mirror of
https://github.com/wassname/simpeg.git
synced 2026-07-01 22:58:26 +08:00
Rowan Cockett
285 lines
12 KiB
Python
285 lines
12 KiB
Python
from scipy import sparse as sp
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from sputils import sdiag, inv3X3BlockDiagonal, inv2X2BlockDiagonal
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from utils import sub2ind, ndgrid, mkvc, getSubArray
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import numpy as np
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class InnerProducts(object):
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"""
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Class creates the inner product matrices that you need!
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"""
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def __init__(self):
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raise Exception('InnerProducts is a base class providing inner product matrices for meshes and cannot run on its own. Inherit to your favorite Mesh class.')
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def getFaceInnerProduct(self, mu=None, returnP=False):
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if self._meshType == 'TENSOR':
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pass
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elif self._meshType == 'LOM':
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pass # todo: we should be doing something slightly different here!
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if self.dim == 2:
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return getFaceInnerProduct2D(self, mu, returnP)
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elif self.dim == 3:
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return getFaceInnerProduct(self, mu, returnP)
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def getEdgeInnerProduct(self, sigma=None, returnP=False):
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if self._meshType == 'TENSOR':
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pass
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elif self._meshType == 'LOM':
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pass # todo: we should be doing something slightly different here!
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return getEdgeInnerProduct(self, sigma, returnP)
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# ------------------------ Geometries ------------------------------
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#
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#
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# node(i,j,k+1) ------ edge2(i,j,k+1) ----- node(i,j+1,k+1)
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# / /
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# / / |
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# edge3(i,j,k) face1(i,j,k) edge3(i,j+1,k)
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# / / |
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# / / |
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# node(i,j,k) ------ edge2(i,j,k) ----- node(i,j+1,k)
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# | | |
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# | | node(i+1,j+1,k+1)
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# | | /
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# edge1(i,j,k) face3(i,j,k) edge1(i,j+1,k)
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# | | /
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# | | /
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# | |/
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# node(i+1,j,k) ------ edge2(i+1,j,k) ----- node(i+1,j+1,k)
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def getFaceInnerProduct(mesh, mu=None, returnP=False):
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if mu is None: # default is ones
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mu = np.ones((mesh.nC, 1))
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m = np.array([mesh.nCx, mesh.nCy, mesh.nCz])
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nc = mesh.nC
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i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2]))
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iijjkk = ndgrid(i, j, k)
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ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
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if mesh._meshType == 'LOM':
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fN1 = mesh.r(mesh.normals, 'F', 'Fx', 'M')
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fN2 = mesh.r(mesh.normals, 'F', 'Fy', 'M')
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fN3 = mesh.r(mesh.normals, 'F', 'Fz', 'M')
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def Pxxx(pos):
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ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
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ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nF[0]
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ind3 = sub2ind(mesh.nFz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nF[0] + mesh.nF[1]
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IND = np.r_[ind1, ind2, ind3].flatten()
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PXXX = sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nF))).tocsr()
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if mesh._meshType == 'LOM':
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I3x3 = inv3X3BlockDiagonal(getSubArray(fN1[0], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(fN1[1], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(fN1[2], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]),
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getSubArray(fN2[0], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(fN2[1], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(fN2[2], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]),
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getSubArray(fN3[0], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(fN3[1], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(fN3[2], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]))
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PXXX = I3x3 * PXXX
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return PXXX
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# no | node | f1 | f2 | f3
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# 000 | i ,j ,k | i , j, k | i, j , k | i, j, k
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# 100 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k
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# 010 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k
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# 110 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k
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# 001 | i ,j ,k | i , j, k | i, j , k | i, j, k+1
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# 101 | i+1,j ,k | i+1, j, k | i, j , k | i, j, k+1
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# 011 | i ,j+1,k | i , j, k | i, j+1, k | i, j, k+1
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# 111 | i+1,j+1,k | i+1, j, k | i, j+1, k | i, j, k+1
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# Square root of cell volume multiplied by 1/8
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v = np.sqrt(0.125*mesh.vol)
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V3 = sdiag(np.r_[v, v, v]) # We will multiply on each side to keep symmetry
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P000 = V3*Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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P100 = V3*Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
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P010 = V3*Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 0]])
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P110 = V3*Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 0]])
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P001 = V3*Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 1]])
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P101 = V3*Pxxx([[1, 0, 0], [0, 0, 0], [0, 0, 1]])
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P011 = V3*Pxxx([[0, 0, 0], [0, 1, 0], [0, 0, 1]])
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P111 = V3*Pxxx([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
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if mu.size == mesh.nC: # Isotropic!
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mu = mkvc(mu) # ensure it is a vector.
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Mu = sdiag(np.r_[mu, mu, mu])
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elif mu.shape[1] == 3: # Diagonal tensor
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Mu = sdiag(np.r_[mu[:, 0], mu[:, 1], mu[:, 2]])
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elif mu.shape[1] == 6: # Fully anisotropic
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row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 3]), sdiag(mu[:, 4])))
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row2 = sp.hstack((sdiag(mu[:, 3]), sdiag(mu[:, 1]), sdiag(mu[:, 5])))
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row3 = sp.hstack((sdiag(mu[:, 4]), sdiag(mu[:, 5]), sdiag(mu[:, 2])))
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Mu = sp.vstack((row1, row2, row3))
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A = P000.T*Mu*P000 + P001.T*Mu*P001 + P010.T*Mu*P010 + P011.T*Mu*P011 + P100.T*Mu*P100 + P101.T*Mu*P101 + P110.T*Mu*P110 + P111.T*Mu*P111
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P = [P000, P001, P010, P011, P100, P101, P110, P111]
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if returnP:
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return A, P
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else:
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return A
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def getFaceInnerProduct2D(mesh, mu=None, returnP=False):
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if mu is None: # default is ones
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mu = np.ones((mesh.nC, 1))
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m = np.array([mesh.nCx, mesh.nCy])
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nc = mesh.nC
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i, j = np.int64(range(m[0])), np.int64(range(m[1]))
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iijj = ndgrid(i, j)
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ii, jj = iijj[:, 0], iijj[:, 1]
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if mesh._meshType == 'LOM':
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fN1 = mesh.r(mesh.normals, 'F', 'Fx', 'M')
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fN2 = mesh.r(mesh.normals, 'F', 'Fy', 'M')
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def Pxx(pos):
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ind1 = sub2ind(mesh.nFx, np.c_[ii + pos[0][0], jj + pos[0][1]])
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ind2 = sub2ind(mesh.nFy, np.c_[ii + pos[1][0], jj + pos[1][1]]) + mesh.nF[0]
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IND = np.r_[ind1, ind2].flatten()
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PXX = sp.coo_matrix((np.ones(2*nc), (range(2*nc), IND)), shape=(2*nc, np.sum(mesh.nF))).tocsr()
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if mesh._meshType == 'LOM':
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# print fN1[0].shape
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# print fN2[0].shape
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# print np.c_[i+pos[0][0],j+pos[0][1],i+pos[1][0],j+pos[1][1]]
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# print fN1[1].shape
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I2x2 = inv2X2BlockDiagonal(getSubArray(fN1[0], [i + pos[0][0], j + pos[0][1]]), getSubArray(fN1[1], [i + pos[0][0], j + pos[0][1]]),
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getSubArray(fN2[0], [i + pos[1][0], j + pos[1][1]]), getSubArray(fN2[1], [i + pos[1][0], j + pos[1][1]]))
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PXX = I2x2 * PXX
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# import matplotlib.pyplot as plt
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# plt.spy(PXX)
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# plt.show()
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return PXX
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# no | node | f1 | f2
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# 00 | i ,j | i , j | i, j
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# 10 | i+1,j | i+1, j | i, j
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# 01 | i ,j+1 | i , j | i, j+1
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# 11 | i+1,j+1 | i+1, j | i, j+1
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# Square root of cell volume multiplied by 1/4
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v = np.sqrt(0.25*mesh.vol)
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V2 = sdiag(np.r_[v, v]) # We will multiply on each side to keep symmetry
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P00 = V2*Pxx([[0, 0], [0, 0]])
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P10 = V2*Pxx([[1, 0], [0, 0]])
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P01 = V2*Pxx([[0, 0], [0, 1]])
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P11 = V2*Pxx([[1, 0], [0, 1]])
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if mu.size == mesh.nC: # Isotropic!
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mu = mkvc(mu) # ensure it is a vector.
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Mu = sdiag(np.r_[mu, mu])
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elif mu.shape[1] == 2: # Diagonal tensor
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Mu = sdiag(np.r_[mu[:, 0], mu[:, 1]])
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elif mu.shape[1] == 3: # Fully anisotropic
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row1 = sp.hstack((sdiag(mu[:, 0]), sdiag(mu[:, 2])))
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row2 = sp.hstack((sdiag(mu[:, 2]), sdiag(mu[:, 1])))
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Mu = sp.vstack((row1, row2))
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A = P00.T*Mu*P00 + P10.T*Mu*P10 + P01.T*Mu*P01 + P11.T*Mu*P11
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P = [P00, P10, P01, P11]
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if returnP:
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return A, P
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else:
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return A
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def getEdgeInnerProduct(mesh, sigma=None, returnP=False):
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if sigma is None: # default is ones
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sigma = np.ones((mesh.nC, 1))
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m = np.array([mesh.nCx, mesh.nCy, mesh.nCz])
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nc = mesh.nC
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i, j, k = np.int64(range(m[0])), np.int64(range(m[1])), np.int64(range(m[2]))
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iijjkk = ndgrid(i, j, k)
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ii, jj, kk = iijjkk[:, 0], iijjkk[:, 1], iijjkk[:, 2]
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if mesh._meshType == 'LOM':
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eT1 = mesh.r(mesh.tangents, 'E', 'Ex', 'M')
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eT2 = mesh.r(mesh.tangents, 'E', 'Ey', 'M')
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eT3 = mesh.r(mesh.tangents, 'E', 'Ez', 'M')
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def Pxxx(pos):
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ind1 = sub2ind(mesh.nEx, np.c_[ii + pos[0][0], jj + pos[0][1], kk + pos[0][2]])
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ind2 = sub2ind(mesh.nEy, np.c_[ii + pos[1][0], jj + pos[1][1], kk + pos[1][2]]) + mesh.nE[0]
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ind3 = sub2ind(mesh.nEz, np.c_[ii + pos[2][0], jj + pos[2][1], kk + pos[2][2]]) + mesh.nE[0] + mesh.nE[1]
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IND = np.r_[ind1, ind2, ind3].flatten()
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PXXX = sp.coo_matrix((np.ones(3*nc), (range(3*nc), IND)), shape=(3*nc, np.sum(mesh.nE))).tocsr()
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if mesh._meshType == 'LOM':
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I3x3 = inv3X3BlockDiagonal(getSubArray(eT1[0], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(eT1[1], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]), getSubArray(eT1[2], [i + pos[0][0], j + pos[0][1], k + pos[0][2]]),
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getSubArray(eT2[0], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(eT2[1], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]), getSubArray(eT2[2], [i + pos[1][0], j + pos[1][1], k + pos[1][2]]),
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getSubArray(eT3[0], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(eT3[1], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]), getSubArray(eT3[2], [i + pos[2][0], j + pos[2][1], k + pos[2][2]]))
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PXXX = I3x3 * PXXX
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return PXXX
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# no | node | e1 | e2 | e3
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# 000 | i ,j ,k | i ,j ,k | i ,j ,k | i ,j ,k
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# 100 | i+1,j ,k | i ,j ,k | i+1,j ,k | i+1,j ,k
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# 010 | i ,j+1,k | i ,j+1,k | i ,j ,k | i ,j+1,k
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# 110 | i+1,j+1,k | i ,j+1,k | i+1,j ,k | i+1,j+1,k
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# 001 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k+1 | i ,j ,k
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# 101 | i+1,j ,k+1 | i ,j ,k+1 | i+1,j ,k+1 | i+1,j ,k
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# 011 | i ,j+1,k+1 | i ,j+1,k+1 | i ,j ,k+1 | i ,j+1,k
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# 111 | i+1,j+1,k+1 | i ,j+1,k+1 | i+1,j ,k+1 | i+1,j+1,k
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# Square root of cell volume multiplied by 1/8
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v = np.sqrt(0.125*mesh.vol)
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V3 = sdiag(np.r_[v, v, v]) # We will multiply on each side to keep symmetry
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P000 = V3*Pxxx([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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P100 = V3*Pxxx([[0, 0, 0], [1, 0, 0], [1, 0, 0]])
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P010 = V3*Pxxx([[0, 1, 0], [0, 0, 0], [0, 1, 0]])
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P110 = V3*Pxxx([[0, 1, 0], [1, 0, 0], [1, 1, 0]])
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P001 = V3*Pxxx([[0, 0, 1], [0, 0, 1], [0, 0, 0]])
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P101 = V3*Pxxx([[0, 0, 1], [1, 0, 1], [1, 0, 0]])
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P011 = V3*Pxxx([[0, 1, 1], [0, 0, 1], [0, 1, 0]])
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P111 = V3*Pxxx([[0, 1, 1], [1, 0, 1], [1, 1, 0]])
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if sigma.size == mesh.nC: # Isotropic!
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sigma = mkvc(sigma) # ensure it is a vector.
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Sigma = sdiag(np.r_[sigma, sigma, sigma])
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elif sigma.shape[1] == 3: # Diagonal tensor
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Sigma = sdiag(np.r_[sigma[:, 0], sigma[:, 1], sigma[:, 2]])
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elif sigma.shape[1] == 6: # Fully anisotropic
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row1 = sp.hstack((sdiag(sigma[:, 0]), sdiag(sigma[:, 3]), sdiag(sigma[:, 4])))
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row2 = sp.hstack((sdiag(sigma[:, 3]), sdiag(sigma[:, 1]), sdiag(sigma[:, 5])))
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row3 = sp.hstack((sdiag(sigma[:, 4]), sdiag(sigma[:, 5]), sdiag(sigma[:, 2])))
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Sigma = sp.vstack((row1, row2, row3))
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A = P000.T*Sigma*P000 + P001.T*Sigma*P001 + P010.T*Sigma*P010 + P011.T*Sigma*P011 + P100.T*Sigma*P100 + P101.T*Sigma*P101 + P110.T*Sigma*P110 + P111.T*Sigma*P111
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P = [P000, P001, P010, P011, P100, P101, P110, P111]
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if returnP:
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return A, P
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else:
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return A
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if __name__ == '__main__':
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from TensorMesh import TensorMesh
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h = [np.array([1, 2, 3, 4]), np.array([1, 2, 1, 4, 2]), np.array([1, 1, 4, 1])]
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mesh = TensorMesh(h)
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mu = np.ones((mesh.nC, 6))
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A, P = mesh.getFaceInnerProduct(mu, returnP=True)
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B, P = mesh.getEdgeInnerProduct(mu, returnP=True)
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