mirror of
https://github.com/wassname/simpeg.git
synced 2026-06-28 11:05:48 +08:00
Lindsey Heagy
891 lines
32 KiB
Python
891 lines
32 KiB
Python
import numpy as np
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from scipy import sparse as sp
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from SimPEG.Utils import mkvc, sdiag, speye, kron3, spzeros, ddx, av, avExtrap
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def checkBC(bc):
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"""
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Checks if boundary condition 'bc' is valid.
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Each bc must be either 'dirichlet' or 'neumann'
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"""
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if(type(bc) is str):
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bc = [bc, bc]
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assert type(bc) is list, 'bc must be a list'
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assert len(bc) == 2, 'bc must have two elements'
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for bc_i in bc:
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assert type(bc_i) is str, "each bc must be a string"
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assert bc_i in ['dirichlet', 'neumann'], ("each bc must be either,"
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"'dirichlet' or 'neumann'")
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return bc
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def ddxCellGrad(n, bc):
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"""
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Create 1D derivative operator from cell-centers to nodes this means we
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go from n to n+1
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For Cell-Centered **Dirichlet**, use a ghost point::
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(u_1 - u_g)/hf = grad
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u_g u_1 u_2
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* | * | * ...
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^
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0
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u_g = - u_1
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grad = 2*u1/dx
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negitive on the other side.
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For Cell-Centered **Neumann**, use a ghost point::
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(u_1 - u_g)/hf = 0
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u_g u_1 u_2
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* | * | * ...
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u_g = u_1
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grad = 0; put a zero in.
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"""
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bc = checkBC(bc)
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D = sp.spdiags((np.ones((n+1, 1))*[-1, 1]).T, [-1, 0], n+1, n,
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format="csr")
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# Set the first side
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if(bc[0] == 'dirichlet'):
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D[0, 0] = 2
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elif(bc[0] == 'neumann'):
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D[0, 0] = 0
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# Set the second side
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if(bc[1] == 'dirichlet'):
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D[-1, -1] = -2
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elif(bc[1] == 'neumann'):
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D[-1, -1] = 0
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return D
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def ddxCellGradBC(n, bc):
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"""
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Create 1D derivative operator from cell-centers to nodes this means we
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go from n to n+1
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For Cell-Centered **Dirichlet**, use a ghost point::
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(u_1 - u_g)/hf = grad
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u_g u_1 u_2
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* | * | * ...
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^
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u_b
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We know the value at the boundary (u_b)::
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(u_g+u_1)/2 = u_b (the average)
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u_g = 2*u_b - u_1
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So plug in to gradient:
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(u_1 - (2*u_b - u_1))/hf = grad
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2*(u_1-u_b)/hf = grad
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Separate, because BC are known (and can move to RHS later)::
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( 2/hf )*u_1 + ( -2/hf )*u_b = grad
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( ^ ) JUST RETURN THIS
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"""
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bc = checkBC(bc)
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ij = (np.array([0, n]), np.array([0, 1]))
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vals = np.zeros(2)
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# Set the first side
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if(bc[0] == 'dirichlet'):
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vals[0] = -2
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elif(bc[0] == 'neumann'):
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vals[0] = 0
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# Set the second side
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if(bc[1] == 'dirichlet'):
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vals[1] = 2
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elif(bc[1] == 'neumann'):
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vals[1] = 0
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D = sp.csr_matrix((vals, ij), shape=(n+1, 2))
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return D
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class DiffOperators(object):
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"""
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Class creates the differential operators that you need!
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"""
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def __init__(self):
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raise Exception('DiffOperators is a base class providing differential'
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'operators on meshes and cannot run on its own.'
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'Inherit to your favorite Mesh class.')
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@property
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def faceDiv(self):
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"""
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Construct divergence operator (face-stg to cell-centres).
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"""
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if getattr(self, '_faceDiv', None) is None:
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n = self.vnC
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# Compute faceDivergence operator on faces
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if(self.dim == 1):
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D = ddx(n[0])
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elif(self.dim == 2):
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D1 = sp.kron(speye(n[1]), ddx(n[0]))
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D2 = sp.kron(ddx(n[1]), speye(n[0]))
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D = sp.hstack((D1, D2), format="csr")
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elif(self.dim == 3):
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D1 = kron3(speye(n[2]), speye(n[1]), ddx(n[0]))
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D2 = kron3(speye(n[2]), ddx(n[1]), speye(n[0]))
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D3 = kron3(ddx(n[2]), speye(n[1]), speye(n[0]))
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D = sp.hstack((D1, D2, D3), format="csr")
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# Compute areas of cell faces & volumes
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S = self.area
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V = self.vol
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self._faceDiv = sdiag(1/V)*D*sdiag(S)
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return self._faceDiv
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@property
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def faceDivx(self):
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"""
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Construct divergence operator in the x component (face-stg to
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cell-centres).
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"""
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if getattr(self, '_faceDivx', None) is None:
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# The number of cell centers in each direction
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n = self.vnC
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# Compute faceDivergence operator on faces
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if(self.dim == 1):
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D1 = ddx(n[0])
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elif(self.dim == 2):
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D1 = sp.kron(speye(n[1]), ddx(n[0]))
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elif(self.dim == 3):
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D1 = kron3(speye(n[2]), speye(n[1]), ddx(n[0]))
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# Compute areas of cell faces & volumes
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S = self.r(self.area, 'F', 'Fx', 'V')
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V = self.vol
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self._faceDivx = sdiag(1/V)*D1*sdiag(S)
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return self._faceDivx
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@property
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def faceDivy(self):
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if(self.dim < 2):
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return None
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if getattr(self, '_faceDivy', None) is None:
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# The number of cell centers in each direction
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n = self.vnC
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# Compute faceDivergence operator on faces
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if(self.dim == 2):
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D2 = sp.kron(ddx(n[1]), speye(n[0]))
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elif(self.dim == 3):
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D2 = kron3(speye(n[2]), ddx(n[1]), speye(n[0]))
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# Compute areas of cell faces & volumes
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S = self.r(self.area, 'F', 'Fy', 'V')
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V = self.vol
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self._faceDivy = sdiag(1/V)*D2*sdiag(S)
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return self._faceDivy
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@property
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def faceDivz(self):
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"""
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Construct divergence operator in the z component (face-stg to
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cell-centres).
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"""
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if(self.dim < 3):
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return None
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if getattr(self, '_faceDivz', None) is None:
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# The number of cell centers in each direction
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n = self.vnC
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# Compute faceDivergence operator on faces
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D3 = kron3(ddx(n[2]), speye(n[1]), speye(n[0]))
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# Compute areas of cell faces & volumes
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S = self.r(self.area, 'F', 'Fz', 'V')
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V = self.vol
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self._faceDivz = sdiag(1/V)*D3*sdiag(S)
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return self._faceDivz
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@property
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def nodalGrad(self):
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"""
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Construct gradient operator (nodes to edges).
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"""
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if getattr(self, '_nodalGrad', None) is None:
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# The number of cell centers in each direction
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n = self.vnC
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# Compute divergence operator on faces
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if(self.dim == 1):
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G = ddx(n[0])
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elif(self.dim == 2):
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D1 = sp.kron(speye(n[1]+1), ddx(n[0]))
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D2 = sp.kron(ddx(n[1]), speye(n[0]+1))
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G = sp.vstack((D1, D2), format="csr")
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elif(self.dim == 3):
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D1 = kron3(speye(n[2]+1), speye(n[1]+1), ddx(n[0]))
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D2 = kron3(speye(n[2]+1), ddx(n[1]), speye(n[0]+1))
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D3 = kron3(ddx(n[2]), speye(n[1]+1), speye(n[0]+1))
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G = sp.vstack((D1, D2, D3), format="csr")
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# Compute lengths of cell edges
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L = self.edge
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self._nodalGrad = sdiag(1/L)*G
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return self._nodalGrad
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@property
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def nodalLaplacian(self):
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"""
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Construct laplacian operator (nodes to edges).
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"""
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if getattr(self, '_nodalLaplacian', None) is None:
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print 'Warning: Laplacian has not been tested rigorously.'
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# The number of cell centers in each direction
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n = self.vnC
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# Compute divergence operator on faces
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if(self.dim == 1):
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D1 = sdiag(1./self.hx) * ddx(mesh.nCx)
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L = - D1.T*D1
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elif(self.dim == 2):
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D1 = sdiag(1./self.hx) * ddx(n[0])
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D2 = sdiag(1./self.hy) * ddx(n[1])
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L1 = sp.kron(speye(n[1]+1), - D1.T * D1)
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L2 = sp.kron(- D2.T * D2, speye(n[0]+1))
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L = L1 + L2
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elif(self.dim == 3):
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D1 = sdiag(1./self.hx) * ddx(n[0])
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D2 = sdiag(1./self.hy) * ddx(n[1])
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D3 = sdiag(1./self.hz) * ddx(n[2])
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L1 = kron3(speye(n[2]+1), speye(n[1]+1), - D1.T * D1)
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L2 = kron3(speye(n[2]+1), - D2.T * D2, speye(n[0]+1))
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L3 = kron3(- D3.T * D3, speye(n[1]+1), speye(n[0]+1))
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L = L1 + L2 + L3
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self._nodalLaplacian = L
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return self._nodalLaplacian
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def setCellGradBC(self, BC):
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"""
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Function that sets the boundary conditions for cell-centred derivative
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operators.
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Examples::
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# Neumann in all directions
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BC = 'neumann'
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# 3D, Dirichlet in y Neumann else
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BC = ['neumann', 'dirichlet', 'neumann']
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# 3D, Neumann in x on bottom of domain, Dirichlet else
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BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet']
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"""
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if(type(BC) is str):
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BC = [BC]*self.dim
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if(type(BC) is list):
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assert len(BC) == self.dim, 'BC list must be the size of your mesh'
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else:
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raise Exception("BC must be a str or a list.")
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for i, bc_i in enumerate(BC):
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BC[i] = checkBC(bc_i)
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# ensure we create a new gradient next time we call it
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self._cellGrad = None
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self._cellGradBC = None
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self._cellGradBC_list = BC
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return BC
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_cellGradBC_list = 'neumann'
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def _cellGradStencil(self):
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BC = self.setCellGradBC(self._cellGradBC_list)
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n = self.vnC
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if(self.dim == 1):
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G = ddxCellGrad(n[0], BC[0])
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elif(self.dim == 2):
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G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC[0]))
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G2 = sp.kron(ddxCellGrad(n[1], BC[1]), speye(n[0]))
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G = sp.vstack((G1, G2), format="csr")
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elif(self.dim == 3):
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G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC[0]))
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G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC[1]), speye(n[0]))
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G3 = kron3(ddxCellGrad(n[2], BC[2]), speye(n[1]), speye(n[0]))
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G = sp.vstack((G1, G2, G3), format="csr")
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return G
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@property
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def cellGrad(self):
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"""
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The cell centered Gradient, takes you to cell faces.
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"""
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if(self._cellGrad is None):
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G = self._cellGradStencil()
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S = self.area # Compute areas of cell faces & volumes
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V = self.aveCC2F*self.vol # Average volume between adjacent cells
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self._cellGrad = sdiag(S/V)*G
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return self._cellGrad
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@property
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def cellGradBC(self):
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"""
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The cell centered Gradient boundary condition matrix
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"""
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if getattr(self, '_cellGradBC', None) is None:
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BC = self.setCellGradBC(self._cellGradBC_list)
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n = self.vnC
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if(self.dim == 1):
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G = ddxCellGradBC(n[0], BC[0])
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elif(self.dim == 2):
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G1 = sp.kron(speye(n[1]), ddxCellGradBC(n[0], BC[0]))
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G2 = sp.kron(ddxCellGradBC(n[1], BC[1]), speye(n[0]))
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G = sp.block_diag((G1, G2), format="csr")
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elif(self.dim == 3):
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G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGradBC(n[0], BC[0]))
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G2 = kron3(speye(n[2]), ddxCellGradBC(n[1], BC[1]), speye(n[0]))
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G3 = kron3(ddxCellGradBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
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G = sp.block_diag((G1, G2, G3), format="csr")
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# Compute areas of cell faces & volumes
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S = self.area
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V = self.aveCC2F*self.vol # Average volume between adjacent cells
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self._cellGradBC = sdiag(S/V)*G
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return self._cellGradBC
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# def cellGradBC():
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# doc = "The cell centered Gradient boundary condition matrix"
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# def fget(self):
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# if(self._cellGradBC is None):
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# BC = self.setCellGradBC(self._cellGradBC_list)
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# n = self.vnC
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# if(self.dim == 1):
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# G = ddxCellGradBC(n[0], BC[0])
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# elif(self.dim == 2):
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# G1 = sp.kron(speye(n[1]), ddxCellGradBC(n[0], BC[0]))
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# G2 = sp.kron(ddxCellGradBC(n[1], BC[1]), speye(n[0]))
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# G = sp.block_diag((G1, G2), format="csr")
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# elif(self.dim == 3):
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# G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGradBC(n[0], BC[0]))
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# G2 = kron3(speye(n[2]), ddxCellGradBC(n[1], BC[1]), speye(n[0]))
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# G3 = kron3(ddxCellGradBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
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# G = sp.block_diag((G1, G2, G3), format="csr")
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# # Compute areas of cell faces & volumes
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# S = self.area
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# V = self.aveCC2F*self.vol # Average volume between adjacent cells
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# self._cellGradBC = sdiag(S/V)*G
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# return self._cellGradBC
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# return locals()
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# _cellGradBC = None
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# cellGradBC = property(**cellGradBC())
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def _cellGradxStencil(self):
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BC = ['neumann', 'neumann']
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n = self.vnC
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if(self.dim == 1):
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G1 = ddxCellGrad(n[0], BC)
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elif(self.dim == 2):
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G1 = sp.kron(speye(n[1]), ddxCellGrad(n[0], BC))
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elif(self.dim == 3):
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G1 = kron3(speye(n[2]), speye(n[1]), ddxCellGrad(n[0], BC))
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return G1
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@property
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def cellGradx(self):
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"""
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Cell centered Gradient in the x dimension. Has neumann boundary
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conditions.
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"""
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if getattr(self, '_cellGradx', None) is None:
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G1 = self._cellGradxStencil()
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# Compute areas of cell faces & volumes
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V = self.aveCC2F*self.vol
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L = self.r(self.area/V, 'F','Fx', 'V')
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self._cellGradx = sdiag(L)*G1
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return self._cellGradx
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def _cellGradyStencil(self):
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if self.dim < 2: return None
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BC = ['neumann', 'neumann']
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n = self.vnC
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if(self.dim == 2):
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G2 = sp.kron(ddxCellGrad(n[1], BC), speye(n[0]))
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elif(self.dim == 3):
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G2 = kron3(speye(n[2]), ddxCellGrad(n[1], BC), speye(n[0]))
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return G2
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@property
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def cellGrady(self):
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if self.dim < 2:
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return None
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if getattr(self, '_cellGrady', None) is None:
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G2 = self._cellGradyStencil()
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# Compute areas of cell faces & volumes
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V = self.aveCC2F*self.vol
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L = self.r(self.area/V, 'F', 'Fy', 'V')
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self._cellGrady = sdiag(L)*G2
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return self._cellGrady
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def _cellGradzStencil(self):
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if self.dim < 3: return None
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BC = ['neumann', 'neumann']
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n = self.vnC
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G3 = kron3(ddxCellGrad(n[2], BC), speye(n[1]), speye(n[0]))
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return G3
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@property
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def cellGradz(self):
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"""
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Cell centered Gradient in the x dimension. Has neumann boundary
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conditions.
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"""
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if self.dim < 3:
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return None
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if getattr(self, '_cellGradz', None) is None:
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G3 = self._cellGradzStencil()
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# Compute areas of cell faces & volumes
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V = self.aveCC2F*self.vol
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L = self.r(self.area/V, 'F', 'Fz', 'V')
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self._cellGradz = sdiag(L)*G3
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return self._cellGradz
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@property
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def edgeCurl(self):
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"""
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Construct the 3D curl operator.
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"""
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if getattr(self, '_edgeCurl', None) is None:
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assert self.dim > 1, "Edge Curl only programed for 2 or 3D."
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n = self.vnC # The number of cell centers in each direction
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L = self.edge # Compute lengths of cell edges
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S = self.area # Compute areas of cell faces
|
|
|
|
# Compute divergence operator on faces
|
|
if self.dim == 2:
|
|
|
|
D21 = sp.kron(ddx(n[1]), speye(n[0]))
|
|
D12 = sp.kron(speye(n[1]), ddx(n[0]))
|
|
C = sp.hstack((-D21, D12), format="csr")
|
|
self._edgeCurl = C*sdiag(1/S)
|
|
|
|
elif self.dim == 3:
|
|
|
|
D32 = kron3(ddx(n[2]), speye(n[1]), speye(n[0]+1))
|
|
D23 = kron3(speye(n[2]), ddx(n[1]), speye(n[0]+1))
|
|
D31 = kron3(ddx(n[2]), speye(n[1]+1), speye(n[0]))
|
|
D13 = kron3(speye(n[2]), speye(n[1]+1), ddx(n[0]))
|
|
D21 = kron3(speye(n[2]+1), ddx(n[1]), speye(n[0]))
|
|
D12 = kron3(speye(n[2]+1), speye(n[1]), ddx(n[0]))
|
|
|
|
O1 = spzeros(np.shape(D32)[0], np.shape(D31)[1])
|
|
O2 = spzeros(np.shape(D31)[0], np.shape(D32)[1])
|
|
O3 = spzeros(np.shape(D21)[0], np.shape(D13)[1])
|
|
|
|
C = sp.vstack((sp.hstack((O1, -D32, D23)),
|
|
sp.hstack((D31, O2, -D13)),
|
|
sp.hstack((-D21, D12, O3))), format="csr")
|
|
|
|
self._edgeCurl = sdiag(1/S)*(C*sdiag(L))
|
|
return self._edgeCurl
|
|
|
|
def getBCProjWF(self, BC, discretization='CC'):
|
|
"""
|
|
|
|
The weak form boundary condition projection matrices.
|
|
|
|
Examples::
|
|
# Neumann in all directions
|
|
BC = 'neumann'
|
|
|
|
# 3D, Dirichlet in y Neumann else
|
|
BC = ['neumann', 'dirichlet', 'neumann']
|
|
|
|
# 3D, Neumann in x on bottom of domain, Dirichlet else
|
|
BC = [['neumann', 'dirichlet'], 'dirichlet', 'dirichlet']
|
|
"""
|
|
|
|
if discretization is not 'CC':
|
|
raise NotImplementedError('Boundary conditions only implemented'
|
|
'for CC discretization.')
|
|
|
|
if(type(BC) is str):
|
|
BC = [BC for _ in self.vnC] # Repeat the str self.dim times
|
|
elif(type(BC) is list):
|
|
assert len(BC) == self.dim, 'BC list must be the size of your mesh'
|
|
else:
|
|
raise Exception("BC must be a str or a list.")
|
|
|
|
for i, bc_i in enumerate(BC):
|
|
BC[i] = checkBC(bc_i)
|
|
|
|
def projDirichlet(n, bc):
|
|
bc = checkBC(bc)
|
|
ij = ([0, n], [0, 1])
|
|
vals = [0, 0]
|
|
if(bc[0] == 'dirichlet'):
|
|
vals[0] = -1
|
|
if(bc[1] == 'dirichlet'):
|
|
vals[1] = 1
|
|
return sp.csr_matrix((vals, ij), shape=(n+1, 2))
|
|
|
|
def projNeumannIn(n, bc):
|
|
bc = checkBC(bc)
|
|
P = sp.identity(n+1).tocsr()
|
|
if(bc[0] == 'neumann'):
|
|
P = P[1:, :]
|
|
if(bc[1] == 'neumann'):
|
|
P = P[:-1, :]
|
|
return P
|
|
|
|
def projNeumannOut(n, bc):
|
|
bc = checkBC(bc)
|
|
ij = ([0, 1], [0, n])
|
|
vals = [0,0]
|
|
if(bc[0] == 'neumann'):
|
|
vals[0] = 1
|
|
if(bc[1] == 'neumann'):
|
|
vals[1] = 1
|
|
return sp.csr_matrix((vals, ij), shape=(2, n+1))
|
|
|
|
n = self.vnC
|
|
indF = self.faceBoundaryInd
|
|
if(self.dim == 1):
|
|
Pbc = projDirichlet(n[0], BC[0])
|
|
indF = indF[0] | indF[1]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
Pin = projNeumannIn(n[0], BC[0])
|
|
|
|
Pout = projNeumannOut(n[0], BC[0])
|
|
|
|
elif(self.dim == 2):
|
|
Pbc1 = sp.kron(speye(n[1]), projDirichlet(n[0], BC[0]))
|
|
Pbc2 = sp.kron(projDirichlet(n[1], BC[1]), speye(n[0]))
|
|
Pbc = sp.block_diag((Pbc1, Pbc2), format="csr")
|
|
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3])]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
P1 = sp.kron(speye(n[1]), projNeumannIn(n[0], BC[0]))
|
|
P2 = sp.kron(projNeumannIn(n[1], BC[1]), speye(n[0]))
|
|
Pin = sp.block_diag((P1, P2), format="csr")
|
|
|
|
P1 = sp.kron(speye(n[1]), projNeumannOut(n[0], BC[0]))
|
|
P2 = sp.kron(projNeumannOut(n[1], BC[1]), speye(n[0]))
|
|
Pout = sp.block_diag((P1, P2), format="csr")
|
|
|
|
elif(self.dim == 3):
|
|
Pbc1 = kron3(speye(n[2]), speye(n[1]), projDirichlet(n[0], BC[0]))
|
|
Pbc2 = kron3(speye(n[2]), projDirichlet(n[1], BC[1]), speye(n[0]))
|
|
Pbc3 = kron3(projDirichlet(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
|
Pbc = sp.block_diag((Pbc1, Pbc2, Pbc3), format="csr")
|
|
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3]), (indF[4] |
|
|
indF[5])]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
P1 = kron3(speye(n[2]), speye(n[1]), projNeumannIn(n[0], BC[0]))
|
|
P2 = kron3(speye(n[2]), projNeumannIn(n[1], BC[1]), speye(n[0]))
|
|
P3 = kron3(projNeumannIn(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
|
Pin = sp.block_diag((P1, P2, P3), format="csr")
|
|
|
|
P1 = kron3(speye(n[2]), speye(n[1]), projNeumannOut(n[0], BC[0]))
|
|
P2 = kron3(speye(n[2]), projNeumannOut(n[1], BC[1]), speye(n[0]))
|
|
P3 = kron3(projNeumannOut(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
|
Pout = sp.block_diag((P1, P2, P3), format="csr")
|
|
|
|
return Pbc, Pin, Pout
|
|
|
|
def getBCProjWF_simple(self, discretization='CC'):
|
|
"""
|
|
The weak form boundary condition projection matrices
|
|
when mixed boundary condition is used
|
|
"""
|
|
|
|
if discretization is not 'CC':
|
|
raise NotImplementedError('Boundary conditions only implemented'
|
|
'for CC discretization.')
|
|
|
|
def projBC(n):
|
|
ij = ([0, n], [0, 1])
|
|
vals = [0, 0]
|
|
vals[0] = 1
|
|
vals[1] = 1
|
|
return sp.csr_matrix((vals, ij), shape=(n+1, 2))
|
|
|
|
def projDirichlet(n, bc):
|
|
bc = checkBC(bc)
|
|
ij = ([0, n], [0, 1])
|
|
vals = [0, 0]
|
|
if(bc[0] == 'dirichlet'):
|
|
vals[0] = -1
|
|
if(bc[1] == 'dirichlet'):
|
|
vals[1] = 1
|
|
return sp.csr_matrix((vals, ij), shape=(n+1, 2))
|
|
|
|
BC = [['dirichlet', 'dirichlet'], ['dirichlet', 'dirichlet'],
|
|
['dirichlet', 'dirichlet']]
|
|
n = self.vnC
|
|
indF = self.faceBoundaryInd
|
|
|
|
if(self.dim == 1):
|
|
Pbc = projDirichlet(n[0], BC[0])
|
|
B = projBC(n[0])
|
|
indF = indF[0] | indF[1]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
elif(self.dim == 2):
|
|
Pbc1 = sp.kron(speye(n[1]), projDirichlet(n[0], BC[0]))
|
|
Pbc2 = sp.kron(projDirichlet(n[1], BC[1]), speye(n[0]))
|
|
Pbc = sp.block_diag((Pbc1, Pbc2), format="csr")
|
|
B1 = sp.kron(speye(n[1]), projBC(n[0]))
|
|
B2 = sp.kron(projBC(n[1]), speye(n[0]))
|
|
B = sp.block_diag((B1, B2), format="csr")
|
|
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3])]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
elif(self.dim == 3):
|
|
Pbc1 = kron3(speye(n[2]), speye(n[1]), projDirichlet(n[0], BC[0]))
|
|
Pbc2 = kron3(speye(n[2]), projDirichlet(n[1], BC[1]), speye(n[0]))
|
|
Pbc3 = kron3(projDirichlet(n[2], BC[2]), speye(n[1]), speye(n[0]))
|
|
Pbc = sp.block_diag((Pbc1, Pbc2, Pbc3), format="csr")
|
|
B1 = kron3(speye(n[2]), speye(n[1]), projBC(n[0]))
|
|
B2 = kron3(speye(n[2]), projBC(n[1]), speye(n[0]))
|
|
B3 = kron3(projBC(n[2]), speye(n[1]), speye(n[0]))
|
|
B = sp.block_diag((B1, B2, B3), format="csr")
|
|
indF = np.r_[(indF[0] | indF[1]), (indF[2] | indF[3]), (indF[4] | indF[5])]
|
|
Pbc = Pbc*sdiag(self.area[indF])
|
|
|
|
return Pbc, B.T
|
|
# --------------- Averaging ---------------------
|
|
|
|
@property
|
|
def aveF2CC(self):
|
|
"Construct the averaging operator on cell faces to cell centers."
|
|
if(self.dim == 1):
|
|
return self.aveFx2CC
|
|
elif(self.dim == 2):
|
|
return (0.5)*sp.hstack((self.aveFx2CC, self.aveFy2CC),
|
|
format="csr")
|
|
elif(self.dim == 3):
|
|
return (1./3.)*sp.hstack((self.aveFx2CC, self.aveFy2CC,
|
|
self.aveFz2CC), format="csr")
|
|
|
|
@property
|
|
def aveF2CCV(self):
|
|
"Construct the averaging operator on cell faces to cell centers."
|
|
if(self.dim == 1):
|
|
return self.aveFx2CC
|
|
elif(self.dim == 2):
|
|
return sp.block_diag((self.aveFx2CC, self.aveFy2CC), format="csr")
|
|
elif(self.dim == 3):
|
|
return sp.block_diag((self.aveFx2CC, self.aveFy2CC, self.aveFz2CC),
|
|
format="csr")
|
|
|
|
@property
|
|
def aveFx2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell faces in the x direction to
|
|
cell centers.
|
|
"""
|
|
|
|
if getattr(self, '_aveFx2CC', None) is None:
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveFx2CC = av(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveFx2CC = sp.kron(speye(n[1]), av(n[0]))
|
|
elif(self.dim == 3):
|
|
self._aveFx2CC = kron3(speye(n[2]), speye(n[1]), av(n[0]))
|
|
return self._aveFx2CC
|
|
|
|
@property
|
|
def aveFy2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell faces in the y direction to
|
|
cell centers.
|
|
"""
|
|
if self.dim < 2:
|
|
return None
|
|
if getattr(self, '_aveFy2CC', None) is None:
|
|
n = self.vnC
|
|
if(self.dim == 2):
|
|
self._aveFy2CC = sp.kron(av(n[1]), speye(n[0]))
|
|
elif(self.dim == 3):
|
|
self._aveFy2CC = kron3(speye(n[2]), av(n[1]), speye(n[0]))
|
|
return self._aveFy2CC
|
|
|
|
@property
|
|
def aveFz2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell faces in the z direction to
|
|
cell centers.
|
|
"""
|
|
if self.dim < 3: return None
|
|
if getattr(self, '_aveFz2CC', None) is None:
|
|
n = self.vnC
|
|
if(self.dim == 3):
|
|
self._aveFz2CC = kron3(av(n[2]), speye(n[1]), speye(n[0]))
|
|
return self._aveFz2CC
|
|
|
|
|
|
@property
|
|
def aveCC2F(self):
|
|
"Construct the averaging operator on cell cell centers to faces."
|
|
if getattr(self, '_aveCC2F', None) is None:
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveCC2F = avExtrap(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveCC2F = sp.vstack((sp.kron(speye(n[1]),
|
|
avExtrap(n[0])),
|
|
sp.kron(avExtrap(n[1]),
|
|
speye(n[0]))), format="csr")
|
|
elif(self.dim == 3):
|
|
self._aveCC2F = sp.vstack((kron3(speye(n[2]), speye(n[1]),
|
|
avExtrap(n[0])),
|
|
kron3(speye(n[2]), avExtrap(n[1]),
|
|
speye(n[0])),
|
|
kron3(avExtrap(n[2]), speye(n[1]),
|
|
speye(n[0]))),
|
|
format="csr")
|
|
return self._aveCC2F
|
|
|
|
@property
|
|
def aveE2CC(self):
|
|
"Construct the averaging operator on cell edges to cell centers."
|
|
if(self.dim == 1):
|
|
return self.aveEx2CC
|
|
elif(self.dim == 2):
|
|
return 0.5*sp.hstack((self.aveEx2CC, self.aveEy2CC), format="csr")
|
|
elif(self.dim == 3):
|
|
return (1./3)*sp.hstack((self.aveEx2CC, self.aveEy2CC,
|
|
self.aveEz2CC), format="csr")
|
|
|
|
@property
|
|
def aveE2CCV(self):
|
|
"Construct the averaging operator on cell edges to cell centers."
|
|
if(self.dim == 1):
|
|
return self.aveEx2CC
|
|
elif(self.dim == 2):
|
|
return sp.block_diag((self.aveEx2CC, self.aveEy2CC), format="csr")
|
|
elif(self.dim == 3):
|
|
return sp.block_diag((self.aveEx2CC, self.aveEy2CC, self.aveEz2CC),
|
|
format="csr")
|
|
|
|
@property
|
|
def aveEx2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell edges in the x direction to
|
|
cell centers.
|
|
"""
|
|
if getattr(self, '_aveEx2CC', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveEx2CC = speye(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveEx2CC = sp.kron(av(n[1]), speye(n[0]))
|
|
elif(self.dim == 3):
|
|
self._aveEx2CC = kron3(av(n[2]), av(n[1]), speye(n[0]))
|
|
return self._aveEx2CC
|
|
|
|
@property
|
|
def aveEy2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell edges in the y direction to
|
|
cell centers.
|
|
"""
|
|
if self.dim < 2:
|
|
return None
|
|
if getattr(self, '_aveEy2CC', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 2):
|
|
self._aveEy2CC = sp.kron(speye(n[1]), av(n[0]))
|
|
elif(self.dim == 3):
|
|
self._aveEy2CC = kron3(av(n[2]), speye(n[1]), av(n[0]))
|
|
return self._aveEy2CC
|
|
|
|
@property
|
|
def aveEz2CC(self):
|
|
"""
|
|
Construct the averaging operator on cell edges in the z direction to
|
|
cell centers.
|
|
"""
|
|
if self.dim < 3:
|
|
return None
|
|
if getattr(self, '_aveEz2CC', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 3):
|
|
self._aveEz2CC = kron3(speye(n[2]), av(n[1]), av(n[0]))
|
|
return self._aveEz2CC
|
|
|
|
@property
|
|
def aveN2CC(self):
|
|
"Construct the averaging operator on cell nodes to cell centers."
|
|
if getattr(self, '_aveN2CC', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveN2CC = av(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveN2CC = sp.kron(av(n[1]), av(n[0])).tocsr()
|
|
elif(self.dim == 3):
|
|
self._aveN2CC = kron3(av(n[2]), av(n[1]), av(n[0])).tocsr()
|
|
return self._aveN2CC
|
|
|
|
@property
|
|
def aveN2E(self):
|
|
"""
|
|
Construct the averaging operator on cell nodes to cell edges, keeping
|
|
each dimension separate.
|
|
"""
|
|
|
|
if getattr(self, '_aveN2E', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveN2E = av(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveN2E = sp.vstack((sp.kron(speye(n[1]+1), av(n[0])),
|
|
sp.kron(av(n[1]), speye(n[0]+1))),
|
|
format="csr")
|
|
elif(self.dim == 3):
|
|
self._aveN2E = sp.vstack((kron3(speye(n[2]+1), speye(n[1]+1),
|
|
av(n[0])),
|
|
kron3(speye(n[2]+1), av(n[1]),
|
|
speye(n[0]+1)),
|
|
kron3(av(n[2]), speye(n[1]+1),
|
|
speye(n[0]+1))),
|
|
format="csr")
|
|
return self._aveN2E
|
|
|
|
@property
|
|
def aveN2F(self):
|
|
"""
|
|
Construct the averaging operator on cell nodes to cell faces, keeping
|
|
each dimension separate.
|
|
"""
|
|
if getattr(self, '_aveN2F', None) is None:
|
|
# The number of cell centers in each direction
|
|
n = self.vnC
|
|
if(self.dim == 1):
|
|
self._aveN2F = av(n[0])
|
|
elif(self.dim == 2):
|
|
self._aveN2F = sp.vstack((sp.kron(av(n[1]), speye(n[0]+1)),
|
|
sp.kron(speye(n[1]+1), av(n[0]))),
|
|
format="csr")
|
|
elif(self.dim == 3):
|
|
self._aveN2F = sp.vstack((kron3(av(n[2]), av(n[1]),
|
|
speye(n[0]+1)),
|
|
kron3(av(n[2]), speye(n[1]+1),
|
|
av(n[0])),
|
|
kron3(speye(n[2]+1), av(n[1]),
|
|
av(n[0]))),
|
|
format="csr")
|
|
return self._aveN2F
|