def run(plotIt=True):
"""
Mesh: Basic: Types
==================
Here we show SimPEG used to create three different types of meshes.
"""
sz = [16, 16]
tM = Mesh.TensorMesh(sz)
qM = Mesh.TreeMesh(sz)
qM.refine(lambda cell: 4
if np.sqrt(((np.r_[cell.center] - 0.5)**2).sum()) < 0.4 else 3)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
if plotIt:
import matplotlib.pyplot as plt
fig, axes = plt.subplots(1, 3, figsize=(14, 5))
opts = {}
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
qM.plotGrid(ax=axes[1], **opts)
axes[1].set_title('TreeMesh')
rM.plotGrid(ax=axes[2], **opts)
axes[2].set_title('CurvilinearMesh')
plt.show()
def run(plotIt=True):
"""
Mesh: Basic Forward 2D DC Resistivity
=====================================
2D DC forward modeling example with Tensor and Curvilinear Meshes
"""
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40, 40]
tM = Mesh.TensorMesh(sz)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
# Step2: Direct Current (DC) operator
def DCfun(mesh, pts):
D = mesh.faceDiv
sigma = 1e-2 * np.ones(mesh.nC)
MsigI = mesh.getFaceInnerProduct(sigma, invProp=True, invMat=True)
A = -D * MsigI * D.T
A[-1, -1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1, -1]
return A, rhs
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM * rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM * rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
#Step4: Making Figure
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
dat = rM.plotImage(phirM, ax=axes[1], clim=(vmin, vmax), grid=True)
cb = plt.colorbar(dat[0], ax=axes[0])
cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1])
cb.set_label("Voltage (V)")
axes[0].set_title('TensorMesh')
axes[1].set_title('CurvilinearMesh')
plt.show()
def doTestFace(self, h, rep, fast, meshType, invProp=False, invMat=False):
if meshType == 'Curv':
hRect = Utils.exampleLrmGrid(h,'rotate')
mesh = Mesh.CurvilinearMesh(hRect)
elif meshType == 'Tree':
mesh = Mesh.TreeMesh(h, levels=3)
mesh.refine(lambda xc: 3)
mesh.number(balance=False)
elif meshType == 'Tensor':
mesh = Mesh.TensorMesh(h)
v = np.random.rand(mesh.nF)
sig = np.random.rand(1) if rep is 0 else np.random.rand(mesh.nC*rep)
def fun(sig):
M = mesh.getFaceInnerProduct(sig, invProp=invProp, invMat=invMat)
Md = mesh.getFaceInnerProductDeriv(sig, invProp=invProp, invMat=invMat, doFast=fast)
return M*v, Md(v)
print meshType, 'Face', h, rep, fast, ('harmonic' if invProp and invMat else 'standard')
return Tests.checkDerivative(fun, sig, num=5, plotIt=False)
def run(plotIt=True):
sz = [16, 16]
tM = Mesh.TensorMesh(sz)
qM = Mesh.TreeMesh(sz)
def refine(cell):
if np.sqrt(((np.r_[cell.center] - 0.5)**2).sum()) < 0.4:
return 4
return 3
qM.refine(refine)
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
if not plotIt:
return
fig, axes = plt.subplots(1, 3, figsize=(14, 5))
opts = {}
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
qM.plotGrid(ax=axes[1], **opts)
axes[1].set_title('TreeMesh')
rM.plotGrid(ax=axes[2], **opts)
axes[2].set_title('CurvilinearMesh')
def run(plotIt=True):
# Step1: Generate Tensor and Curvilinear Mesh
sz = [40, 40]
# Tensor Mesh
tM = Mesh.TensorMesh(sz)
# Curvilinear Mesh
rM = Mesh.CurvilinearMesh(Utils.meshutils.exampleLrmGrid(sz, 'rotate'))
# Step2: Direct Current (DC) operator
def DCfun(mesh, pts):
D = mesh.faceDiv
G = D.T
sigma = 1e-2 * np.ones(mesh.nC)
Msigi = mesh.getFaceInnerProduct(1. / sigma)
MsigI = Utils.sdInv(Msigi)
A = D * MsigI * G
A[-1, -1] /= mesh.vol[-1] # Remove null space
rhs = np.zeros(mesh.nC)
txind = Utils.meshutils.closestPoints(mesh, pts)
rhs[txind] = np.r_[1, -1]
return A, rhs
pts = np.vstack((np.r_[0.25, 0.5], np.r_[0.75, 0.5]))
#Step3: Solve DC problem (LU solver)
AtM, rhstM = DCfun(tM, pts)
AinvtM = SolverLU(AtM)
phitM = AinvtM * rhstM
ArM, rhsrM = DCfun(rM, pts)
AinvrM = SolverLU(ArM)
phirM = AinvrM * rhsrM
if not plotIt: return
import matplotlib.pyplot as plt
import matplotlib
from matplotlib.mlab import griddata
#Step4: Making Figure
fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2))
label = ["(a)", "(b)"]
opts = {}
vmin, vmax = phitM.min(), phitM.max()
dat = tM.plotImage(phitM, ax=axes[0], clim=(vmin, vmax), grid=True)
#TODO: At the moment Curvilinear Mesh do not have plotimage
Xi = tM.gridCC[:, 0].reshape(sz[0], sz[1], order='F')
Yi = tM.gridCC[:, 1].reshape(sz[0], sz[1], order='F')
PHIrM = griddata(rM.gridCC[:, 0],
rM.gridCC[:, 1],
phirM,
Xi,
Yi,
interp='linear')
axes[1].contourf(Xi, Yi, PHIrM, 100, vmin=vmin, vmax=vmax)
cb = plt.colorbar(dat[0], ax=axes[0])
cb.set_label("Voltage (V)")
cb = plt.colorbar(dat[0], ax=axes[1])
cb.set_label("Voltage (V)")
tM.plotGrid(ax=axes[0], **opts)
axes[0].set_title('TensorMesh')
rM.plotGrid(ax=axes[1], **opts)
axes[1].set_title('CurvilinearMesh')
for i in range(2):
axes[i].set_xlim(0.025, 0.975)
axes[i].set_ylim(0.025, 0.975)
axes[i].text(0., 1.0, label[i], fontsize=20)
if i == 0:
axes[i].set_ylabel("y")
else:
axes[i].set_ylabel(" ")
axes[i].set_xlabel("x")
plt.show()
