def pcg_solve(A, w, coeff_field, pde, stats, pcg_eps, pcg_maxiter):
b = prepare_rhs(A, w, coeff_field, pde)
P = PreconditioningOperator(coeff_field.mean_func,
pde.assemble_solve_operator)
w, zeta, numit = pcg(A, b, P, w0=w, eps=pcg_eps, maxiter=pcg_maxiter)
logger.info("PCG finished with zeta=%f after %i iterations", zeta, numit)
b2 = A * w
stats["RESIDUAL-L2"] = error_norm(b, b2, "L2")
stats["RESIDUAL-H1A"] = error_norm(b, b2, pde.energy_norm)
stats["DOFS"] = sum([b[mu]._fefunc.function_space().dim() for mu in b.keys()])
stats["CELLS"] = sum([b[mu]._fefunc.function_space().mesh().num_cells() for mu in b.keys()])
logger.info("[pcg] Residual = [%s (L2)] [%s (H1A)] with [%s dofs] and [%s cells]", stats["RESIDUAL-L2"], stats["RESIDUAL-H1A"], stats["DOFS"], stats["CELLS"])
return w, zeta
def run_mc(err, w, pde, A, coeff_field, mesh0, ref_maxm, MC_N, MC_HMAX, param_sol_cache=None, direct_sol_cache=None, stored_rv_samples=None, quadrature_degree = -1):
# create reference mesh and function space
sub_spaces = w[Multiindex()].basis.num_sub_spaces
degree = w[Multiindex()].basis.degree
projection_basis = get_projection_basis(mesh0, mesh_refinements=0, degree=degree, sub_spaces=sub_spaces)
logger.info("projection_basis dim = %i \t hmin of mi[0] = %s, reference mesh = (%s, %s)", projection_basis.dim, w[Multiindex()].basis.minh, projection_basis.minh, projection_basis.maxh)
# get realization of coefficient field
err_L2, err_H1 = 0, 0
# set quadrature degree
if quadrature_degree > -1:
quadrature_degree_old = parameters["form_compiler"]["quadrature_degree"]
parameters["form_compiler"]["quadrature_degree"] = quadrature_degree
logger.debug("MC error sampling quadrature order = " + str(quadrature_degree))
# setup caches for sample solutions
# param_sol_cache = None #param_sol_cache or MCCache()
# direct_sol_cache = None #direct_sol_cache or MCCache()
logger.info("---- MC caches %s/%s ----", param_sol_cache, direct_sol_cache)
# main MC loop
for i in range(MC_N):
logger.info("---- MC Iteration %i/%i ----", i + 1 , MC_N)
# create new samples if required or reuse existing samples
if stored_rv_samples is None or len(stored_rv_samples) <= i:
sample_rvs = coeff_field.sample_rvs()
RV_samples = [sample_rvs[j] for j in range(max(w.max_order, ref_maxm))]
if stored_rv_samples is not None:
stored_rv_samples.append(RV_samples)
else:
RV_samples = stored_rv_samples[i]
logger.info("-- RV_samples: %s", RV_samples)
# evaluate solutions
with timing(msg="parameteric sample solution", logfunc=logger.info):
sample_sol_param = compute_parametric_sample_solution(RV_samples, coeff_field, w, projection_basis, param_sol_cache)
with timing(msg="direct sample solution", logfunc=logger.info):
sample_sol_direct = compute_direct_sample_solution(pde, RV_samples, coeff_field, A, ref_maxm, projection_basis, direct_sol_cache)
# evaluate errors
with timing(msg="L2_err_1", logfunc=logger.info):
cerr_L2 = error_norm(sample_sol_param._fefunc, sample_sol_direct._fefunc, "L2")
with timing(msg="H1A_err_1", logfunc=logger.info):
cerr_H1 = error_norm(sample_sol_param._fefunc, sample_sol_direct._fefunc, pde.energy_norm)
# cerr_H1 = errornorm(sample_sol_param._fefunc, sample_sol_direct._fefunc, "H1")
logger.debug("-- current error L2 = %s H1A = %s", cerr_L2, cerr_H1)
err_L2 += 1.0 / MC_N * cerr_L2
err_H1 += 1.0 / MC_N * cerr_H1
if i + 1 == MC_N:
# deterministic part
with timing(msg="direct a0", logfunc=logger.info):
sample_sol_direct_a0 = compute_direct_sample_solution(pde, RV_samples, coeff_field, A, 0, projection_basis, direct_sol_cache)
with timing(msg="L2_err_2", logfunc=logger.info):
L2_a0 = error_norm(sample_sol_param._fefunc, sample_sol_direct_a0._fefunc, "L2")
with timing(msg="H1A_err_2", logfunc=logger.info):
H1_a0 = error_norm(sample_sol_param._fefunc, sample_sol_direct_a0._fefunc, pde.energy_norm)
# H1_a0 = errornorm(sample_sol_param._fefunc, sample_sol_direct_a0._fefunc, "H1")
logger.debug("-- DETERMINISTIC error L2 = %s H1A = %s", L2_a0, H1_a0)
# stochastic part
sample_sol_direct_am = sample_sol_direct - sample_sol_direct_a0
logger.debug("-- STOCHASTIC norm L2 = %s H1 = %s", sample_sol_direct_am.norm("L2"), sample_sol_direct_am.norm("H1"))
# restore quadrature degree
if quadrature_degree > -1:
parameters["form_compiler"]["quadrature_degree"] = quadrature_degree_old
logger.info("MC Error: L2: %s, H1A: %s", err_L2, err_H1)
err.append((err_L2, err_H1, L2_a0, H1_a0))