pymordemos.heat

Module Contents

pymordemos.heat.fom_properties(fom, w, stable_lti=True)

Show properties of the full-order model.

Parameters

fom

The full-order Model from iosys or a TransferFunction.

w

Array of frequencies.

stable_lti

Whether the FOM is stable (assuming it is an LTIModel).

pymordemos.heat.main(diameter: float = Argument(0.1, help='Diameter option for the domain discretizer.'), r: int = Argument(5, help='Order of the ROMs.'))

2D heat equation demo.

Discretization of the PDE:

$$\begin{array}{r}\begin{array}{rlr}{\partial }_{t}z(x,y,t)& =\mathrm{\Delta }z(x,y,t),& 0<x,y<1,t>0\\ -\mathrm{\nabla }z(0,y,t)\cdot n& =z(0,y,t)-u(t),& 0<y<1,t>0\\ -\mathrm{\nabla }z(1,y,t)\cdot n& =z(1,y,t),& 0<y<1,t>0\\ -\mathrm{\nabla }z(x,0,t)\cdot n& =z(x,0,t),& 0<x<1,t>0\\ -\mathrm{\nabla }z(x,1,t)\cdot n& =z(x,1,t),& 0<x<1,t>0\\ z(x,y,0)& =0& 0<x,y<1\\ y(t)& ={\int }_0^{1}z(1,y,t)dy,& t>0\end{array}\end{array}$$

where $u(t)$ is the input and $y(t)$ is the output.

pymordemos.heat.run_mor_method(fom, w, reductor, reductor_short_name, r, stable=True, **reduce_kwargs)

Run a model order reduction method.

Parameters

fom

The full-order Model from iosys or a TransferFunction.

w

Array of frequencies.

reductor

The reductor object.

reductor_short_name

A short name for the reductor.

r

The order of the reduced-order model.

stable

Whether the FOM is stable.

reduce_kwargs

Optional keyword arguments for the reduce method.