 1 to 3 spatial dimensions plus one time dimension

  • number of fiels: n_dim (1 temperature field, n_dim-1 spatial gradients)

  • last dimension is the time dimension, the remaining ones are spacial dimensions

e.g. n_dim = 2: - first dimension is x-dimension, second dimension is time dimension - first field is temperature, second field is derivative of temperature with respect to x

Parameters:

diffusivity_fun (function) – Function to compute the thermal diffusivity.

Returns:

Function to compute the PDE residual.

Return type:

heat_fun (function)

Notes

  • This models works for DOFs as a jnp.ndarray.