autopdex.models.mixed_reference_domain_potential

autopdex.models.mixed_reference_domain_potential(integrand_fun, ansatz_fun, ref_int_coor, ref_int_weights, mapping_key)[source]

Constructs a multi-field ‘user potential’ for integration of a potential in the reference configuration of finite elements. Works for DOFs as a dict of jnp.ndarrays.

Parameters:

  • integrand_fun (callable) – Function that evaluates the integrand given the integration point, trial ansatz, settings, static settings, and element number.

  • ansatz_fun (dict of callables) – Functions that constructs the ansatz functions for each field. Keywords have to match with those defined in the DOFs dictionary.

  • ref_int_coor (jnp.ndarray) – Reference integration coordinates for the isoparametric element.

  • ref_int_weights (jnp.ndarray) – Reference integration weights for the isoparametric element.

  • mapping_key (string) – Which solution space to use for the isoparametric mapping.

Returns:

function

A function that evaluates the integrand for the isoparametric element.

The returned function has the following parameters:

  • fI (dict of jnp.ndarray): Element nodal values.

  • xI (dict of jnp.ndarray): Element nodal coordinates.

  • elem_number (int): Element number.

  • settings (dict): Settings for the computation.

  • static_settings (dict): Static settings for the computation.

Exemplary integrand function:

–> def integrand_fun(x_int, ansatz_fun, settings, static_settings, elem_number, set): –> # Definition of custom functional –> x = ansatz_fun[‘physical coor’](x_int) # Physical coordinates via isoparametric mapping –> phi_fun = ansatz_fun[‘phi’] # Field approximation function with key words as defined in the DOFs dictionary –> phi = phi_fun(x_int) –> dphi_dx = jax.jacrev(phi_fun)(x_int) –> –> x_1 = x –> x_2 = x - jnp.array([1., 0.5]) –> source_term = 20 * (jnp.sin(10 * x_1 @ x_1) - jnp.cos(10 * x_2 @ x_2)) –> return (1/2) * dphi_dx @ dphi_dx - source_term * phi # Returns a scalar potential that is to be integrated in reference configuration

Notes

This models works for DOFs as a dict of jnp.ndarrays.