mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-27 19:48:52 +08:00
Rowan Cockett
559 lines
22 KiB
Python
559 lines
22 KiB
Python
from SimPEG import Utils, np, sp
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from BaseMesh import BaseMesh, BaseRectangularMesh
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from View import TensorView
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from DiffOperators import DiffOperators
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from InnerProducts import InnerProducts
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class BaseTensorMesh(BaseMesh):
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__metaclass__ = Utils.SimPEGMetaClass
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_meshType = 'BASETENSOR'
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_unitDimensions = [1, 1, 1]
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def __init__(self, h_in, x0_in=None):
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assert type(h_in) in [list, tuple], 'h_in must be a list'
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assert len(h_in) in [1,2,3], 'h_in must be of dimension 1, 2, or 3'
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h = range(len(h_in))
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for i, h_i in enumerate(h_in):
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if Utils.isScalar(h_i) and type(h_i) is not np.ndarray:
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# This gives you something over the unit cube.
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h_i = self._unitDimensions[i] * np.ones(int(h_i))/int(h_i)
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elif type(h_i) is list:
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h_i = Utils.meshTensor(h_i)
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assert isinstance(h_i, np.ndarray), ("h[%i] is not a numpy array." % i)
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assert len(h_i.shape) == 1, ("h[%i] must be a 1D numpy array." % i)
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h[i] = h_i[:] # make a copy.
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x0 = np.zeros(len(h))
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if x0_in is not None:
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assert len(h) == len(x0_in), "Dimension mismatch. x0 != len(h)"
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for i in range(len(h)):
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x_i, h_i = x0_in[i], h[i]
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if Utils.isScalar(x_i):
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x0[i] = x_i
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elif x_i == '0':
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x0[i] = 0.0
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elif x_i == 'C':
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x0[i] = -h_i.sum()*0.5
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elif x_i == 'N':
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x0[i] = -h_i.sum()
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else:
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raise Exception("x0[%i] must be a scalar or '0' to be zero, 'C' to center, or 'N' to be negative." % i)
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if isinstance(self, BaseRectangularMesh):
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BaseRectangularMesh.__init__(self, np.array([x.size for x in h]), x0)
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else:
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BaseMesh.__init__(self, np.array([x.size for x in h]), x0)
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# Ensure h contains 1D vectors
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self._h = [Utils.mkvc(x.astype(float)) for x in h]
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@property
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def h(self):
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"""h is a list containing the cell widths of the tensor mesh in each dimension."""
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return self._h
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@property
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def hx(self):
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"Width of cells in the x direction"
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return self._h[0]
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@property
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def hy(self):
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"Width of cells in the y direction"
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return None if self.dim < 2 else self._h[1]
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@property
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def hz(self):
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"Width of cells in the z direction"
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return None if self.dim < 3 else self._h[2]
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@property
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def vectorNx(self):
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"""Nodal grid vector (1D) in the x direction."""
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return np.r_[0., self.hx.cumsum()] + self.x0[0]
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@property
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def vectorNy(self):
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"""Nodal grid vector (1D) in the y direction."""
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return None if self.dim < 2 else np.r_[0., self.hy.cumsum()] + self.x0[1]
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@property
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def vectorNz(self):
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"""Nodal grid vector (1D) in the z direction."""
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return None if self.dim < 3 else np.r_[0., self.hz.cumsum()] + self.x0[2]
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@property
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def vectorCCx(self):
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"""Cell-centered grid vector (1D) in the x direction."""
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return np.r_[0, self.hx[:-1].cumsum()] + self.hx*0.5 + self.x0[0]
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@property
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def vectorCCy(self):
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"""Cell-centered grid vector (1D) in the y direction."""
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return None if self.dim < 2 else np.r_[0, self.hy[:-1].cumsum()] + self.hy*0.5 + self.x0[1]
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@property
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def vectorCCz(self):
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"""Cell-centered grid vector (1D) in the z direction."""
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return None if self.dim < 3 else np.r_[0, self.hz[:-1].cumsum()] + self.hz*0.5 + self.x0[2]
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@property
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def gridCC(self):
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"""Cell-centered grid."""
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return self._getTensorGrid('CC')
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@property
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def gridN(self):
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"""Nodal grid."""
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return self._getTensorGrid('N')
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@property
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def gridFx(self):
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"""Face staggered grid in the x direction."""
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if self.nFx == 0: return
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return self._getTensorGrid('Fx')
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@property
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def gridFy(self):
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"""Face staggered grid in the y direction."""
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if self.nFy == 0 or self.dim < 2: return
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return self._getTensorGrid('Fy')
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@property
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def gridFz(self):
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"""Face staggered grid in the z direction."""
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if self.nFz == 0 or self.dim < 3: return
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return self._getTensorGrid('Fz')
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@property
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def gridEx(self):
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"""Edge staggered grid in the x direction."""
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if self.nEx == 0: return
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return self._getTensorGrid('Ex')
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@property
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def gridEy(self):
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"""Edge staggered grid in the y direction."""
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if self.nEy == 0 or self.dim < 2: return
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return self._getTensorGrid('Ey')
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@property
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def gridEz(self):
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"""Edge staggered grid in the z direction."""
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if self.nEz == 0 or self.dim < 3: return
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return self._getTensorGrid('Ez')
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def _getTensorGrid(self, key):
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if getattr(self, '_grid' + key, None) is None:
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setattr(self, '_grid' + key, Utils.ndgrid(self.getTensor(key)))
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return getattr(self, '_grid' + key)
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def getTensor(self, key):
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""" Returns a tensor list.
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:param str key: What tensor (see below)
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:rtype: list
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:return: list of the tensors that make up the mesh.
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key can be::
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'CC' -> scalar field defined on cell centers
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'N' -> scalar field defined on nodes
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'Fx' -> x-component of field defined on faces
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'Fy' -> y-component of field defined on faces
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'Fz' -> z-component of field defined on faces
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'Ex' -> x-component of field defined on edges
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'Ey' -> y-component of field defined on edges
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'Ez' -> z-component of field defined on edges
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"""
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if key == 'Fx':
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ten = [self.vectorNx , self.vectorCCy, self.vectorCCz]
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elif key == 'Fy':
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ten = [self.vectorCCx, self.vectorNy , self.vectorCCz]
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elif key == 'Fz':
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ten = [self.vectorCCx, self.vectorCCy, self.vectorNz ]
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elif key == 'Ex':
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ten = [self.vectorCCx, self.vectorNy , self.vectorNz ]
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elif key == 'Ey':
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ten = [self.vectorNx , self.vectorCCy, self.vectorNz ]
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elif key == 'Ez':
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ten = [self.vectorNx , self.vectorNy , self.vectorCCz]
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elif key == 'CC':
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ten = [self.vectorCCx, self.vectorCCy, self.vectorCCz]
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elif key == 'N':
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ten = [self.vectorNx , self.vectorNy , self.vectorNz ]
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return [t for t in ten if t is not None]
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# --------------- Methods ---------------------
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def isInside(self, pts, locType='N'):
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"""
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Determines if a set of points are inside a mesh.
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:param numpy.ndarray pts: Location of points to test
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:rtype numpy.ndarray
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:return inside, numpy array of booleans
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"""
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pts = Utils.asArray_N_x_Dim(pts, self.dim)
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tensors = self.getTensor(locType)
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if locType == 'N' and self._meshType == 'CYL':
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#NOTE: for a CYL mesh we add a node to check if we are inside in the radial direction!
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tensors[0] = np.r_[0.,tensors[0]]
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tensors[1] = np.r_[tensors[1], 2.0*np.pi]
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inside = np.ones(pts.shape[0],dtype=bool)
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for i, tensor in enumerate(tensors):
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TOL = np.diff(tensor).min() * 1.0e-10
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inside = inside & (pts[:,i] >= tensor.min()-TOL) & (pts[:,i] <= tensor.max()+TOL)
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return inside
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def getInterpolationMat(self, loc, locType, zerosOutside=False):
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""" Produces interpolation matrix
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:param numpy.ndarray loc: Location of points to interpolate to
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:param str locType: What to interpolate (see below)
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:rtype: scipy.sparse.csr.csr_matrix
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:return: M, the interpolation matrix
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locType can be::
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'Ex' -> x-component of field defined on edges
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'Ey' -> y-component of field defined on edges
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'Ez' -> z-component of field defined on edges
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'Fx' -> x-component of field defined on faces
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'Fy' -> y-component of field defined on faces
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'Fz' -> z-component of field defined on faces
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'N' -> scalar field defined on nodes
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'CC' -> scalar field defined on cell centers
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"""
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if self._meshType == 'CYL' and self.isSymmetric and locType in ['Ex','Ez','Fy']:
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raise Exception('Symmetric CylMesh does not support %s interpolation, as this variable does not exist.' % locType)
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loc = Utils.asArray_N_x_Dim(loc, self.dim)
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if zerosOutside is False:
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assert np.all(self.isInside(loc)), "Points outside of mesh"
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else:
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indZeros = np.logical_not(self.isInside(loc))
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loc[indZeros, :] = np.array([v.mean() for v in self.getTensor('CC')])
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if locType in ['Fx','Fy','Fz','Ex','Ey','Ez']:
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ind = {'x':0, 'y':1, 'z':2}[locType[1]]
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assert self.dim >= ind, 'mesh is not high enough dimension.'
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nF_nE = self.vnF if 'F' in locType else self.vnE
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components = [Utils.spzeros(loc.shape[0], n) for n in nF_nE]
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components[ind] = Utils.interpmat(loc, *self.getTensor(locType))
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# remove any zero blocks (hstack complains)
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components = [comp for comp in components if comp.shape[1] > 0]
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Q = sp.hstack(components)
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elif locType in ['CC', 'N']:
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Q = Utils.interpmat(loc, *self.getTensor(locType))
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else:
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raise NotImplementedError('getInterpolationMat: locType=='+locType+' and mesh.dim=='+str(self.dim))
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if zerosOutside:
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Q[indZeros, :] = 0
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return Q.tocsr()
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def _fastInnerProduct(self, projType, prop=None, invProp=False, invMat=False):
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"""
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Fast version of getFaceInnerProduct.
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This does not handle the case of a full tensor prop.
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:param numpy.array prop: material property (tensor properties are possible) at each cell center (nC, (1, 3, or 6))
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:param str projType: 'E' or 'F'
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:param bool returnP: returns the projection matrices
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:param bool invProp: inverts the material property
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:param bool invMat: inverts the matrix
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:rtype: scipy.csr_matrix
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:return: M, the inner product matrix (nF, nF)
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"""
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assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
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if prop is None:
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prop = np.ones(self.nC)
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if invProp:
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prop = 1./prop
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if Utils.isScalar(prop):
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prop = prop*np.ones(self.nC)
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if prop.size == self.nC:
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Av = getattr(self, 'ave'+projType+'2CC')
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Vprop = self.vol * Utils.mkvc(prop)
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M = self.dim * Utils.sdiag(Av.T * Vprop)
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elif prop.size == self.nC*self.dim:
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Av = getattr(self, 'ave'+projType+'2CCV')
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V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
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M = Utils.sdiag(Av.T * V * Utils.mkvc(prop))
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else:
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return None
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if invMat:
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return Utils.sdInv(M)
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else:
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return M
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def _fastInnerProductDeriv(self, projType, prop, invProp=False, invMat=False):
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"""
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:param str projType: 'E' or 'F'
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:param TensorType tensorType: type of the tensor
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:param bool invProp: inverts the material property
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:param bool invMat: inverts the matrix
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:rtype: function
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:return: dMdmu, the derivative of the inner product matrix
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"""
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assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
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tensorType = Utils.TensorType(self, prop)
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dMdprop = None
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if invMat:
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MI = self._fastInnerProduct(projType, prop, invProp=invProp, invMat=invMat)
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if tensorType == 0:
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Av = getattr(self, 'ave'+projType+'2CC')
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V = Utils.sdiag(self.vol)
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ones = sp.csr_matrix((np.ones(self.nC), (range(self.nC), np.zeros(self.nC))), shape=(self.nC,1))
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if not invMat and not invProp:
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dMdprop = self.dim * Av.T * V * ones
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elif invMat and invProp:
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dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * ones * Utils.sdiag(1./prop**2)
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if tensorType == 1:
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Av = getattr(self, 'ave'+projType+'2CC')
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V = Utils.sdiag(self.vol)
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if not invMat and not invProp:
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dMdprop = self.dim * Av.T * V
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elif invMat and invProp:
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dMdprop = self.dim * Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
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if tensorType == 2: # anisotropic
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Av = getattr(self, 'ave'+projType+'2CCV')
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V = sp.kron(sp.identity(self.dim), Utils.sdiag(self.vol))
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if not invMat and not invProp:
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dMdprop = Av.T * V
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elif invMat and invProp:
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dMdprop = Utils.sdiag(MI.diagonal()**2) * Av.T * V * Utils.sdiag(1./prop**2)
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if dMdprop is not None:
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def innerProductDeriv(v=None):
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if v is None:
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print 'Depreciation Warning: TensorMesh.innerProductDeriv. You should be supplying a vector. Use: sdiag(u)*dMdprop'
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return dMdprop
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return Utils.sdiag(v) * dMdprop
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return innerProductDeriv
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else:
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return None
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class TensorMesh(BaseTensorMesh, BaseRectangularMesh, TensorView, DiffOperators, InnerProducts):
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"""
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TensorMesh is a mesh class that deals with tensor product meshes.
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Any Mesh that has a constant width along the entire axis
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such that it can defined by a single width vector, called 'h'.
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::
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hx = np.array([1,1,1])
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hy = np.array([1,2])
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hz = np.array([1,1,1,1])
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mesh = Mesh.TensorMesh([hx, hy, hz])
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Example of a padded tensor mesh using :func:`SimPEG.Utils.meshutils.meshTensor`:
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.. plot::
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:include-source:
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from SimPEG import Mesh, Utils
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M = Mesh.TensorMesh([[(10,10,-1.3),(10,40),(10,10,1.3)], [(10,10,-1.3),(10,20)]])
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M.plotGrid()
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For a quick tensor mesh on a (10x12x15) unit cube::
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mesh = Mesh.TensorMesh([10, 12, 15])
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"""
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__metaclass__ = Utils.SimPEGMetaClass
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_meshType = 'TENSOR'
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def __init__(self, h_in, x0=None):
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BaseTensorMesh.__init__(self, h_in, x0)
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def __str__(self):
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outStr = ' ---- {0:d}-D TensorMesh ---- '.format(self.dim)
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def printH(hx, outStr=''):
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i = -1
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while True:
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i = i + 1
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if i > hx.size:
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break
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elif i == hx.size:
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break
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h = hx[i]
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n = 1
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for j in range(i+1, hx.size):
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if hx[j] == h:
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n = n + 1
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i = i + 1
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else:
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break
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if n == 1:
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outStr += ' {0:.2f},'.format(h)
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else:
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outStr += ' {0:d}*{1:.2f},'.format(n,h)
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return outStr[:-1]
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if self.dim == 1:
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outStr += '\n x0: {0:.2f}'.format(self.x0[0])
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outStr += '\n nCx: {0:d}'.format(self.nCx)
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outStr += printH(self.hx, outStr='\n hx:')
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pass
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elif self.dim == 2:
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outStr += '\n x0: {0:.2f}'.format(self.x0[0])
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outStr += '\n y0: {0:.2f}'.format(self.x0[1])
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outStr += '\n nCx: {0:d}'.format(self.nCx)
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outStr += '\n nCy: {0:d}'.format(self.nCy)
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outStr += printH(self.hx, outStr='\n hx:')
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outStr += printH(self.hy, outStr='\n hy:')
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elif self.dim == 3:
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outStr += '\n x0: {0:.2f}'.format(self.x0[0])
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outStr += '\n y0: {0:.2f}'.format(self.x0[1])
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outStr += '\n z0: {0:.2f}'.format(self.x0[2])
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outStr += '\n nCx: {0:d}'.format(self.nCx)
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outStr += '\n nCy: {0:d}'.format(self.nCy)
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outStr += '\n nCz: {0:d}'.format(self.nCz)
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outStr += printH(self.hx, outStr='\n hx:')
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outStr += printH(self.hy, outStr='\n hy:')
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outStr += printH(self.hz, outStr='\n hz:')
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return outStr
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# --------------- Geometries ---------------------
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@property
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def vol(self):
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"""Construct cell volumes of the 3D model as 1d array."""
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if getattr(self, '_vol', None) is None:
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vh = self.h
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# Compute cell volumes
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if self.dim == 1:
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self._vol = Utils.mkvc(vh[0])
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elif self.dim == 2:
|
|
# Cell sizes in each direction
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|
self._vol = Utils.mkvc(np.outer(vh[0], vh[1]))
|
|
elif self.dim == 3:
|
|
# Cell sizes in each direction
|
|
self._vol = Utils.mkvc(np.outer(Utils.mkvc(np.outer(vh[0], vh[1])), vh[2]))
|
|
return self._vol
|
|
|
|
@property
|
|
def area(self):
|
|
"""Construct face areas of the 3D model as 1d array."""
|
|
if getattr(self, '_area', None) is None:
|
|
# Ensure that we are working with column vectors
|
|
vh = self.h
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
# Compute areas of cell faces
|
|
if(self.dim == 1):
|
|
self._area = np.ones(n[0]+1)
|
|
elif(self.dim == 2):
|
|
area1 = np.outer(np.ones(n[0]+1), vh[1])
|
|
area2 = np.outer(vh[0], np.ones(n[1]+1))
|
|
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2)]
|
|
elif(self.dim == 3):
|
|
area1 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(vh[1], vh[2])))
|
|
area2 = np.outer(vh[0], Utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
|
|
area3 = np.outer(vh[0], Utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
|
|
self._area = np.r_[Utils.mkvc(area1), Utils.mkvc(area2), Utils.mkvc(area3)]
|
|
return self._area
|
|
|
|
@property
|
|
def edge(self):
|
|
"""Construct edge legnths of the 3D model as 1d array."""
|
|
if getattr(self, '_edge', None) is None:
|
|
# Ensure that we are working with column vectors
|
|
vh = self.h
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
# Compute edge lengths
|
|
if(self.dim == 1):
|
|
self._edge = Utils.mkvc(vh[0])
|
|
elif(self.dim == 2):
|
|
l1 = np.outer(vh[0], np.ones(n[1]+1))
|
|
l2 = np.outer(np.ones(n[0]+1), vh[1])
|
|
self._edge = np.r_[Utils.mkvc(l1), Utils.mkvc(l2)]
|
|
elif(self.dim == 3):
|
|
l1 = np.outer(vh[0], Utils.mkvc(np.outer(np.ones(n[1]+1), np.ones(n[2]+1))))
|
|
l2 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(vh[1], np.ones(n[2]+1))))
|
|
l3 = np.outer(np.ones(n[0]+1), Utils.mkvc(np.outer(np.ones(n[1]+1), vh[2])))
|
|
self._edge = np.r_[Utils.mkvc(l1), Utils.mkvc(l2), Utils.mkvc(l3)]
|
|
return self._edge
|
|
|
|
@property
|
|
def faceBoundaryInd(self):
|
|
"""
|
|
Find indices of boundary faces in each direction
|
|
"""
|
|
if self.dim==1:
|
|
indxd = (self.gridFx==min(self.gridFx))
|
|
indxu = (self.gridFx==max(self.gridFx))
|
|
return indxd, indxu
|
|
elif self.dim==2:
|
|
indxd = (self.gridFx[:,0]==min(self.gridFx[:,0]))
|
|
indxu = (self.gridFx[:,0]==max(self.gridFx[:,0]))
|
|
indyd = (self.gridFy[:,1]==min(self.gridFy[:,1]))
|
|
indyu = (self.gridFy[:,1]==max(self.gridFy[:,1]))
|
|
return indxd, indxu, indyd, indyu
|
|
elif self.dim==3:
|
|
indxd = (self.gridFx[:,0]==min(self.gridFx[:,0]))
|
|
indxu = (self.gridFx[:,0]==max(self.gridFx[:,0]))
|
|
indyd = (self.gridFy[:,1]==min(self.gridFy[:,1]))
|
|
indyu = (self.gridFy[:,1]==max(self.gridFy[:,1]))
|
|
indzd = (self.gridFz[:,2]==min(self.gridFz[:,2]))
|
|
indzu = (self.gridFz[:,2]==max(self.gridFz[:,2]))
|
|
return indxd, indxu, indyd, indyu, indzd, indzu
|
|
|
|
@property
|
|
def cellBoundaryInd(self):
|
|
"""
|
|
Find indices of boundary faces in each direction
|
|
"""
|
|
if self.dim==1:
|
|
indxd = (self.gridCC==min(self.gridCC))
|
|
indxu = (self.gridCC==max(self.gridCC))
|
|
return indxd, indxu
|
|
elif self.dim==2:
|
|
indxd = (self.gridCC[:,0]==min(self.gridCC[:,0]))
|
|
indxu = (self.gridCC[:,0]==max(self.gridCC[:,0]))
|
|
indyd = (self.gridCC[:,1]==min(self.gridCC[:,1]))
|
|
indyu = (self.gridCC[:,1]==max(self.gridCC[:,1]))
|
|
return indxd, indxu, indyd, indyu
|
|
elif self.dim==3:
|
|
indxd = (self.gridCC[:,0]==min(self.gridCC[:,0]))
|
|
indxu = (self.gridCC[:,0]==max(self.gridCC[:,0]))
|
|
indyd = (self.gridCC[:,1]==min(self.gridCC[:,1]))
|
|
indyu = (self.gridCC[:,1]==max(self.gridCC[:,1]))
|
|
indzd = (self.gridCC[:,2]==min(self.gridCC[:,2]))
|
|
indzu = (self.gridCC[:,2]==max(self.gridCC[:,2]))
|
|
return indxd, indxu, indyd, indyu, indzd, indzu
|