def homog_GaNi_full_potential(Agani, Aga, pars):
N = Agani.N # double grid number
dim = N.__len__()
F = DFT(name='FN', inverse=False, N=N) # discrete Fourier transform (DFT)
iF = DFT(name='FiN', inverse=True, N=N) # inverse DFT
P = get_preconditioner(N, pars)
E = np.zeros(dim)
E[0] = 1 # macroscopic load
EN = Tensor(name='EN', N=N, shape=(dim, ),
Fourier=False) # constant trig. pol.
EN.set_mean(E)
def DFAFGfun(X):
assert (X.Fourier)
FAX = F(Agani * iF(grad(X)))
return -div(FAX)
B = div(F(Agani(EN)))
x0 = Tensor(N=N, shape=(),
Fourier=True) # initial approximation to solvers
PDFAFGPfun = lambda Fx: P * DFAFGfun(P * Fx)
PB = P * B
tic = Timer(name='CG (potential)')
iPU, info = linear_solver(solver='CG',
Afun=PDFAFGPfun,
B=PB,
x0=x0,
par=pars.solver,
callback=None)
tic.measure()
print(('iterations of CG={}'.format(info['kit'])))
print(('norm of residuum={}'.format(info['norm_res'])))
Fu = P * iPU
if Aga is None: # GaNi homogenised properties
print('!!!!! homogenised properties are GaNi only !!!!!')
XEN = iF(grad(Fu)) + EN
AH = Agani(XEN) * XEN
else:
Nbar = 2 * np.array(N) - 1
iF2 = DFT(name='FiN', inverse=True, N=Nbar) # inverse DFT
XEN = iF2(grad(Fu).project(Nbar)) + EN.project(Nbar)
AH = Aga(XEN) * XEN
return Struct(AH=AH, Fu=Fu, info=info, time=tic.vals[0][0], pars=pars)
Fourier coefficients of phi
Fphi = FN*phi = FN(phi) =""")
Fphi = FN*phi
print(Fphi)
print("Fphi.val =")
print(Fphi.val)
print("""
In order to create a plot of this polynomial, it is
evaluated on a fine grid sizing
M = 16*N =""")
M = 16*N
print(M)
print("phi_fine = phi.project(M) =")
phi_fine = phi.project(M)
print(phi_fine)
print("""The procedure is provided by VecTri.enlarge(M) function, which consists of
a calculation of Fourier coefficients, putting zeros to Fourier coefficients
with high frequencies, and inverse FFT that evaluates the polynomial on
a fine grid.
""")
print("""In order to plot this polynomial, we also set a size of a cell
Y =""")
Y = np.ones(d) # size of a cell
print(Y)
print(""" and evaluate the coordinates of grid points, which are stored in
numpy.ndarray of following shape:
coord.shape =""")
Fourier coefficients of phi
Fphi = FN*phi = FN(phi) =""")
Fphi = FN * phi
print(Fphi)
print("Fphi.val =")
print(Fphi.val)
print("""
In order to create a plot of this polynomial, it is
evaluated on a fine grid sizing
M = 16*N =""")
M = 16 * N
print(M)
print("phi_fine = phi.project(M) =")
phi_fine = phi.project(M)
print(phi_fine)
print(
"""The procedure is provided by VecTri.enlarge(M) function, which consists of
a calculation of Fourier coefficients, putting zeros to Fourier coefficients
with high frequencies, and inverse FFT that evaluates the polynomial on
a fine grid.
""")
print("""In order to plot this polynomial, we also set a size of a cell
Y =""")
Y = np.ones(d) # size of a cell
print(Y)
print(""" and evaluate the coordinates of grid points, which are stored in
numpy.ndarray of following shape:
coord.shape =""")