scrimp.examples

We provide some examples coming from our publications.

The equations are explained here.

Wave

  • file: examples/wave.py

  • authors: Giuseppe Ferraro, Ghislain Haine

  • date: 22 nov. 2022

  • brief: 2D wave equations

examples.wave.wave_eq()

A structure-preserving discretization of the wave equation with mixed boundary control

Formulation DAE (energy/co-energy), Grad-Grad, Mixed boundary condition on the Rectangle Undamped case.

  • file: examples/wave_coenergy.py

  • authors: Giuseppe Ferraro, Ghislain Haine

  • date: 22 nov. 2022

  • brief: wave equations in co-energy formulation, two sub-domains

examples.wave_coenergy.wave_coenergy_eq()

A structure-preserving discretization of the wave equation with boundary control

Formulation co-energy, Grad-Grad, output feedback law at the boundary, damping on a subdomain

Heat

  • file: examples/heat.py

  • authors: Giuseppe Ferraro, Ghislain Haine

  • date: 22 nov. 2022

  • brief: 2D heat equation with Lyapunov Hamiltonian

examples.heat.heat_eq()

A structure-preserving discretization of the heat equation with mixed boundary control

Formulation with substitution of the co-state, Lyapunov L^2 functional, Div-Div, Mixed boundary condition on the Rectangle (including impedance-like absorbing boundary condition).

Heat-Wave coupling

  • file: sandbox/heat_hw.py

  • authors: Giuseppe Ferraro, Ghislain Haine

  • date: 15 dec. 2022

  • brief: a 2D coupled heat-wave system

examples.heat_wave.heat_wave_eq(heat_region=1, wave_region=2)

A structure-preserving discretization of a coupled heat-wave equation

Co-energy formulations, heat: div-div, wave: grad-grad, gyrator interconnection On the Concentric built-in geometry: 1: internal disk, 2: exterior annulus

Args:

heat_region (int): the label of the region where the heat equation lies wave_region (int): the label of the region where the wave equation lies

Shallow water

  • file: examples/shallow_water.py

  • authors: Ghislain Haine

  • date: 22 nov. 2022

  • brief: inviscid shallow water equations

examples.shallow_water.shallow_water_eq()

A structure-preserving discretization of the inviscid shallow-water equation

Formulation Grad-Grad, homogeneous boundary condition, on a tank