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SEOGI KANG
18fd590eff
Some funtions for sparse matrix: sputils.py -> Updated we've discussed before Test example for divergence
76 lines
1.9 KiB
Python
76 lines
1.9 KiB
Python
import numpy as np
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from scipy import sparse
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from utils import mkvc
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from sputils import ddx, sdiag, speye, kron3
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def getvol(h):
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# Cell sizes in each direction
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h1 = h[0]
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h2 = h[1]
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h3 = h[2]
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# Compute cell volumes
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v12 = h1.T*h2
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V = mkvc(v12.reshape(-1,1)*h3)
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return V
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def getarea(h):
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# Cell sizes in each direction
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h1 = h[0]
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h2 = h[1]
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h3 = h[2]
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# The number of cell centers in each direction
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n1 = np.size(h1)
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n2 = np.size(h2)
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n3 = np.size(h3)
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# Compute areas of cell faces
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area1 = np.ones((n1+1,1))*mkvc(h2.T*h3)
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area2 = h1.T*mkvc(np.ones((n2+1,1))*h3)
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area3 = h1.T*mkvc(h2.T*np.ones(n3+1))
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area = np.hstack((np.hstack((mkvc(area1), mkvc(area2))), mkvc(area3)))
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return area
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def getDivMatrix(h):
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"""Consturct the 3D divergence operator on Faces."""
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# Cell sizes in each direction
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h1 = h[0]
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h2 = h[1]
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h3 = h[2]
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# The number of cell centers in each direction
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n1 = np.size(h1)
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n2 = np.size(h2)
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n3 = np.size(h3)
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# Compute areas of cell faces
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#area1 = np.ones((n1+1,1))*mkvc(h2.T*h3)
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#area2 = h1.T*mkvc(np.ones((n2+1,1))*h3)
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#area3 = h1.T*mkvc(h2.T*np.ones(n3+1))
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#area = np.hstack((np.hstack((mkvc(area1), mkvc(area2))), mkvc(area3)))
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area = getarea(h)
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S = sdiag(area)
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# Compute cell volumes
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#v12 = h1.T*h2
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#V = mkvc(v12.reshape(-1,1)*h3)
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V = getvol(h)
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# Compute divergence operator on faces
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d1 = ddx(n1)
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d2 = ddx(n2)
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d3 = ddx(n3)
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D1 = kron3(speye(n3), speye(n2), d1)
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D2 = kron3(speye(n3), d2, speye(n1))
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D3 = kron3(d3, speye(n2), speye(n1))
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D = sparse.hstack((sparse.hstack((D1, D2)), D3))
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return sdiag(1/V)*D*S
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