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check_Error_by_spaces.py
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check_Error_by_spaces.py
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# coding: utf8
from time import time
import numpy as np
import numpy.linalg as la
import scipy.sparse.linalg as spla
import bempp.api as bem
def create_spaces(grid, diri, neum):
trial, test = diri
triad = bem.function_space(grid, trial[0], trial[1])
testd = bem.function_space(grid, test[0], test[1])
spaced = (triad, testd)
trial, test = neum
trian = bem.function_space(grid, trial[0], trial[1])
testn = bem.function_space(grid, test[0], test[1])
spacen = (trian, testn)
return spaced, spacen
def get_opAi(spaces, k, sign=1):
tt = time()
spaced, spacen = spaces
triad, testd = spaced
trian, testn = spacen
opK = bem.operators.boundary.helmholtz.double_layer(triad, triad, testd, k)
opV = bem.operators.boundary.helmholtz.single_layer(trian, triad, testd, k)
opW = bem.operators.boundary.helmholtz.hypersingular(triad, trian, testn, k)
opQ = bem.operators.boundary.helmholtz.adjoint_double_layer(trian, trian, testn, k)
opA = bem.BlockedOperator(2, 2)
opA[0, 0], opA[0, 1] = - sign * opK, opV
opA[1, 0], opA[1, 1] = opW, sign * opQ
#print("collect A:", time()-tt)
return opA
def get_opXij(spaces, k=None, sign=None):
tt = time()
spaced, spacen = spaces
triad, testd = spaced
trian, testn = spacen
opId = bem.operators.boundary.sparse.identity(triad, triad, testd)
opIn = bem.operators.boundary.sparse.identity(trian, trian, testn)
opX = bem.BlockedOperator(2, 2)
opX[0, 0], opX[1, 1] = opId, -opIn
#print("collect X:", time()-tt)
return opX
def get_opJi(spaces, k=None, sign=None):
tt = time()
spaced, spacen = spaces
triad, testd = spaced
trian, testn = spacen
opId = bem.operators.boundary.sparse.identity(triad, triad, testd)
opIn = bem.operators.boundary.sparse.identity(trian, trian, testn)
opJ = bem.BlockedOperator(2, 2)
opJ[0, 0], opJ[1, 1] = opId, opIn
#print("collect J:", time()-tt)
return opJ
def get_iJi(spaces, k=None, sign=None):
tt = time()
iJ = bem.BlockedDiscreteOperator(2, 2)
opJ = get_opJi(spaces)
opId, opIn = opJ[0, 0], opJ[1, 1]
for ii, opI in enumerate([opId, opIn]):
Iw = opI.weak_form()
II = Iw.sparse_operator
II = II.astype(complex)
iII = spla.splu(II)
iIl = spla.LinearOperator(II.shape, matvec=iII.solve, dtype=complex)
iJ[ii, ii] = iIl
#print("compute iJ:", time()-tt)
return iJ
def check_Ci(spaces, k, sign=1):
tt = time()
opA = get_opAi(spaces, k, sign)
Aw = opA.weak_form()
opJ = get_opJi(spaces)
Jw = opJ.weak_form()
iJ = get_iJi(spaces)
C = lambda x: 0.5*Jw(x) + Aw(x)
CC = lambda x: C( iJ( C(x)))
x = np.random.rand(Aw.shape[0]) + 1j * np.random.rand(Aw.shape[0])
nx = la.norm(x)
y = C(x)
z = CC(x)
print("D:", diri, "N:", neum,
"errorX1e-2:", int(1e8 * la.norm(y - z)/nx) / 1e6,
"cputime:", int(10 * (time() - tt)) / 10,
"dof:", Aw.shape[0],
)
#
def get_Diag(spaces, get_op, k=None):
if k is None:
k = [None, None]
D = bem.BlockedDiscreteOperator(2, 2)
op0 = get_op(spaces, k[0], sign=1)
op1 = get_op(spaces, k[1], sign=-1)
for ii, op in enumerate([op0, op1]):
try:
Dw = op.weak_form()
except:
Dw = op
D[ii, ii] = Dw
return D
def get_A(spaces, k):
A = get_Diag(spaces, get_opAi, k)
return A
def get_J(spaces):
J = get_Diag(spaces, get_opJi)
return J
def get_iJ(spaces):
iJ = get_Diag(spaces, get_iJi)
return iJ
def get_X(spaces):
X = bem.BlockedDiscreteOperator(2, 2)
opX = get_opXij(spaces)
Xw = opX.weak_form()
X[0, 1], X[1, 0] = Xw, Xw
return X
def check_C(spaces, k):
tt = time()
A = get_A(spaces, k)
J = get_J(spaces)
iJ = get_iJ(spaces)
C = lambda x: 0.5*J(x) + A(x)
CC = lambda x: C( iJ( C(x)))
x = np.random.rand(A.shape[0]) + 1j * np.random.rand(A.shape[0])
nx = la.norm(x)
y = C(x)
z = CC(x)
print("D:", diri, "N:", neum,
"errorX1e-2:", int(1e8 * la.norm(y - z)/nx) / 1e6,
"cputime:", int(10 * (time() - tt)) / 10,
"dof:", A.shape[0],
)
def mtf(spaces, k):
tt = time()
A = get_A(spaces, k)
X = get_X(spaces)
M = A - 0.5 * X
print("cputime:", time() - tt)
return M
def rhs(spaces, funs):
spaced, spacen = spaces
triad, testd = spaced
trian, testn = spacen
fd, fn = funs
gfd = bem.GridFunction(testd, fun=fd)
gfn = bem.GridFunction(testn, fun=fn)
pd, pn = gfd.projections(), gfn.projections()
b = pd
for p in [pn, pd, pn]:
b = np.concatenate((b, -p))
return b
def check_sol(spaces, k, x, b, diri, neum,
A=None, X=None, J=None):
if A is None:
A = get_A(spaces, k)
if X is None:
X = get_X(spaces)
if J is None:
J = get_J(spaces)
nx = la.norm(x)
ya, yt = A(x), J(x)
za, zt = J(x), X(x)
era = la.norm(ya - za)/nx
ert = la.norm(yt - zt)/nx
print("D:", diri, "N:", neum,
"erAX1e-2:", int(1e8 * era) / 1e6,
"erTX1e-2:", int(1e8 * ert) / 1e6,
)
return era, ert
if __name__ == "__main__":
k = 0.3 * np.pi
eps = np.sqrt( 2 )
nlmdba = 20
iincident = 0
lmbda = 2 * np.pi / k
kk = [k, eps*k]
#grid = bem.shapes.sphere(h=lmbda/(nlmdba*eps))
grid = bem.shapes.cube(h=lmbda/(nlmdba*eps))
# space
# (diri, neum)
# diri = (trial, test)
spaces = [
((("DP", 0), ("DP", 0)), (("DP", 0), ("DP", 0))),
((("P", 1), ("P", 1)), (("P", 1), ("P", 1))),
((("B-DP", 1), ("B-DP", 1)), (("DUAL", 0), ("DUAL", 0))),
((("B-P", 1), ("B-P", 1)), (("DUAL", 0), ("DUAL", 0))),
# ((("DP", 1), ("DP", 1)), (("DP", 1), ("DP", 1))),
# ((("DP", 2), ("DP", 2)), (("DP", 2), ("DP", 2))),
# ((("DP", 3), ("DP", 3)), (("DP", 3), ("DP", 3))),
# ((("P", 2), ("P", 2)), (("P", 2), ("P", 2))),
# ((("P", 3), ("P", 3)), (("P", 3), ("P", 3))),
# ((("B-DP", 1), ("B-DP", 1)), (("B-DP", 1), ("B-DP", 1))),
# ((("B-P", 1), ("B-P", 1)), (("B-P", 1), ("B-P", 1))),
# ((("DUAL", 0), ("DUAL", 0)), (("B-P", 1), ("B-P", 1))),
# ((("DUAL", 0), ("DUAL", 0)), (("B-DP", 1), ("B-DP", 1))),
]
for diri, neum in spaces:
space = create_spaces(grid, diri, neum)
check_Ci(space, k)
print('')
for diri, neum in spaces:
space = create_spaces(grid, diri, neum)
check_C(space, kk)
print('')
def fdir(x, n, d, res):
res[0] = -np.exp( 1j * k * x[iincident])
def fneu(x, n, d, res):
res[0] = -1j * n[iincident] * k * np.exp( 1j * k * x[iincident])
funs = fdir, fneu
from krylov import gmres
for diri, neum in spaces:
space = create_spaces(grid, diri, neum)
M = mtf(space, kk)
b = rhs(space, funs)
MM = spla.LinearOperator(M.shape, matvec=M.matvec, dtype=complex)
res = []
tol = 1e-5
restart, maxiter = None, MM.shape[0]
xx, info = gmres(MM, b,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
print(info, len(res))
check_sol(space, kk, xx, b, diri, neum)