def prepare_rhs(A, w, coeff_field, pde):
b = 0 * w
zero = Multiindex()
b[zero].coeffs = pde.assemble_rhs(basis=b[zero].basis, coeff=coeff_field.mean_func,
withNeumannBC=True)
f = pde.f
if f.value_rank() == 0:
zero_func = Constant(0.0)
else:
zero_func = Constant((0.0,) * f.value_size())
zero_func = zero_function(b[zero].basis._fefs)
for m in range(w.max_order):
eps_m = zero.inc(m)
am_f, am_rv = coeff_field[m]
beta = am_rv.orth_polys.get_beta(0)
if eps_m in b.active_indices():
g0 = b[eps_m].copy()
g0.coeffs = pde.assemble_rhs(basis=b[eps_m].basis, coeff=am_f, withNeumannBC=False, f=zero_func) # this equates to homogeneous Neumann bc
pde.set_dirichlet_bc_entries(g0, homogeneous=True)
b[eps_m] += beta[1] * g0
g0 = b[zero].copy()
g0.coeffs = pde.assemble_rhs(basis=b[zero].basis, coeff=am_f, f=zero_func)
pde.set_dirichlet_bc_entries(g0, homogeneous=True)
b[zero] += beta[0] * g0
return b
# PART A: Simulation Options
# ============================================================
# initial mesh elements
initial_mesh_N = CONF_initial_mesh_N
# plotting flag
PLOT_SOLUTION = False
# ============================================================
# PART B: Problem Setup
# ============================================================
# define initial multiindices
mis = list(Multiindex.createCompleteOrderSet(CONF_initial_Lambda, 1))
#mis = list(Multiindex.createCompleteOrderSet(0, 1))
#mis = [mis[0], mis[2]]
#mis = [mis[0]]
print "MIS", mis
# setup domain and meshes
mesh0, boundaries, dim = SampleDomain.setupDomain(CONF_domain, initial_mesh_N=initial_mesh_N)
if RANDOM_MESHES:
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=10, randref=(0.5, 0.4))
else:
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=0)
# define coefficient field
# NOTE: for proper treatment of corner points, see elasticity_residual_estimator
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials", "constant")
domain = "square"
# initial mesh elements
initial_mesh_N = 5 * 8
# decay exponent
decay_exp = 2
# ============================================================
# PART B: Problem Setup
# ============================================================
# define initial multiindices
mis = list(Multiindex.createCompleteOrderSet(1, 1))
# mis = list(Multiindex.createCompleteOrderSet(0, 1))
# print mis
# os.sys.exit()
# setup meshes
mesh0 = UnitInterval(initial_mesh_N)
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=0)
w = SampleProblem.setupMultiVector(dict([(mu, m) for mu, m in zip(mis, meshes)]), setup_vec)
# define coefficient field
rvs = lambda i: UniformRV(a=-1, b=1)
a0 = Constant(1.0)
a = lambda i: Expression("B", B=1.0 / (4.0 + i * i))
coeff_field = ParametricCoefficientField(a0, a, rvs)