pymor.models.examples

Module Contents

pymor.models.examples.heat_equation_1d_example(diameter=0.01, nt=100)[source]

Return parametric 1D heat equation example with one output.

Parameters:

  • diameter – Diameter option for the domain discretizer.

  • nt – Number of time steps.

Returns:

fom – Heat equation problem as an InstationaryModel.

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:

fom – Heat equation problem as an InstationaryModel.

pymor.models.examples.heat_equation_non_parametric_example(diameter=0.1, nt=100)[source]

Return non-parametric heat equation example with one output.

Parameters:

  • diameter – Diameter option for the domain discretizer.

  • nt – Number of time steps.

Returns:

fom – Heat equation problem as an InstationaryModel.

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:

fom – Mass-spring-damper model as an LTIModel (if as_lti is True) or PHLTIModel (if as_lti is False).

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

Return Penzl’s example.

Returns:

fom – Penzl’s FOM example as an LTIModel.

pymor.models.examples.penzl_mimo_example(n, m=2, p=3)[source]

Return modified multiple-input multiple-output Penzl’s example.

Parameters:

n – Model order.

Returns:

fom – Penzl’s FOM example as an LTIModel.

pymor.models.examples.thermal_block_example(diameter=1 / 100)[source]

Return 2x2 thermal block example.

Parameters:

diameter – Grid element diameter.

Returns:

fom – Thermal block problem as a StationaryModel.

pymor.models.examples.transfer_function_delay_example(tau=1, a=-0.1)[source]

Return transfer function of a 1D system with input delay.

Parameters:

  • tau – Time delay.

  • a – The matrix A in the 1D system as a scalar.

Returns:

tf – Delay model as a TransferFunction.