def __init__( self, model, time, referenceTimeSeries, forwardTimeSeries, ddConductivity, *args, **kwargs ):
TransientFEModel.__init__( self, model.size )
# Check model type
# The adjoint system is linear with respect to its state, the system
# it's derived from must be nonlinear. A simpler structure is used
# for solving linear systems.
assert type(model) is NonlinearTransientFEModel, "Invalid model type!"
self.femodel = model
self.time = time
self.referenceSolution = referenceTimeSeries
self.forwardSolution = forwardTimeSeries
self.timeIndex = 0
self._load = None
self.nonsymmetricStiffness = None
# Transform model members
# TODO: ddConductivity
self.elements = []
for element in model.elements:
self.elements.append(
AdjointHeatElement1D( element,
self.femodel,
self.forwardSolution,
self.referenceSolution,
ddConductivity ) )
self.computeLoad()
integrationOrder = 2 * polynomialOrder + 1
finiteDifferenceImplicity = 0.5
# Adjoint
numberOfAdjointIterations = 50
regularization = 8.0
# Postprocessing
numberOfSamples = 100
convergencePlot = ConvergencePlot()
# ---------------------------------------------------------
# REFERENCE SOLUTION
# ---------------------------------------------------------
# Initialize FE model
model = TransientFEModel(nElements * polynomialOrder + 1, loadFunction=load)
# Create elements
basisFunctions = IntegratedHierarchicBasisFunctions(
polynomialOrder=polynomialOrder)
initialLoad = lambda x: load(time[0], x)
model.elements = [
LinearHeatElement1D(
capacity,
conductivity, (i * length / nElements, (i + 1) * length / nElements),
np.asarray(range(i * polynomialOrder, (i + 1) * polynomialOrder + 1)),
initialLoad,
basisFunctions=basisFunctions,
integrationOrder=integrationOrder) for i in range(nElements)
]
# Load
load = lambda t, x: 0.0
# Discretization
time = np.linspace(0.0, 1.0, 200)
nElements = 10
polynomialOrder = 3
# Integration
integrationOrder = 2*polynomialOrder + 1
finiteDifferenceImplicity = 0.5
# ---------------------------------------------------------
# Initialize FE model
model = TransientFEModel( nElements*polynomialOrder + 1, loadFunction=load )
# Create elements
basisFunctions = IntegratedHierarchicBasisFunctions( polynomialOrder=polynomialOrder )
initialLoad = lambda x: load( time[0], x )
model.elements = [ LinearHeatElement1D( capacity,
conductivity,
(i*length/nElements, (i+1)*length/nElements),
np.asarray( range(i*polynomialOrder, (i+1)*polynomialOrder+1) ),
initialLoad,
basisFunctions=basisFunctions,
integrationOrder=integrationOrder )
for i in range(nElements) ]
# Integrate
model.allocateZeros( )
def resetMatrices( self, stiffness=True, mass=True, load=False ):
TransientFEModel.resetMatrices( self, stiffness=stiffness, mass=mass, load=load )
if stiffness:
self.nonsymmetricStiffness.data = np.zeros( self.nonsymmetricStiffness.data.shape, dtype=self.nonsymmetricStiffness.data.dtype )
def allocateZeros( self ):
DoFs = TransientFEModel.allocateZeros(self)
self.nonsymmetricStiffness = sparse.csr_matrix( ( np.zeros( DoFs.shape[1] ), DoFs ),
shape=self.shape )
def integrate( self, *args, stiffness=True, mass=True, load=False, **kwargs ):
self.resetMatrices( stiffness=stiffness, mass=mass, load=load )
TransientFEModel.integrate(self,*args,stiffness=stiffness,mass=mass,load=load,**kwargs)
if stiffness:
for element in self.elements:
element.integrateNonsymmetricStiffness(self.nonsymmetricStiffness)