def cube(k):
cglob = -1j * k
cloc = cloc0 + cloc1 * k + cloc2 * k**2
print("k: ", k, "cloc: ", cloc)
mus = {'k': k, 'c_glob': cglob, 'c_loc': cloc}
resolution = int(
np.ceil(float(k * 1.5 + 50) / coarse_grid_resolution) *
coarse_grid_resolution)
n = int(k / 5 + 30)
gq, lq = localize_problem(p,
coarse_grid_resolution,
resolution,
mus=mus)
d = gq["d"]
u = d.solve(mus)
e_r = []
e_d = []
for i in range(it):
print(i, )
sys.stdout.flush()
bases = create_bases2(gq, lq, n, transfer='robin')
ru_r = reconstruct_solution(gq, lq, bases)
del bases
dif_r = u - ru_r
e_r.append(gq["full_norm"](dif_r)[0] / gq["full_norm"](u)[0])
bases = create_bases2(gq, lq, n, transfer='dirichlet')
ru_d = reconstruct_solution(gq, lq, bases)
del bases
dif_d = u - ru_d
e_d.append(gq["full_norm"](dif_d)[0] / gq["full_norm"](u)[0])
return np.mean(e_d), np.mean(e_r)
def evaluation(it,
lim,
k,
boundary,
save,
cglob=0,
cloc=0,
plot=False,
resolution=200,
coarse_grid_resolution=10):
p = helmholtz(boundary=boundary)
mus = {'k': k, 'c_glob': cglob, 'c_loc': cloc}
gq, lq = localize_problem(p, coarse_grid_resolution, resolution, mus=mus)
d = gq["d"]
u = d.solve(mus)
h1_dirichlet = []
h1_robin = []
nrang = np.arange(0, lim, 5)
for n in nrang:
print("n: ", n)
h1d = []
h1r = []
for j in range(it):
print(j, )
sys.stdout.flush()
basis_dirichlet = create_bases2(gq, lq, n)
ru_dirichlet = reconstruct_solution(gq, lq, basis_dirichlet)
del basis_dirichlet
basis_robin = create_bases2(gq, lq, n, transfer='robin')
ru_robin = reconstruct_solution(gq, lq, basis_robin)
del basis_robin
dif_dirichlet = u - ru_dirichlet
dif_robin = u - ru_robin
h1d.append(gq["full_norm"](dif_dirichlet)[0] /
gq["full_norm"](u)[0])
h1r.append(gq["full_norm"](dif_robin)[0] / gq["full_norm"](u)[0])
h1_dirichlet.append(h1d)
h1_robin.append(h1r)
means_dirichlet_h1 = np.mean(h1_dirichlet, axis=1)
means_robin_h1 = np.mean(h1_robin, axis=1)
data = np.vstack([nrang, means_dirichlet_h1, means_robin_h1]).T
open(save, "w").writelines([" ".join(map(str, v)) + "\n" for v in data])
if plot:
from matplotlib import pyplot as plt
plt.figure()
plt.semilogy(nrang, means_dirichlet_h1, label="Dirichlet h1")
plt.semilogy(nrang, means_robin_h1, label="Robin h1")
plt.legend(loc='upper right')
plt.xlabel('Basis size')
plt.show()
def knerr2D(it,
boundary,
save,
cglob=None,
cloc0=0,
cloc1=1,
cloc2=1,
krang=np.arange(0.1, 200.1, 10.),
nrang=np.arange(0, 100, 5),
plot=False,
resolution=100,
coarse_grid_resolution=10):
err_r = np.zeros((len(krang), len(nrang)))
p = helmholtz(boundary=boundary)
usecglob = (cglob is None)
xi = 0
for k in krang:
yi = 0
if usecglob:
cglob = -1j * k
cloc = cloc0 + cloc1 * k + cloc2 * k**2
mus = {'k': k, 'c_glob': cglob, 'c_loc': cloc}
gq, lq = localize_problem(p,
coarse_grid_resolution,
resolution,
mus=mus)
d = gq["d"]
u = d.solve(mus)
for n in nrang:
print(k, n)
e_r = []
for i in range(min(20 - n / 5, it)):
print(i, )
sys.stdout.flush()
bases = create_bases2(gq, lq, n, transfer='robin')
ru_r = reconstruct_solution(gq, lq, bases)
del bases
dif_r = u - ru_r
e_r.append(gq["full_norm"](dif_r)[0] / gq["full_norm"](u)[0])
err_r[xi][yi] = np.mean(e_r)
yi += 1
xi += 1
X, Y = np.meshgrid(krang, nrang)
data = np.vstack([X.T.ravel(), Y.T.ravel(), err_r.ravel()]).T
open(save, "w").writelines([" ".join(map(str, v)) + "\n" for v in data])
if plot:
import matplotlib.pyplot as plt
from matplotlib import cm
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X,
Y,
err_r,
cstride=1,
rstride=1,
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
fig.colorbar(surf, shrink=0.5, aspect=5)
plt.show()
def resolution(it,
k,
n,
boundary,
save,
cloc=0,
returnvals=False,
coarse_grid_resolution=10):
cglob = -1j * k
mus = {'k': k, 'c_glob': cglob, 'c_loc': cloc}
p = helmholtz(boundary=boundary)
space = np.arange(20, 160, 10)
err = []
for resolution in space:
print(resolution)
gq, lq = localize_problem(p,
coarse_grid_resolution,
resolution,
mus=mus)
d = gq["d"]
u = d.solve(mus)
E = []
for i in range(it):
bases = create_bases2(gq, lq, n, transfer='robin')
ru = reconstruct_solution(gq, lq, bases)
E.append(gq["full_norm"](u - ru)[0] / gq["full_norm"](u)[0])
err.append(E)
errs = np.mean(err, axis=1)
data = np.vstack([space, errs]).T
open(save, "w").writelines([" ".join(map(str, v)) + "\n" for v in data])
if returnvals:
return [space, errs]
def test1(transfer='robin',
boundary='dirichlet',
n=15,
k=6.,
cloc=6.,
title='test',
resolution=100,
coarse_grid_resolution=10,
m=1):
cglob = -1j * k
mus = {'k': k, 'c_glob': cglob, 'c_loc': cloc}
p = helmholtz(boundary=boundary)
gq, lq = localize_problem(p, coarse_grid_resolution, resolution, mus, m=m)
basis = create_bases2(gq, lq, n, transfer=transfer, silent=False)
ru = reconstruct_solution(gq, lq, basis, silent=False)
d = gq["d"]
u = d.solve(mus)
dif = u - ru
print(gq["full_norm"](dif)[0] / gq["full_norm"](u)[0])
d.visualize((dif.real, dif.imag, u.real, u.imag, ru.real, ru.imag),
legend=('dif.real', 'dif.imag', 'u.real', 'u.imag', 'ru.real',
'ru.imag'),
separate_colorbars=True,
title=title)
def cube():
bases = create_bases2(gq, lq, n, transfer='robin')
ru_r = reconstruct_solution(gq, lq, bases)
del bases
dif_r = u - ru_r
return gq["full_norm"](dif_r)[0] / gq["full_norm"](u)[0]