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DAMASK_EICMD
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polishing

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Martin Diehl 2019-11-28 18:22:34 +01:00
parent 3e65d44e07
commit f2e722ed2e
1 changed files with 36 additions and 28 deletions
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64
python/damask/grid_filters.py
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@ -1,14 +1,14 @@
import numpy as np import numpy as np
def __ks(size,field): def __ks(size,field,first_order=False):
"""Get differential operator.""" """Get wave numbers operator."""
grid = np.array(np.shape(field)[0:3]) grid = np.array(np.shape(field)[0:3])
k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0] k_sk = np.where(np.arange(grid[0])>grid[0]//2,np.arange(grid[0])-grid[0],np.arange(grid[0]))/size[0]
if grid[0]%2 == 0: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) if grid[0]%2 == 0 and first_order: k_sk[grid[0]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1] k_sj = np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1]))/size[1]
if grid[1]%2 == 0: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011) if grid[1]%2 == 0 and first_order: k_sj[grid[1]//2] = 0 # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
k_si = np.arange(grid[2]//2+1)/size[2] k_si = np.arange(grid[2]//2+1)/size[2]
@ -19,7 +19,7 @@ def __ks(size,field):
def curl(size,field): def curl(size,field):
"""Calculate curl of a vector or tensor field in Fourier space.""" """Calculate curl of a vector or tensor field in Fourier space."""
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field) k_s = __ks(size,field,True)
e = np.zeros((3, 3, 3)) e = np.zeros((3, 3, 3))
e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol e[0, 1, 2] = e[1, 2, 0] = e[2, 0, 1] = +1.0 # Levi-Civita symbol
@ -35,7 +35,7 @@ def curl(size,field):
def divergence(size,field): def divergence(size,field):
"""Calculate divergence of a vector or tensor field in Fourier space.""" """Calculate divergence of a vector or tensor field in Fourier space."""
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field) k_s = __ks(size,field,True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2)) field_fourier = np.fft.rfftn(field,axes=(0,1,2))
divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1 divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else # vector, 3 -> 1
@ -47,7 +47,7 @@ def divergence(size,field):
def gradient(size,field): def gradient(size,field):
"""Calculate gradient of a vector or scalar field in Fourier space.""" """Calculate gradient of a vector or scalar field in Fourier space."""
n = np.prod(field.shape[3:]) n = np.prod(field.shape[3:])
k_s = __ks(size,field) k_s = __ks(size,field,True)
field_fourier = np.fft.rfftn(field,axes=(0,1,2)) field_fourier = np.fft.rfftn(field,axes=(0,1,2))
gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3 gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else # scalar, 1 -> 3
@ -56,29 +56,37 @@ def gradient(size,field):
return np.fft.irfftn(gradient,axes=(0,1,2),s=field.shape[0:3]) return np.fft.irfftn(gradient,axes=(0,1,2),s=field.shape[0:3])
#-------------------------------------------------------------------------------------------------- def coord_node(grid,size):
def displacementFluctFFT(F,size): """Positions of nodes (undeformed)."""
"""Calculate displacement field from deformation gradient field.""" x, y, z = np.meshgrid(np.linspace(0,size[2],1+grid[2]),
integrator = 0.5j * size / np.pi np.linspace(0,size[1],1+grid[1]),
np.linspace(0,size[0],1+grid[0]),
indexing = 'ij')
kk, kj, ki = np.meshgrid(np.where(np.arange(grid[2])>grid[2]//2,np.arange(grid[2])-grid[2],np.arange(grid[2])), return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
np.where(np.arange(grid[1])>grid[1]//2,np.arange(grid[1])-grid[1],np.arange(grid[1])),
np.arange(grid[0]//2+1),
indexing = 'ij')
k_s = np.concatenate((ki[:,:,:,None],kj[:,:,:,None],kk[:,:,:,None]),axis = 3)
k_sSquared = np.einsum('...l,...l',k_s,k_s)
k_sSquared[0,0,0] = 1.0 # ignore global average frequency
#--------------------------------------------------------------------------------------------------
# integration in Fourier space
displacement_fourier = -np.einsum('ijkml,ijkl,l->ijkm', def coord_cell(grid,size):
np.fft.rfftn(F,axes=(0,1,2)), """Positions of cell centers (undeformed)."""
k_s, delta = size/grid*0.5
integrator, x, y, z = np.meshgrid(np.linspace(delta[2],size[2]-delta[2],grid[2]),
) / k_sSquared[...,np.newaxis] np.linspace(delta[1],size[1]-delta[1],grid[1]),
np.linspace(delta[0],size[0]-delta[0],grid[0]),
indexing = 'ij')
#-------------------------------------------------------------------------------------------------- return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3)
# backtransformation to real space
return np.fft.irfftn(displacement_fourier,grid[::-1],axes=(0,1,2))
def displacement_fluct(size,F):
"""Calculate displacement field from deformation gradient field."""
integrator = 0.5j * size / np.pi
k_s = __ks(size,F,False)
displacement = -np.einsum('ijkml,ijkl,l->ijkm',
np.fft.rfftn(F,axes=(0,1,2)),
k_s,
integrator,
) / k_sSquared[...,np.newaxis]
return np.fft.irfftn(displacement,axes=(0,1,2))