def test_marking():
# PDE data
# ========
# define source term and diffusion coefficient
# f = Expression("10.*exp(-(pow(x[0] - 0.6, 2) + pow(x[1] - 0.4, 2)) / 0.02)", degree=3)
f = Constant("1.0")
diffcoeff = Constant("1.0")
# setup multivector
#==================
# solution evaluation function
def eval_poisson(vec=None):
if vec == None:
# set default vector for new indices
# mesh0 = refine(Mesh(lshape_xml))
mesh0 = UnitSquare(4, 4)
fs = FunctionSpace(mesh0, "CG", 1)
vec = FEniCSVector(Function(fs))
pde = FEMPoisson()
fem_A = pde.assemble_lhs(diffcoeff, vec.basis)
fem_b = pde.assemble_rhs(f, vec.basis)
solve(fem_A, vec.coeffs, fem_b)
return vec
# define active multiindices
mis = [Multiindex([0]),
Multiindex([1]),
Multiindex([0, 1]),
Multiindex([0, 2])]
# setup initial multivector
w = MultiVectorWithProjection()
Marking.refine(w, {}, mis, eval_poisson)
logger.info("active indices of after initialisation: %s", w.active_indices())
# define coefficient field
# ========================
# define coefficient field
a0 = Expression("1.0", element=FiniteElement('Lagrange', ufl.triangle, 1))
# a = [Expression('2.+sin(2.*pi*I*x[0]+x[1]) + 10.*exp(-pow(I*(x[0] - 0.6)*(x[1] - 0.3), 2) / 0.02)', I=i, degree=3,
a = (Expression('A*cos(pi*I*x[0])*cos(pi*I*x[1])', A=1 / i ** 2, I=i, degree=2,
element=FiniteElement('Lagrange', ufl.triangle, 1)) for i in count())
rvs = (NormalRV(mu=0.5) for _ in count())
coeff_field = ParametricCoefficientField(a, rvs, a0=a0)
# refinement loop
# ===============
theta_eta = 0.3
theta_zeta = 0.8
min_zeta = 1e-10
maxh = 1 / 10
theta_delta = 0.8
refinements = 1
for refinement in range(refinements):
logger.info("*****************************")
logger.info("REFINEMENT LOOP iteration %i", refinement + 1)
logger.info("*****************************")
# evaluate residual and projection error estimates
# ================================================
mesh_markers_R, mesh_markers_P, new_multiindices = Marking.estimate_mark(w, coeff_field, f, theta_eta,
theta_zeta, theta_delta, min_zeta, maxh)
mesh_markers = mesh_markers_R.copy()
mesh_markers.update(mesh_markers_P)
Marking.refine(w, mesh_markers, new_multiindices.keys(), eval_poisson)
# show refined meshes
plot_meshes = False
if plot_meshes:
for mu, vec in w.iteritems():
plot(vec.basis.mesh, title=str(mu), interactive=False, axes=True)
plot(vec._fefunc)
interactive()
