def test_has_spatial_order_of_accuracy():
expected_order = 2
k = 4
ntests = 6
ndofs = []
err_list = []
for i in range(ntests):
ndofs.append(2**(i + 4) - 1)
prob = Poisson1D(ndofs[-1])
xvalues = np.array([(i + 1) * prob.dx for i in range(prob.ndofs)])
uinit = np.sin(np.pi * k * xvalues)
uexact = (np.pi * k)**2 * uinit
ucomp = prob.A.dot(uinit)
err_list.append(
np.linalg.norm(uexact - ucomp, np.inf) /
np.linalg.norm(uexact, np.inf))
order = []
for i in range(1, len(err_list)):
order.append(
np.log(err_list[i - 1] / err_list[i]) /
np.log(ndofs[i] / ndofs[i - 1]))
order = np.array(order)
assert (order > expected_order * 0.9).all() and (order < expected_order * 1.1).all(), \
'Order of accuracy of the spatial discretization is not ' + str(expected_order)
def exact_is_fixpoint(smoo_class):
ndofs = 127
prob = Poisson1D(ndofs)
smoo = smoo_class(prob.A, 2.0 / 3.0)
k = 6
xvalues = np.array([(i + 1) * prob.dx for i in range(prob.ndofs)])
rhs = np.sin(np.pi * k * xvalues)
uex = spLA.spsolve(smoo.A, rhs)
u = uex
for i in range(10):
u = smoo.smooth(rhs, u)
err = np.linalg.norm(u - uex, np.inf)
assert err <= 1E-14, 'Exact solution is not a fixpoint of the iteration!'
def setUp(self):
ndofs = 31
nlevels = int(np.log2(ndofs + 1))
self.prob = Poisson1D(ndofs=ndofs)
self.mymg = MyMultigrid(ndofs, nlevels=nlevels)
self.mymg.attach_transfer(LinearTransfer)
self.mymg.attach_smoother(WeightedJacobi, self.prob.A, omega=2.0 / 3.0)
k = 6
xvalues = np.array([(i + 1) * self.prob.dx
for i in range(self.prob.ndofs)])
self.u = np.sin(np.pi * k * xvalues)
self.nu0 = 1
self.nu1 = 2
self.nu2 = 2
def attach_smoother_works(mult):
prob = Poisson1D(ndofs=ndofs)
mult.attach_transfer(LinearTransfer)
mult.attach_smoother(WeightedJacobi, prob.A, omega=2.0 / 3.0)
assert isinstance(mult.Acoarse, sp.csc_matrix), type(mult.Acoarse)
import numpy as np
import scipy.linalg as LA
from matplotlib import rc
from project.gauss_seidel import GaussSeidel
from project.poisson1d import Poisson1D
from project.weighted_jacobi import WeightedJacobi
if __name__ == "__main__":
rc('font', family='sans-serif', size=32)
rc('legend', fontsize='small')
rc('xtick', labelsize='small')
rc('ytick', labelsize='small')
prob = Poisson1D(ndofs=63)
urand = np.random.rand(prob.ndofs)
niter = 100
smoother_list = [(WeightedJacobi(prob=prob,
omega=2.0 / 3.0), 'Jacobi_w23'),
(GaussSeidel(prob=prob), 'GaussSeidel')]
for smoother, fname in smoother_list:
u = urand
uex = prob.u_exact
err = [LA.norm(u - uex, np.inf)]
for i in range(niter):
def setup():
global list, ndofs, prob
list = get_derived_from_in_package(SmootherBase, 'project')
ndofs = 10
prob = Poisson1D(ndofs)
if __name__ == "__main__":
# build SimplePFASSTCollocationProblem
num_nodes = 3
num_subintervals = 2
num_space = 16
k = 1
dt = 0.01
GRC = CollGaussRadau_Right(num_nodes, 0.0, 1.0)
Q = GRC.Qmat[1:, 1:]
QD = GRC.QDmat
# matrix_plot(QD)
# print QD.shape, Q.shape
nodes = GRC.nodes
CTSB = CollocationTimeStepBase(0.0, dt, Q, nodes)
CTSB_delta = CollocationTimeStepBase(0.0, dt, QD, nodes)
SpaceProblem = Poisson1D(num_space)
omega_h = np.linspace(1 / (num_space + 1), 1.0, num_space)
u_init = np.sin(2 * np.pi * np.linspace(1 /
(num_space + 1), 1.0, num_space))
u_init_gen = lambda x: np.sin(2 * np.pi * x)
# show_call_order(SimplePFASSTCollocationProblem, '__init__')
PFASSTCollocProb = SimplePFASSTCollocationProblem(num_subintervals, CTSB,
SpaceProblem, u_init_gen)
PFASSTPrecondProb = SimplePFASSTCollocationProblem(num_subintervals,
CTSB_delta,
SpaceProblem,
u_init_gen)
sol = splinalg.spsolve(PFASSTCollocProb.A, PFASSTCollocProb.rhs)
sol_precond = splinalg.spsolve(PFASSTPrecondProb.A, PFASSTPrecondProb.rhs)
from project.poisson1d import Poisson1D
from project.weighted_jacobi import WeightedJacobi
# from project.gauss_seidel import GaussSeidel
from project.linear_transfer import LinearTransfer
from project.mymultigrid import MyMultigrid
from pymg.problem_base import ProblemBase
from project.solversmoother import SolverSmoother
norm_type = 2
ntests = 1
ndofs = 15
iter_max = 10
# nlevels = int(np.log2(ndofs + 1))
nlevels = 2
prob = Poisson1D(ndofs=ndofs)
mymg = MyMultigrid(ndofs=ndofs, nlevels=nlevels)
mymg.attach_transfer(LinearTransfer)
mymg.attach_smoother(WeightedJacobi, prob.A, omega=2.0 / 3.0)
k = 6
xvalues = np.array([(i + 1) * prob.dx for i in range(prob.ndofs)])
prob.rhs = (np.pi * k)**2 * np.sin(np.pi * k * xvalues)
uex = spla.spsolve(prob.A, prob.rhs)
res = 1
err = []
err_so = [] # Smoother only error
u = np.zeros(uex.size)
u_so = np.zeros(uex.size)
w_jac = mymg.smoo[0]
# do the multigrid iterationssteps along side with the
# smoother only steps