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prototype of defining regularization mesh within Regularization.py for constructing operators for regularization that are not true differential operators

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This commit is contained in:
Lindsey Heagy
2016-02-24 18:03:42 -08:00
parent b5f4d8e999
commit 4e871a43a9
3 changed files with 344 additions and 250 deletions
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SimPEG/Mesh/DiffOperators.py
+49 -80
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@@ -307,24 +307,28 @@ class DiffOperators(object):
return BC
_cellGradBC_list = 'neumann'
def _cellGradStencil(self):
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.vnC
if(self.dim == 1):
G = ddxCellGrad(n[0], BC[0])
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
G = sp.vstack((G1, G2), format="csr")
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
G = sp.vstack((G1, G2, G3), format="csr")
return G
def cellGrad():
doc = "The cell centered Gradient, takes you to cell faces."
def fget(self):
if(self._cellGrad is None):
BC = self.setCellGradBC(self._cellGradBC_list)
n = self.vnC
if(self.dim == 1):
G = ddxCellGrad(n[0], BC[0])
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
G = sp.vstack((G1, G2), format="csr")
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
G = sp.vstack((G1, G2, G3), format="csr")
G = self._cellGradStencil()
# Compute areas of cell faces & volumes
S = self.area
V = self.aveCC2F*self.vol # Average volume between adjacent cells
@@ -361,19 +365,24 @@ class DiffOperators(object):
_cellGradBC = None
cellGradBC = property(**cellGradBC())
def _cellGradxStencil(self):
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 1):
G1 = ddxCellGrad(n[0], BC)
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
return G1
def cellGradx():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if getattr(self, '_cellGradx', None) is None:
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 1):
G1 = ddxCellGrad(n[0], BC)
elif(self.dim == 2):
G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
elif(self.dim == 3):
G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
G1 = self._cellGradxStencil()
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fx', 'V')
@@ -382,17 +391,22 @@ class DiffOperators(object):
return locals()
cellGradx = property(**cellGradx())
def _cellGradyStencil(self):
if self.dim < 2: return None
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 2):
G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
elif(self.dim == 3):
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
return G2
def cellGrady():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if self.dim < 2: return None
if getattr(self, '_cellGrady', None) is None:
BC = ['neumann', 'neumann']
n = self.vnC
if(self.dim == 2):
G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
elif(self.dim == 3):
G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
G2 = self._cellGradyStencil()
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fy', 'V')
@@ -401,14 +415,19 @@ class DiffOperators(object):
return locals()
cellGrady = property(**cellGrady())
def _cellGradzStencil(self):
if self.dim < 3: return None
BC = ['neumann', 'neumann']
n = self.vnC
G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
return G3
def cellGradz():
doc = "Cell centered Gradient in the x dimension. Has neumann boundary conditions."
def fget(self):
if self.dim < 3: return None
if getattr(self, '_cellGradz', None) is None:
BC = ['neumann', 'neumann']
n = self.vnC
G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
G3 = self._cellGradzStencil()
# Compute areas of cell faces & volumes
V = self.aveCC2F*self.vol
L = self.r(self.area/V, 'F','Fz', 'V')
@@ -565,56 +584,6 @@ class DiffOperators(object):
return Pbc, Pin, Pout
def unitCellGradx():
doc = """Cell centered Gradient in the x dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGradx', None) is None:
n = self.vnC
gx = ddx(n[0]-1)
gx_square = sp.vstack((gx,gx[-1,:]*-1), format="csr")
self._unitCellGradx = kron3(speye(n[2]), speye(n[1]), gx_square)
return self._unitCellGradx
return locals()
unitCellGradx = property(**unitCellGradx())
def unitCellGrady():
doc = """Cell centered Gradient in they dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGrady', None) is None:
n = self.vnC
gy = ddx(n[1]-1)
gy_square = sp.vstack((gy,gy[-1,:]*-1), format="csr")
self._unitCellGrady = kron3(speye(n[2]), gy_square, speye(n[0]))
return self._unitCellGrady
return locals()
unitCellGrady = property(**unitCellGrady())
def unitCellGradz():
doc = """Cell centered Gradient in they dimension used for
regularization. The gradient operator is square (nC-by-nC)"""
def fget(self):
if self.dim < 3: return None
if getattr(self, '_unitCellGradz', None) is None:
n = self.vnC
gz = ddx(n[2]-1)
gz_square = sp.vstack((gz,gz[-1,:]*-1), format="csr")
self._unitCellGradz = kron3( gz_square , speye(n[1]), speye(n[0]))
return self._unitCellGradz
return locals()
unitCellGradz = property(**unitCellGradz())
# --------------- Averaging ---------------------