def computeError4level(self, meanApprox4lvl, lastSpace, meanExact = None):
if meanExact == None:
solMesh = lastSpace.mesh()
solFamily = lastSpace.ufl_element().family()
solDegree = lastSpace.ufl_element().degree()
refSpace = FunctionSpace(refine(refine(solMesh)), solFamily, solDegree)
meanExact = self.solveMean(refSpace)
refSpace = meanExact.function_space()
error4lvl = list(
np.sqrt(assemble(
(project(meanApprox, refSpace) - interpolate(meanExact, refSpace)) ** 2 * dx
)) for meanApprox in meanApprox4lvl)
return error4lvl
def addLevel(self):
self.optNumSamples4Level.append(0)
self.y4Level.append([])
lastSpace = self.space4Level[-1]
lastMesh = lastSpace.mesh()
lastFamiliy = lastSpace.ufl_element().family()
lastDegree = lastSpace.ufl_element().degree()
if self.adaptiveMesh:
solution = self.problem.solveMean(lastSpace)
_, cell_markers = self.problem.estimate(solution)
self.space4Level.append(FunctionSpace(refine(lastMesh, cell_markers),
lastFamiliy, lastDegree))
else:
self.space4Level.append(FunctionSpace(refine(lastMesh),
lastFamiliy, lastDegree))
self.variance4level.append(None)
self.compCost4lvl.append(0)
def __init__(self, coarse_mesh, nref, p_coarse, p_fine, sym=False):
"""
:param dolfin.cpp.mesh.Mesh coarse_mesh:
:param int nref:
:param int p_coarse:
:param int p_fine:
:param bool sym:
:return:
"""
print0("Creating approximation spaces")
self.V_coarse = FunctionSpace(coarse_mesh, "CG", p_coarse)
self.ndof_coarse = self.V_coarse.dim()
refined_mesh = coarse_mesh
for ref in xrange(nref):
refined_mesh = refine(refined_mesh) # creates a new Mesh, initial coarse mesh is unchanged
self.V_fine = FunctionSpace(refined_mesh, "CG", p_fine)
self.ndof_fine = self.V_fine.dim()
H = coarse_mesh.hmax()
h = refined_mesh.hmax()
self.alpha = log(H)/log(h)
self.beta = p_fine + 1
if comm.rank == 0:
prop = Table("Approximation properties")
prop.set("ndof", "coarse", self.ndof_coarse)
prop.set("ndof", "fine", self.ndof_fine)
prop.set("h", "coarse", H)
prop.set("h", "fine", h)
info(prop)
print "alpha = {}, beta = {}".format(self.alpha, self.beta)
self.bc_coarse = None
self.A_fine = PETScMatrix()
self.B_fine = PETScMatrix()
self.A_coarse = PETScMatrix()
self.B_coarse = PETScMatrix()
self.sym = sym
self.switch_gep_matrices = False