pymor.models.examples

Module Contents

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

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)

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)

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)

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()

Return Penzl’s example.

Returns

fom

Penzl’s FOM example as an LTIModel.

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

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)

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)

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.