functions for spatial coordinates on regular grids

python/damask/grid_filters.py

@@ -2,7 +2,7 @@ import numpy as np
 
 def __ks(size,field,first_order=False):
     """Get wave numbers operator."""
-    grid = np.array(np.shape(field)[0:3])
+    grid = np.array(np.shape(field)[:3])
 
     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 and first_order: k_sk[grid[0]//2] = 0                                         # Nyquist freq=0 for even grid (Johnson, MIT, 2011)
@@ -29,7 +29,7 @@ def curl(size,field):
     curl = (np.einsum('slm,ijkl,ijkm ->ijks', e,k_s,field_fourier)*2.0j*np.pi if n == 3 else        # vector, 3   -> 3
             np.einsum('slm,ijkl,ijknm->ijksn',e,k_s,field_fourier)*2.0j*np.pi)                      # tensor, 3x3 -> 3x3
 
-    return np.fft.irfftn(curl,axes=(0,1,2),s=field.shape[0:3])
+    return np.fft.irfftn(curl,axes=(0,1,2),s=field.shape[:3])
 
 
 def divergence(size,field):
@@ -41,7 +41,7 @@ def divergence(size,field):
     divergence = (np.einsum('ijkl,ijkl ->ijk', k_s,field_fourier)*2.0j*np.pi if n == 3 else         # vector, 3   -> 1
                   np.einsum('ijkm,ijklm->ijkl',k_s,field_fourier)*2.0j*np.pi)                       # tensor, 3x3 -> 3
 
-    return np.fft.irfftn(divergence,axes=(0,1,2),s=field.shape[0:3])
+    return np.fft.irfftn(divergence,axes=(0,1,2),s=field.shape[:3])
 
 
 def gradient(size,field):
@@ -53,21 +53,11 @@ def gradient(size,field):
     gradient = (np.einsum('ijkl,ijkm->ijkm', field_fourier,k_s)*2.0j*np.pi if n == 1 else           # scalar, 1 -> 3
                 np.einsum('ijkl,ijkm->ijklm',field_fourier,k_s)*2.0j*np.pi)                         # vector, 3 -> 3x3
 
-    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[:3])
 
 
-def coord_node(grid,size):
+def coord0_cell(grid,size):
-    """Positions of nodes (undeformed)."""
+    """Cell center positions (undeformed)."""
-    x, y, z = np.meshgrid(np.linspace(0,size[2],1+grid[2]),
-                          np.linspace(0,size[1],1+grid[1]),
-                          np.linspace(0,size[0],1+grid[0]),
-                          indexing = 'ij')
-    
-    return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) 
-
-
-def coord_cell(grid,size):
-    """Positions of cell centers (undeformed)."""
     delta = size/grid*0.5
     x, y, z = np.meshgrid(np.linspace(delta[2],size[2]-delta[2],grid[2]),
                           np.linspace(delta[1],size[1]-delta[1],grid[1]),
@@ -76,17 +66,50 @@ def coord_cell(grid,size):
 
     return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) 
 
-
+def displacement_fluct_cell(size,F):
-def displacement_fluct(size,F):
+    """Cell center displacement field from fluctuation part of the deformation gradient field."""
-    """Calculate displacement field from deformation gradient field."""
+    integrator = 0.5j*size/np.pi
-    integrator = 0.5j * size / np.pi
 
     k_s = __ks(size,F,False)
+    k_s_squared = np.einsum('...l,...l',k_s,k_s)
+    k_s_squared[0,0,0] = 1.0
 
     displacement = -np.einsum('ijkml,ijkl,l->ijkm',
                               np.fft.rfftn(F,axes=(0,1,2)),
                               k_s,
                               integrator,
-                             ) / k_sSquared[...,np.newaxis]
+                             ) / k_s_squared[...,np.newaxis]
 
-    return np.fft.irfftn(displacement,axes=(0,1,2))
+    return np.fft.irfftn(displacement,axes=(0,1,2),s=F.shape[:3])
+
+def displacement_avg_cell(size,F):
+    """Cell center displacement field from average part of the deformation gradient field."""
+    F_avg = np.average(F,axis=(0,1,2))
+    return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),coord0_cell(F.shape[:3],size))
+
+
+def coord0_node(grid,size):
+    """Nodal positions (undeformed)."""
+    x, y, z = np.meshgrid(np.linspace(0,size[2],1+grid[2]),
+                          np.linspace(0,size[1],1+grid[1]),
+                          np.linspace(0,size[0],1+grid[0]),
+                          indexing = 'ij')
+    
+    return np.concatenate((z[:,:,:,None],y[:,:,:,None],x[:,:,:,None]),axis = 3) 
+
+def displacement_fluct_node(size,F):
+    return cell_2_node(displacement_fluct_cell(size,F))
+
+def displacement_avg_node(size,F):
+    F_avg = np.average(F,axis=(0,1,2))
+    return np.einsum('ml,ijkl->ijkm',F_avg-np.eye(3),coord0_node(F.shape[0:3],size))
+
+
+def cell_2_node(cell_data):
+    """Interpolate cell data to nodal data."""
+  
+    n = (  cell_data + np.roll(cell_data,1,(0,1,2))
+         + np.roll(cell_data,1,(0,))  + np.roll(cell_data,1,(1,))  + np.roll(cell_data,1,(2,))
+         + np.roll(cell_data,1,(0,1)) + np.roll(cell_data,1,(1,2)) + np.roll(cell_data,1,(2,0))) *0.125
+  
+    return np.pad(n,((0,1),(0,1),(0,1))+((0,0),)*len(cell_data.shape[3:]),mode='wrap')