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()
def AdaptiveSolver(A, coeff_field, pde,
mis, w0, mesh0, degree,
gamma=0.9,
cQ=1.0,
ceta=6.0,
# marking parameters
theta_eta=0.4, # residual marking bulk parameter
theta_zeta=0.1, # projection marking threshold factor
min_zeta=1e-8, # minimal projection error to be considered
maxh=0.1, # maximal mesh width for projection maximum norm evaluation
newmi_add_maxm=20, # maximal search length for new new multiindices (to be added to max order of solution w)
theta_delta=10.0, # number new multiindex activation bound
max_Lambda_frac=1 / 10, # max fraction of |Lambda| for new multiindices
marking_strategy="SEPARATE with CELLPROJECTION", # separate (as initially in EGSZ) or relative marking wrt overall error, projection refinement based on cell or mesh errors
# residual error
quadrature_degree= -1,
# projection error
projection_degree_increase=1,
refine_projection_mesh=1,
# pcg solver
pcg_eps=1e-6,
pcg_maxiter=100,
# adaptive algorithm threshold
error_eps=1e-2,
# refinements
max_refinements=5,
max_dof=1e10,
do_refinement={"RES":True, "PROJ":True, "MI":False},
do_uniform_refinement=False,
w_history=None,
sim_stats=None):
# define store function for timings
from functools import partial
def _store_stats(val, key, stats):
stats[key] = val
# define tuple type
EstimatorData = namedtuple('EstimatorData', ['xi', 'gamma', 'cQ', 'ceta'])
# get rhs
f = pde.f
# setup w and statistics
w = w0
if sim_stats is None:
assert w_history is None or len(w_history) == 0
sim_stats = []
try:
start_iteration = max(len(sim_stats) - 1, 0)
except:
start_iteration = 0
logger.info("START/CONTINUE EXPERIMENT at iteration %i", start_iteration)
# data collection
import resource
refinement = None
for refinement in range(start_iteration, max_refinements + 1):
logger.info("************* REFINEMENT LOOP iteration %i (of %i or max_dof %i) *************", refinement, max_refinements, max_dof)
# memory usage info
logger.info("\n======================================\nMEMORY USED: " + str(resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + "\n======================================\n")
# pcg solve
# ---------
stats = {}
with timing(msg="pcg_solve", logfunc=logger.info, store_func=partial(_store_stats, key="TIME-PCG", stats=stats)):
w, zeta = pcg_solve(A, w, coeff_field, pde, stats, pcg_eps, pcg_maxiter)
logger.info("DIM of w = %s", w.dim)
if w_history is not None and (refinement == 0 or start_iteration < refinement):
w_history.append(w)
# error evaluation
# ----------------
# residual and projection errors
logger.debug("evaluating ResidualEstimator.evaluateError")
with timing(msg="ResidualEstimator.evaluateError", logfunc=logger.info, store_func=partial(_store_stats, key="TIME-ESTIMATOR", stats=stats)):
xi, resind, projind, mierror, estparts, errors, timing_stats = ResidualEstimator.evaluateError(w, coeff_field, pde, f, zeta, gamma, ceta, cQ,
newmi_add_maxm, maxh, quadrature_degree, projection_degree_increase,
refine_projection_mesh)
reserrmu = [(mu, sqrt(sum(resind[mu].coeffs ** 2))) for mu in resind.keys()]
projerrmu = [(mu, sqrt(sum(projind[mu].coeffs ** 2))) for mu in projind.keys()]
res_part, proj_part, pcg_part = estparts[0], estparts[1], estparts[2]
err_res, err_proj, err_pcg = errors[0], errors[1], errors[2]
logger.info("Overall Estimator Error xi = %s while residual error is %s, projection error is %s, pcg error is %s", xi, res_part, proj_part, pcg_part)
stats.update(timing_stats)
stats["EST"] = xi
stats["RES-PART"] = res_part
stats["PROJ-PART"] = proj_part
stats["PCG-PART"] = pcg_part
stats["ERR-RES"] = err_res
stats["ERR-PROJ"] = err_proj
stats["ERR-PCG"] = err_pcg
stats["ETA-ERR"] = errors[0]
stats["DELTA-ERR"] = errors[1]
stats["ZETA-ERR"] = errors[2]
stats["RES-mu"] = reserrmu
stats["PROJ-mu"] = projerrmu
stats["PROJ-MAX-ZETA"] = 0
stats["PROJ-MAX-INACTIVE-ZETA"] = 0
stats["MARKING-RES"] = 0
stats["MARKING-PROJ"] = 0
stats["MARKING-MI"] = 0
stats["TIME-MARKING"] = 0
stats["MI"] = [(mu, vec.basis.dim) for mu, vec in w.iteritems()]
if refinement == 0 or start_iteration < refinement:
sim_stats.append(stats)
# print "SIM_STATS:", sim_stats[refinement]
logger.debug("squared error components: eta=%s delta=%s zeta=%", errors[0], errors[1], errors[2])
# exit when either error threshold or max_refinements or max_dof is reached
if refinement > max_refinements:
logger.info("SKIPPING REFINEMENT after FINAL SOLUTION in ITERATION %i", refinement)
break
if sim_stats[refinement]["DOFS"] >= max_dof:
logger.info("REACHED %i DOFS, EXITING refinement loop", sim_stats[refinement]["DOFS"])
break
if xi <= error_eps:
logger.info("error reached requested accuracy, xi=%f", xi)
break
# marking
# -------
if refinement < max_refinements:
if not do_uniform_refinement:
logger.debug("starting Marking.mark")
estimator_data = EstimatorData(xi=xi, gamma=gamma, cQ=cQ, ceta=ceta)
mesh_markers_R, mesh_markers_P, new_multiindices, proj_zeta, new_multiindices_all = Marking.mark(resind, projind, mierror, w.max_order,
theta_eta, theta_zeta, theta_delta,
min_zeta, maxh, max_Lambda_frac,
estimator_data, marking_strategy)
sim_stats[-1]["PROJ-MAX-ZETA"] = proj_zeta[0]
sim_stats[-1]["PROJ-MAX-INACTIVE-ZETA"] = proj_zeta[1]
sim_stats[-1]["PROJ-INACTIVE-ZETA"] = new_multiindices_all
# assert len(new_multiindices_all) == 0 or proj_zeta[1] == max([v for v in new_multiindices_all.values()])
logger.info("PROJECTION error values: max_zeta = %s and max_inactive_zeta = %s with threshold factor theta_zeta = %s (=%s)",
proj_zeta[0], proj_zeta[1], theta_zeta, theta_zeta * proj_zeta[0])
logger.info("MARKING will be carried out with %s (res) + %s (proj) cells and %s new multiindices",
sum([len(cell_ids) for cell_ids in mesh_markers_R.itervalues()]),
sum([len(cell_ids) for cell_ids in mesh_markers_P.itervalues()]), len(new_multiindices))
stats["MARKING-RES"] = sum([len(cell_ids) for cell_ids in mesh_markers_R.itervalues()])
stats["MARKING-PROJ"] = sum([len(cell_ids) for cell_ids in mesh_markers_P.itervalues()])
stats["MARKING-MI"] = len(new_multiindices)
if do_refinement["RES"]:
mesh_markers = mesh_markers_R.copy()
else:
mesh_markers = defaultdict(set)
logger.info("SKIP residual refinement")
if do_refinement["PROJ"]:
for mu, cells in mesh_markers_P.iteritems():
if len(cells) > 0:
mesh_markers[mu] = mesh_markers[mu].union(cells)
else:
logger.info("SKIP projection refinement")
if not do_refinement["MI"] or refinement == max_refinements:
new_multiindices = {}
logger.info("SKIP new multiindex refinement")
else:
logger.info("UNIFORM REFINEMENT active")
mesh_markers = {}
for mu, vec in w.iteritems():
from dolfin import cells
mesh_markers[mu] = list([c.index() for c in cells(vec._fefunc.function_space().mesh())])
new_multiindices = {}
# carry out refinement of meshes
with timing(msg="Marking.refine", logfunc=logger.info, store_func=partial(_store_stats, key="TIME-MARKING", stats=stats)):
Marking.refine(w, mesh_markers, new_multiindices.keys(), partial(setup_vector, pde=pde, mesh=mesh0, degree=degree))
if refinement:
logger.info("ENDED refinement loop after %i of %i refinements with %i dofs and %i active multiindices",
refinement, max_refinements, sim_stats[refinement]["DOFS"], len(sim_stats[refinement]["MI"]))
# except Exception as ex:
# import pickle
# logger.error("EXCEPTION during AdaptiveSolver: %s", str(ex))
# print "DIM of w:", w.dim
# if not w_history is None:
# w_history.append(w)
# wname = "W-PCG-FAILED.pkl"
# try:
# with open(wname, 'wb') as fout:
# pickle.dump(w, fout)
# except Exception as ex:
# logger.error("NEXT EXCEPTION %s", str(ex))
# logger.info("exported last multivector w to %s", wname)
# finally:
return w, sim_stats