`pymor.models.examples`¶

Module Contents¶

pymor.models.examples.heat_equation_example(grid_intervals=50, nt=50)[source]¶

Return heat equation example with a high-conductivity and two parametrized channels.

Parameters

grid_intervals: Number of intervals in each direction of the two-dimensional RectDomain.
nt: Number of time steps.

Returns

pymor.models.examples.msd_example(n=6, m=2, m_i=4, k_i=4, c_i=1, as_lti=False)[source]¶

Mass-spring-damper model as (port-Hamiltonian) linear time-invariant system.

Taken from [GPBvdS12].

Parameters

n: The order of the model.
m: The number or inputs and outputs of the model.
m_i: The weight of the masses.
k_i: The stiffness of the springs.
c_i: The amount of damping.
as_lti: If True, the matrices of the standard linear time-invariant system are returned. Otherwise, the matrices of the port-Hamiltonian linear time-invariant system are returned.

Returns

A: The LTI NumPy array A, if as_lti is True.
B: The LTI NumPy array B, if as_lti is True.
C: The LTI NumPy array C, if as_lti is True.
D: The LTI NumPy array D, if as_lti is True.
J: The pH NumPy array J, if as_lti is False.
R: The pH NumPy array R, if as_lti is False.
G: The pH NumPy array G, if as_lti is False.
P: The pH NumPy array P, if as_lti is False.
S: The pH NumPy array S, if as_lti is False.
N: The pH NumPy array N, if as_lti is False.
E: The LTI NumPy array E, if as_lti is True, or the pH NumPy array E, if as_lti is False.

pymor.models.examples.penzl_example()[source]¶

Return Penzl’s example.

Returns

pymor.models.examples.thermal_block_example()[source]¶

Return 2x2 thermal block example.

Returns