1. Module reducedbasis

1.1. Import

The work has not yet been merged in develop. To include the module at current state, you need to checkout the branch feature/pyrb, and move to the directory mor/pyfeelpp-mor/feelpp/mor.

Line to import the module :

from reducedbasis.reducedbasis import *

To set the environment, those module also need to be imported :

import sys
from feelpp.toolboxes.heat import *
from feelpp.toolboxes.core import *
from feelpp.mor import *
import feelpp

1.2. Set the model

To declare the objects, use these lines :

DIM = 2
heatBox=heat(dim=DIM,order=1)
heatBox.init()
model = toolboxmor(dim=DIM, time_dependent=False)
model.setFunctionSpaces( Vh=heatBox.spaceTemperature())

  • DIM is the dimension of the case (should be 2 or 3)

  • time_dependent depends if the case is time-steady or time-dependant.

Those functions define how the DEIM matrix and right-hand side are updated according to the parameter mu.

def assembleDEIM(mu):
    for i in range(0,mu.size()):
        heatBox.addParameterInModelProperties(mu.parameterName(i),mu(i))
    heatBox.updateParameterValues()
    return heatBox.assembleRhs()

def assembleMDEIM(mu):
    for i in range(0,mu.size()):
        heatBox.addParameterInModelProperties(mu.parameterName(i),mu(i))
    heatBox.updateParameterValues()
    return heatBox.assembleMatrix()

model.setAssembleDEIM(fct=assembleDEIM)
model.setAssembleMDEIM(fct=assembleMDEIM)
model.initModel()
When the function assembleDEIM is called, the value of the parameters of the object heatBox is updated.

Creation of DEIM and MDEIM toolboxes, with the associated assembly functions.

heatBoxDEIM=heat(dim=DIM,order=1)
meshDEIM = model.getDEIMReducedMesh()
heatBoxDEIM.setMesh(meshDEIM)
heatBoxDEIM.init()

def assembleOnlineDEIM(mu):
    for i in range(0,mu.size()):
        heatBoxDEIM.addParameterInModelProperties(mu.parameterName(i),mu(i))
    heatBoxDEIM.updateParameterValues()
    return heatBoxDEIM.assembleRhs()

model.setOnlineAssembleDEIM(assembleOnlineDEIM)

heatBoxMDEIM=heat(dim=DIM,order=1)
meshMDEIM = model.getMDEIMReducedMesh()
heatBoxMDEIM.setMesh(meshMDEIM)
heatBoxMDEIM.init()

def assembleOnlineMDEIM(mu):
    for i in range(0,mu.size()):
        heatBoxMDEIM.addParameterInModelProperties(mu.parameterName(i),mu(i))
    heatBoxMDEIM.updateParameterValues()
    return heatBoxMDEIM.assembleMatrix()

model.setOnlineAssembleMDEIM(assembleOnlineMDEIM)

Then finalize the initialization :

model.postInitModel()
model.setInitialized(True)

1.3. Access to a parameter

Dmu = model.parameterSpace()
mu = Dmu.element(True, False)

See the dedicated page for the API of ParameterSpaceElement