def test_createGrid(self):
mesh = pg.createGrid(3)
self.assertEqual(mesh.xmax(), 2.0)
mesh = pg.createGrid(3, 3)
self.assertEqual(mesh.ymax(), 2.0)
mesh = pg.createGrid(3, 3, 3)
self.assertEqual(mesh.zmax(), 2.0)
def test_Neumann(self):
"""
"""
def _test_(mesh, show=False):
vTest = 0.1
u = pg.solve(mesh, a=1, f=0,
bc={'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]}, verbose=0)
if show:
if mesh.dim() == 1:
pg.plt.plot(pg.x(mesh), u)
elif mesh.dim() == 2:
pg.show(grid, pg.abs(v))
pg.show(grid, v, showMesh=1)
pg.wait()
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v), np.ones(mesh.cellCount())*vTest)
return v
_test_(pg.createGrid(x=np.linspace(-2, 1, 11)), show=False) #1D
_test_(pg.createGrid(x=np.linspace(-2, 2, 41), y=np.linspace(0, 1, 21))) #2D reg
_test_(pg.createGrid(x=np.linspace(-0.04, 0.01, 21), y=np.linspace(-0.4, 0, 21))) #2D scaled
_test_(pg.createGrid(x=np.linspace(-2, 1, 11), y=np.linspace( 0, 1, 11),
z=np.linspace( 0, 1, 11))) #3D
grid = pg.createGrid(x=np.linspace(-2, 2, 41), y=np.linspace(0, 1, 21))
grid.rotate([0, 0, np.pi/4])
v = _test_(grid) #2D reg - rotated
def test_Neumann(self):
"""
"""
def _test_(mesh):
vTest = 0.1
u = pg.solve(mesh,
a=1,
bc={
'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]
})
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v),
np.ones(mesh.cellCount()) * vTest)
return v
_test_(pg.createGrid(x=np.linspace(-2, 1, 11))) #1D
_test_(pg.createGrid(x=np.linspace(-2, 2, 41),
y=np.linspace(0, 1, 21))) #2D reg
_test_(
pg.createGrid(x=np.linspace(-0.04, 0.01, 21),
y=np.linspace(-0.4, 0, 21))) #2D scaled
_test_(
pg.createGrid(x=np.linspace(-2, 1, 11),
y=np.linspace(0, 1, 11),
z=np.linspace(0, 1, 11))) #3D
grid = pg.createGrid(x=np.linspace(-2, 2, 41), y=np.linspace(0, 1, 21))
grid.rotate([0, 0, np.pi / 4])
v = _test_(grid) #2D reg - rotated
def test_Neumann(self):
"""
"""
def _test_(mesh, show=False):
vTest = 0.1
u = pg.solve(mesh, a=1, f=0,
bc={'Node': [mesh.findNearestNode([0.0, 0.0]), 0.],
'Neumann': [[1, -vTest], [2, vTest]]}, verbose=0)
if show:
if mesh.dim() == 1:
pg.plt.plot(pg.x(mesh), u)
elif mesh.dim() == 2:
pg.show(grid, pg.abs(v))
pg.show(grid, v, showMesh=1)
pg.wait()
v = pg.solver.grad(mesh, u)
#print("|v|:", min(pg.abs(v)), max(pg.abs(v)), pg.mean(pg.abs(v)))
np.testing.assert_allclose(pg.abs(v), np.ones(mesh.cellCount())*vTest)
return v
_test_(pg.createGrid(x=np.linspace(-2, 1, 11)), show=False) #1D
_test_(pg.createGrid(x=np.linspace(-2, 2, 41), y=np.linspace(0, 1, 21))) #2D reg
_test_(pg.createGrid(x=np.linspace(-0.04, 0.01, 21), y=np.linspace(-0.4, 0, 21))) #2D scaled
_test_(pg.createGrid(x=np.linspace(-2, 1, 11), y=np.linspace( 0, 1, 11),
z=np.linspace( 0, 1, 11))) #3D
grid = pg.createGrid(x=np.linspace(-2, 2, 41), y=np.linspace(0, 1, 21))
grid.rotate([0, 0, np.pi/4])
v = _test_(grid) #2D reg - rotated
def test_Helmholtz(self):
"""
d² u / d x² + k u + f = 0
k = 2
a) P1(exact)
u = x
f = -2x
b) P2(exact)
u = x*x
f = -(2 + 2x*x)
"""
h = np.pi / 2 / 21
x = np.arange(0.0, np.pi / 2, h)
mesh = pg.createGrid(x)
### test a)
k = 2.0
u = lambda _x: _x
f = lambda _x: -(k * u(_x))
x = pg.x(mesh)
dirichletBC = [[1, u(min(x))], [2, u(max(x))]]
uFEM = pg.solve(mesh, a=1, b=k, f=f(x), bc={'Dirichlet': dirichletBC})
np.testing.assert_allclose(uFEM, u(x))
### test b)
u = lambda _x: _x * _x
f = lambda _x: -(2. + k * u(_x))
mesh = mesh.createP2()
x = pg.x(mesh)
dirichletBC = [[1, u(min(x))], [2, u(max(x))]]
uFEM = pg.solve(mesh, a=1, b=k, f=f(x), bc={'Dirichlet': dirichletBC})
np.testing.assert_allclose(uFEM, u(x), atol=1e-6)
def test_Helmholtz(self):
"""
d² u / d x² + k u + f = 0
k = 2
a) P1(exact)
u = x
f = -2x
b) P2(exact)
u = x*x
f = -(2 + 2x*x)
"""
h = np.pi/2 / 21
x = np.arange(0.0, np.pi/2, h)
mesh = pg.createGrid(x)
### test a)
k = 2.0
u = lambda _x: _x
f = lambda _x: -(k * u(_x))
x = pg.x(mesh)
dirichletBC = [[1, u(min(x))], [2, u(max(x))]]
uFEM = pg.solve(mesh, a=1, b=k, f=f(x), bc={'Dirichlet': dirichletBC})
np.testing.assert_allclose(uFEM, u(x))
### test b)
u = lambda _x: _x * _x
f = lambda _x: -(2. + k *u(_x))
mesh = mesh.createP2()
x = pg.x(mesh)
dirichletBC = [[1, u(min(x))], [2, u(max(x))]]
uFEM = pg.solve(mesh, a=1, b=k, f=f(x), bc={'Dirichlet': dirichletBC})
np.testing.assert_allclose(uFEM, u(x), atol=1e-6)
def createModel2(maxArea=0.2, nx=20, grid=True):
mesh = None
if grid:
nx = nx
ny = nx
mesh = pg.createGrid(x=np.linspace(-10, 10, nx),
y=np.linspace(0, 20, ny))
else:
layer1 = pt.createRectangle(start=[-10, 20],
end=[10, 10],
marker=2,
boundaryMarker=[1, -1, 2, 4])
layer2 = pt.createRectangle(start=[-10, 10],
end=[10, 0],
marker=1,
boundaryMarker=[1, 3, 2, -1])
mesh = createMesh([layer1, layer2],
quality=32,
area=maxArea,
smooth=[1, 10])
density = mesh.cellAttributes() * 0.0 + 2.0
for c in mesh.cells():
if c.center().y() > 0 and c.center().x() < 0:
density[c.id()] = 1.0
return mesh, density
def testColRange():
n = 5
mesh = pg.createGrid(n, n)
fig, ax = plt.subplots(2,3, figsize=(8,8))
ax[0][0].set_title("pyGIMLi (CellData)")
data = np.arange(mesh.cellCount())
pg.show(mesh, data, ax=ax[0][0], label='default (nLevs=5, nCols=256)')
pg.show(mesh, data, ax=ax[1][0], nCols=4, nLevs=5, label="nLevs=5 nCols=4, \n(aka. poor man's contour)")
ax[0][1].set_title("pyGIMLi (CellData) shading='gouraud'")
data = np.arange(mesh.cellCount())
pg.show(mesh, data, ax=ax[0][1], shading='gouraud', label='default (nLevs=5, nCols=256)')
pg.show(mesh, data, ax=ax[1][1], shading='gouraud', nCols=4, nLevs=5, label="nLevs=5 nCols=4, \n(aka. poor man's contour)")
ax[0][2].set_title("pyGIMLi (NodeData)")
data = np.arange(mesh.nodeCount())
pg.show(mesh, data, ax=ax[0][2],
label='default (nLevs=5, nCols=4)')
pg.show(mesh, data, ax=ax[1][2], nCols=12, nLevs=4,
label='nLevs=4, nCols=12')
for a in ax.flatten():
a.yaxis.set_visible(False)
a.xaxis.set_visible(False)
fig.tight_layout()
def test_Interpolate(self):
grid = pg.createGrid(x=[0.0, 1.0], y=[0.0, 1.0])
u = pg.RVector(grid.nodeCount(), 1.)
# test with pg.interpolate
queryPos = [0.2, 0.2]
uI = pg.interpolate(srcMesh=grid,
inVec=u,
destPos=[queryPos, queryPos])
np.testing.assert_allclose(uI[0], 1.)
# test manual interpolation
c = grid.findCell(queryPos)
uI = c.pot(queryPos, u)
np.testing.assert_allclose(uI, 1.)
# test with manual interpolationMatrix generation
I = pg.RSparseMapMatrix(1, grid.nodeCount())
cI = c.N(c.shape().rst(queryPos))
for i in range(c.nodeCount()):
I.addVal(0, c.node(i).id(), cI[i])
uI = I.mult(u)
np.testing.assert_allclose(uI[0], 1)
# test with automatic interpolationMatrix generation
I = grid.interpolationMatrix([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0],
[0.0, 1.0]])
uI = I * u
np.testing.assert_allclose(uI, u)
# api test https://github.com/gimli-org/gimli/issues/131
x = np.linspace(grid.xmin(), grid.xmax(), 11)
np.testing.assert_allclose(pg.interpolate(grid, pg.x(grid), x), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x, x * 0.), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x, y=x * 0), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x, x * 0, x * 0), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x, y=x * 0,
z=x * 0), x)
x = pg.Vector(x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x, x * 0.), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x, y=x * 0), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x, x * 0, x * 0), x)
np.testing.assert_allclose(
pg.interpolate(grid, pg.x(grid.positions()), x=x, y=x * 0,
z=x * 0), x)
def createModel(maxArea=0.2, nx=80, grid=True):
mesh=None
dens=None
if grid:
nx = nx
ny = nx/2
mesh = pg.createGrid(x=np.linspace(-10, 10, nx),
y=np.linspace(-10, 0, ny))
density = mesh.cellAttributes()*0.0 + 1.0
xstart = (nx-1)*int(ny/1.3) + int(nx/2)
yoff =nx-1
for i in range(int(ny/20)):
density[xstart-nx*0.35+i*yoff: xstart+nx*0.35+i*yoff] *= 2
else:
layer1 = pt.createRectangle(start=[-10, 0], end=[10, -10],
marker=1, boundaryMarker=[1, 3, 2, 4])
block = pt.createRectangle(start=[-10+0.35*10, -1.8918918918918912],
end=[10-0.35*10, -2.2972972972972965],
marker=2)
mesh = createMesh([layer1, block], quality=32, area=maxArea,
smooth=[1,10])
density = mesh.cellAttributes()*0.0 + 1.0
density[mesh.cellMarker()==2] = 2
return mesh, density
def createModel2(maxArea=0.2, nx=20, grid=True):
mesh=None
if grid:
nx = nx
ny = nx
mesh = pg.createGrid(x=np.linspace(-10, 10, nx),
y=np.linspace(0, 20, ny))
else:
layer1 = pt.createRectangle(start=[-10, 20], end=[10, 10],
marker=2, boundaryMarker=[1, -1, 2, 4])
layer2 = pt.createRectangle(start=[-10, 10], end=[10, 0],
marker=1, boundaryMarker=[1, 3, 2, -1])
mesh = createMesh([layer1, layer2], quality=32, area=maxArea,
smooth=[1,10])
density = mesh.cellAttributes()*0.0 + 2.0
for c in mesh.cells():
if c.center().y() > 0 and c.center().x() < 0:
density[c.id()] = 1.0
return mesh, density
def test_meshAccess(self):
x = [.5, 1, 2, 3, 42]
y = [.5, 1, 2, 3]
z = [.5, 1, 3]
mesh = pg.createGrid(x, y, z)
def test_ComplexMatrix(self):
verbose = False
grid = pg.createGrid(3, 3)
# print(grid)
alpha = pg.math.toComplex(np.ones(grid.cellCount()),
np.ones(grid.cellCount()) * 1.0)
A = pg.solver.createStiffnessMatrix(grid, a=alpha)
pg.solver.solver._assembleUDirichlet(A, None, [0], [0.0])
#pg.solver.showSparseMatrix(A)
#pg.solver.assembleDirichletBC(A, [[grid.boundary(0), 0.0]])
b = pg.math.toComplex(np.ones(A.rows()), np.ones(A.rows()) * 0.0)
x = pg.solver.linSolve(A, b, verbose=verbose, solver='pg')
np.testing.assert_allclose(A.mult(x), b, rtol=1e-10)
x2 = pg.solver.linSolve(A, b, verbose=verbose, solver='scipy')
np.testing.assert_allclose(x2, x, rtol=1e-10)
x3 = pg.solver.linSolve(pg.utils.squeezeComplex(A),
pg.utils.squeezeComplex(b),
verbose=verbose,
solver='pg')
np.testing.assert_allclose(pg.utils.toComplex(x3), x, rtol=1e-10)
def test_Interpolate(self):
grid = pg.createGrid(x=[0.0, 1.0], y=[0.0, 1.0])
u = pg.RVector(grid.nodeCount(), 1.)
# test with pg.interpolate
queryPos = [0.2, 0.2]
uI = pg.interpolate(srcMesh=grid,
inVec=u,
destPos=[queryPos, queryPos])
np.testing.assert_allclose(uI[0], 1.)
# test manual interpolation
c = grid.findCell(queryPos)
uI = c.pot(queryPos, u)
np.testing.assert_allclose(uI, 1.)
# test with manual interpolationMatrix generation
I = pg.RSparseMapMatrix(1, grid.nodeCount())
cI = c.N(c.shape().rst(queryPos))
for i in range(c.nodeCount()):
I.addVal(0, c.node(i).id(), cI[i])
uI = I.mult(u)
np.testing.assert_allclose(uI[0], 1)
# test with automatic interpolationMatrix generation
I = grid.interpolationMatrix([[0.0, 0.0], [1.0, 0.0], [1.0, 1.0],
[0.0, 1.0]])
uI = I * u
np.testing.assert_allclose(uI, u)
def createModel(maxArea=0.2, nx=80, grid=True):
mesh = None
dens = None
if grid:
nx = nx
ny = nx / 2
mesh = pg.createGrid(x=np.linspace(-10, 10, nx),
y=np.linspace(-10, 0, ny))
density = mesh.cellAttributes() * 0.0 + 1.0
xstart = (nx - 1) * int(ny / 1.3) + int(nx / 2)
yoff = nx - 1
for i in range(int(ny / 20)):
density[xstart - nx * 0.35 + i * yoff:xstart + nx * 0.35 +
i * yoff] *= 2
else:
layer1 = pt.createRectangle(start=[-10, 0],
end=[10, -10],
marker=1,
boundaryMarker=[1, 3, 2, 4])
block = pt.createRectangle(
start=[-10 + 0.35 * 10, -1.8918918918918912],
end=[10 - 0.35 * 10, -2.2972972972972965],
marker=2)
mesh = createMesh([layer1, block],
quality=32,
area=maxArea,
smooth=[1, 10])
density = mesh.cellAttributes() * 0.0 + 1.0
density[mesh.cellMarker() == 2] = 2
return mesh, density
def test_Constraints(self):
""" Test FOP """
grid = pg.createGrid(x=[0., 1., 2.], y=[0., 1., 2.])
fop = TestMod(grid)
fop.createConstraints()
#pg.solver.showSparseMatrix(fop.constraints(), full=True)
fop.regionManager().setConstraintType(2)
fop.createConstraints()
def test_MeshCreateSecNodes(self):
x = [0, 1, 2, 3, 42]
y = [0, 1, 2, 3]
z = [0, 1, 3]
mesh = pg.createGrid(x, y, z)
mesh.createSecondaryNodes(n=1)
self.assertEqual(mesh.secondaryNodeCount(), mesh.boundaryCount() + \
(len(x)-1)*len(y)*len(z) + \
(len(y)-1)*len(z)*len(x) + \
(len(z)-1)*len(x)*len(y))
def test_Constraints(self):
""" Test FOP """
grid = pg.createGrid(x=[0., 1., 2.], y=[0., 1., 2.])
fop = TestMod(grid)
fop.createConstraints()
#pg.solver.showSparseMatrix(fop.constraints(), full=True)
fop.regionManager().setConstraintType(2)
fop.createConstraints()
def test(N):
x = np.linspace(0, 1, N)
pg.tic()
mesh = pg.createGrid(x, x, x)
print(mesh)
pg.toc()
A = pg.RSparseMatrix()
A.fillStiffnessMatrix(mesh)
pg.toc()
def test_SimpleMeshExport(self):
mesh = pg.createGrid(3, 3)
verts = mesh.positions()
cellIds = [c.ids() for c in mesh.cells()]
mesh2 = pg.Mesh(2)
[mesh2.createNode(v) for v in verts]
[mesh2.createCell(c) for c in cellIds]
np.testing.assert_array_equal(mesh2.nodeCount(), mesh.nodeCount())
np.testing.assert_array_equal(mesh2.cellCount(), mesh.cellCount())
def test(N):
x = np.linspace(0, 1, N)
pg.tic()
mesh = pg.createGrid(x, x, x)
print(mesh)
pg.toc()
A = pg.RSparseMatrix()
A.fillStiffnessMatrix(mesh)
pg.toc()
def testColorbar():
grid = pg.createGrid(x=np.linspace(10., 110., 11)-5, y=np.linspace(0., 20, 2))
fig, axs = plt.subplots(nrows=3, ncols=3, figsize=((10,6)))
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter()), label='log x',
ax=axs[0][0], showMesh=True, cMap='Paired', logScale=True)
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter())+5., label='log x',
ax=axs[1][0], showMesh=True, cMap='Paired', logScale=True)
pg.viewer.mpl.setMappableData(cbar.mappable, pg.x(grid.cellCenter()))
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter()), logScale=True,
ax=axs[2][0], showMesh=True, cMap='Paired')
###########################################################################
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter()), label='lin x',
ax=axs[0][1], logScale=False, cMap='Paired')
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter())+5, label='lin x',
ax=axs[1][1], logScale=False, cMap='Paired')
pg.viewer.mpl.setMappableData(cbar.mappable, pg.x(grid.cellCenter()))
###########################################################################
grid = pg.createGrid(x=np.linspace(10., 110., 11)-25, y=np.linspace(0., 20, 2))
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter()), label='log with neg. x',
ax=axs[0][2], showMesh=True, cMap='Paired', logScale=True)
ax, cbar = pg.show(grid, data=pg.x(grid.cellCenter())-45, label='log with neg. x',
ax=axs[1][2], showMesh=True, cMap='Paired', logScale=True)
pg.viewer.mpl.setMappableData(cbar.mappable, pg.x(grid.cellCenter()))
ax.figure.tight_layout()
pg.show(grid, pg.x(grid.cellCenter()), tri=True, shading='gouraud',
cMap='Spectral_r', logScale=False, cMin=0.01, cMax=10,
levels=[10, 55, 100],
orientation="vertical",
colorBar=True)
pg.show(grid, pg.x(grid.cellCenter()), tri=True, shading='gouraud',
cMap='Spectral_r', logScale=False, cMin=0.01, cMax=10,
levels=[10, 55, 100],
orientation="horizontal",
colorBar=True)
def test_R3VectorToNumpy(self):
'''
implemented through hand_made_wrapper.py
'''
mesh = pg.createGrid(x=[0, 1, 2], y=[0, 1, 2])
v = np.asarray(mesh.nodeCenters())
self.assertEqual(type(v), np.ndarray)
self.assertEqual(len(v), mesh.nodeCount())
a = np.array(mesh.cellCenter())
self.assertEqual(type(a), np.ndarray)
self.assertEqual(len(a), mesh.cellCount())
def test_R3VectorToNumpy(self):
'''
implemented through hand_made_wrapper.py
'''
mesh = pg.createGrid(x=[0, 1, 2], y=[0, 1, 2])
v = np.asarray(mesh.nodeCenters())
self.assertEqual(type(v), np.ndarray)
self.assertEqual(len(v), mesh.nodeCount())
a = np.array(mesh.cellCenter())
self.assertEqual(type(a), np.ndarray)
self.assertEqual(len(a), mesh.cellCount())
def test_R3VectorToNumpy(self):
"""Implemented through hand_made_wrapper.py"""
mesh = pg.createGrid(x=[0, 1, 2], y=[0, 1, 2], z=[1, 2])
v = np.asarray(mesh.positions())
self.assertEqual(type(v), np.ndarray)
self.assertEqual(len(v), mesh.nodeCount())
a = np.array(mesh.cellCenter())
self.assertEqual(type(a), np.ndarray)
self.assertEqual(len(a), mesh.cellCount())
self.assertEqual(mesh.positions()[0], v[0])
def testNumpyFromR3Vec():
mesh = pg.createGrid(x=[0, 1, 2], y=[0, 1, 2])
print(mesh)
print((mesh.nodeCenters()))
for i in mesh.nodeCenters():
print(i)
x = np.asarray(mesh.nodeCenters())
print(x)
x = np.array(mesh.nodeCenters())
print(x)
x = np.array(mesh.cellCenter())
print(x)
print((mesh.cell(0).center()))
print((np.array(mesh.cell(0).center())))
def test_Helmholtz(self):
"""
d² u / d x² + k u + f = 0
k = 2
a) P1(exact)
u = x
f = -k x
b) P2(exact)
u = x*x
f = -(2 + 2x*x)
"""
h = np.pi / 2 / 21
x = np.arange(0.0, np.pi / 2, h)
mesh = pg.createGrid(x)
### test a)
k = 2.0
u = lambda _x: _x
f = lambda _x, _k: -_k * u(_x)
x = pg.x(mesh)
dirichletBC = {1: u(min(x)), 2: u(max(x))}
uFEM = pg.solve(mesh,
a=1,
b=k,
f=f(x, k),
bc={'Dirichlet': dirichletBC})
# pg.plt.plot(x, uFEM, '.')
# pg.plt.plot(pg.sort(x), u(pg.sort(x)))
# pg.wait()
np.testing.assert_allclose(uFEM, u(x))
### test b)
u = lambda _x: _x * _x
f = lambda _x, _k: -(2. + k * u(_x))
mesh = mesh.createP2()
x = pg.x(mesh)
dirichletBC = {1: u(min(x)), 2: u(max(x))}
uFEM = pg.solve(mesh,
a=1,
b=k,
f=f(x, k),
bc={'Dirichlet': dirichletBC})
np.testing.assert_allclose(uFEM, u(x), atol=1e-6)
def setUp(self):
# Dummy data container
self.data = pg.DataContainer()
self.data.createSensor([0.0, 0.0])
self.data.createSensor([1.0, 2.0])
self.data.resize(1)
self.data.set("s", pg.Vector(1, 1.0))
self.data.set("g", pg.Vector(1, 2.0))
self.data.registerSensorIndex("s")
self.data.registerSensorIndex("g")
# Without secondary nodes
self.mesh = pg.createGrid([0, 1, 2], [0, 1, 2])
# Slowness
self.slo = [1, 2, 1, 4]
self.mgr = TravelTimeManager()
def calcInvBlock(mesh, dens, out='gravInv'):
# extract block delta density
densBlock = pg.RVector(dens)
densMarker2 = dens[pg.find(mesh.cellMarker() == 2)[0]]
#densBlock[(mesh.cellMarker() == 1) | (mesh.cellMarker() == 3)] = densMarker2
densBlock[pg.find((mesh.cellMarker() == 1)
| (mesh.cellMarker() == 3))] = densMarker2
densBlock -= densMarker2
# define meausrement positions
gravPointsX = np.linspace(-20, 20, 41)
sensorPositions = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
# solve analytical
gz = solveGravimetry(mesh, densBlock, pnts=sensorPositions, complete=False)
# noisyfy
errAbs = 0.00001
dzerr = np.random.randn(len(sensorPositions)) * errAbs
gz = gz + dzerr
# createParamesh
paraMesh = pg.createGrid(x=np.linspace(-20, 20, 41),
y=np.linspace(-20, 0, 21))
# init Gravimetry manager (should do meshing, simulation and noisying)
Grav = Gravimetry(verbose=True)
model = Grav.invert(sensorPositions, gz, errAbs, verbose=1, mesh=paraMesh)
fig, ax = plt.subplots()
ax.plot(pg.x(sensorPositions), gz, label='gz')
ax.plot(pg.x(sensorPositions), Grav.inv.response(), label='response')
ax.legend()
ax.grid()
ax.set_xlabel('$x$ [m]')
ax.set_ylabel('$\partial u / \partial z$ [mGal]')
plt.show(block=False)
ax.figure.savefig(out, bbox_inches='tight')
return Grav, densBlock
def calcInvBlock(mesh, dens, out='gravInv'):
# extract block delta density
densBlock = pg.RVector(dens)
densMarker2 = dens[pg.find(mesh.cellMarker() == 2)[0]]
# densBlock[(mesh.cellMarker() == 1)|(mesh.cellMarker() == 3)] = densMarker2
densBlock[pg.find((mesh.cellMarker() == 1) | (mesh.cellMarker() == 3))] = \
densMarker2
densBlock -= densMarker2
# define meausrement positions
gravPointsX = np.linspace(-20, 20, 41)
sensorPositions = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
# solve analytical
gz = solveGravimetry(mesh, densBlock, pnts=sensorPositions, complete=False)
# noisyfy
errAbs = 0.00001
dzerr = np.random.randn(len(sensorPositions)) * errAbs
gz = gz + dzerr
# createParamesh
paraMesh = pg.createGrid(x=np.linspace(-20, 20, 41),
y=np.linspace(-20, 0, 21))
# init Gravimetry manager (should do meshing, simulation and noisying)
Grav = Gravimetry(verbose=True)
model = Grav.invert(sensorPositions, gz, errAbs, verbose=1, mesh=paraMesh)
fig, ax = plt.subplots()
ax.plot(pg.x(sensorPositions), gz, label='gz')
ax.plot(pg.x(sensorPositions), Grav.inv.response(), label='response')
ax.legend()
ax.grid()
ax.set_xlabel('$x$ [m]')
ax.set_ylabel('$\partial u / \partial z$ [mGal]')
plt.show(block=False)
ax.figure.savefig(out, bbox_inches='tight')
return Grav, densBlock
def modelCavity0(maxArea=0.0025):
mesh = pg.createGrid(x=np.linspace(.0, 1.0, 17),
y=np.linspace(.0, 1.0, 17))
mesh = pg.meshtools.refineQuad2Tri(mesh, style=2)
velBoundary=[[1,[0.0, 0.0]],
[2,[0.0, 0.0]],
[3,[1.0, 0.0]],
[4,[0.0, 0.0]],
]
c = mesh.findCell((0.0, 0.0))
for b in range(c.boundaryCount()):
if c.boundary(b).marker()==4:
c.boundary(b).setMarker(7)
preBoundary=[[7, 0.0],]
a = pg.RVector(mesh.cellCount(), 1.0)
return mesh, velBoundary, preBoundary, a, 100
def invertGravimetry(gravPoints, dz):
dzerr = np.random.randn(len(gravPoints)) * 0.0001
dz = dz + dzerr
mesh = pg.createGrid(x=np.linspace(-20, 20, 41), y=np.linspace(-20, 0, 21))
grav = Gravimetry(verbose=True)
model = grav.invert(gravPoints, dz, verbose=1, mesh=mesh)
plt.plot(pg.x(gravPoints), dz)
plt.plot(pg.x(gravPoints), grav.inv.response())
paraDomain = grav.fop.regionManager().paraDomain()
pg.show(paraDomain, model, colorBar=1, hold=1)
pg.showNow()
plt.show()
pass
def invertGravimetry(gravPoints, dz):
dzerr = np.random.randn(len(gravPoints)) * 0.0001
dz = dz + dzerr
mesh = pg.createGrid(x=np.linspace(-20, 20, 41),
y=np.linspace(-20, 0, 21))
grav = Gravimetry(verbose=True)
model = grav.invert(gravPoints, dz, verbose=1, mesh=mesh)
plt.plot(pg.x(gravPoints), dz)
plt.plot(pg.x(gravPoints), grav.inv.response())
paraDomain=grav.fop.regionManager().paraDomain()
pg.show(paraDomain, model, colorBar=1, hold=1)
pg.showNow()
plt.show()
pass
def modelCavity0(maxArea=0.0025):
mesh = pg.createGrid(x=np.linspace(.0, 1.0, 17),
y=np.linspace(.0, 1.0, 17))
mesh = pg.meshtools.refineQuad2Tri(mesh, style=2)
velBoundary = [
[1, [0.0, 0.0]],
[2, [0.0, 0.0]],
[3, [1.0, 0.0]],
[4, [0.0, 0.0]],
]
c = mesh.findCell((0.0, 0.0))
for b in range(c.boundaryCount()):
if c.boundary(b).marker() == 4:
c.boundary(b).setMarker(7)
preBoundary = [
[7, 0.0],
]
a = pg.RVector(mesh.cellCount(), 1.0)
return mesh, velBoundary, preBoundary, a, 100
def test_VTK_DataRead(self):
grid = pg.createGrid(np.arange(4), np.arange(3), np.arange(2))
cM = np.arange(grid.cellCount())
grid.setCellMarkers(cM)
import tempfile as tmp
_, fn = tmp.mkstemp(suffix='.vtk')
grid.exportVTK(fn)
mesh = pg.load(fn)
np.testing.assert_array_equal(mesh.cellMarkers(), cM)
np.testing.assert_array_equal(mesh['Marker'], cM)
mesh = pg.meshtools.readMeshIO(fn)
np.testing.assert_array_equal(mesh['Marker'], cM)
fn = pg.getExampleFile('meshes/test_tetgen_dataCol.vtk')
mesh = pg.load(fn)
np.testing.assert_array_equal(mesh.cellMarkers(), cM)
np.testing.assert_array_equal(mesh['Marker'], cM)
mesh = pg.meshtools.readMeshIO(fn)
np.testing.assert_array_equal(mesh['Marker'], cM)
def load_grav_pygimli_plate():
# Half plate
thickness = 1
mesh = pg.createGrid(x=np.linspace(0, 5000),
y=[-depth - thickness / 2., -depth + thickness / 2.0])
pg.show(mesh, ax=ax[0, 1])
ga = gradUHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
gza = gradGZHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
g, gz = solveGravimetry(mesh, rho, pnts, complete=True)
plot(x, ax[1, 1], ga, gza, ax[2, 1], g, gz)
labels = ["Horizontal cylinder", "Half plate"]
for ax, label in zip(ax[0], labels):
ax.set_title(label)
ax.set_aspect("equal")
ax.set_xlim(left=x[0], right=x[-1])
ax.set_ylim(bottom=-depth * 2, top=1)
fig.tight_layout()
return g
# This yields:
#
# Now we know the name space :gimliapi:`GIMLI` and can create a first mesh.
# A mesh is represented by a collection of nodes, cells and boundaries, i.e., geometrical entities.
#
# .. note::
#
# A regular spaced mesh consisting of rectangles or hexahedrons is usually called grid.
# However, a grid is just a kind of a mesh and GIMLi does not separate between them.
# The only difference is the way of mesh creation.
#
# GIMLi provides a collection of tools for mesh import, export and generation.
# A simple grid generation is built-in but we also provide wrappers for unstructured mesh generations, e.g., :term:`Triangle`, :term:`Tetgen` and :term:`Gmsh`.
# To create a 2d grid you need to give two arrays or lists for the sampling points in x and y direction, respectively.
grid = pg.createGrid(x=[-1.0, 0.0, 1.0, 4.0], y=(-1.0, 0.0, 1.0, 4.0))
###############################################################################
# The returned object ``grid`` is an instance of :gimliapi:`GIMLI::Mesh` and provides various methods for modification and io-operations. General informations can be simple printed.
#
print(grid)
###############################################################################
# yields:
#
# Or you can access them manually:
#
print('Mesh: Nodes:', grid.nodeCount(),
'Cells:', grid.cellCount(),
'Boundaries:', grid.boundaryCount())
def _test_ConvectionAdvection():
"""Test agains a refernce solution."""
N = 21 # 21 reference
maxIter = 11 # 11 reference
Nx = N
Ny = N
x = np.linspace(-1.0, 1.0, Nx + 1)
y = np.linspace(-1.0, 1.0, Ny + 1)
grid = pg.createGrid(x=x, y=y)
a = pg.RVector(grid.cellCount(), 1.0)
b7 = grid.findBoundaryByMarker(1)[0]
for b in grid.findBoundaryByMarker(1):
if b.center()[1] < b.center()[1]:
b7 = b
b7.setMarker(7)
swatch = pg.Stopwatch(True)
velBoundary = [[1, [0.0, 0.0]],
[2, [0.0, 0.0]],
[3, [1.0, 0.0]],
[4, [0.0, 0.0]],
[7, [0.0, 0.0]]]
preBoundary = [[7, 0.0]]
vel, pres, pCNorm, divVNorm = __solveStokes(grid, a,
velBoundary, preBoundary,
maxIter=maxIter,
verbose=1)
print("time", len(pCNorm), swatch.duration(True))
# referencesolution = 1.2889506342694153
referencesolutionDivV = 0.029187181920161752
print("divNorm: ", divVNorm[-1])
print("to reference: ", divVNorm[-1] - referencesolutionDivV)
fig = plt.figure()
ax1 = fig.add_subplot(1, 3, 1)
ax2 = fig.add_subplot(1, 3, 2)
ax3 = fig.add_subplot(1, 3, 3)
show(grid, data=pg.meshtools.cellDataToNodeData(grid, pres),
logScale=False, showLater=True, colorBar=True, ax=ax1, cbar='b2r')
show(grid, data=pg.logTransDropTol(
pg.meshtools.cellDataToNodeData(grid, vel[:, 0]), 1e-2),
logScale=False, showLater=True, colorBar=True, ax=ax2)
show(grid, data=pg.logTransDropTol(
pg.meshtools.cellDataToNodeData(grid, vel[:, 1]), 1e-2),
logScale=False, showLater=True, colorBar=True, ax=ax3)
show(grid, data=vel, ax=ax1)
show(grid, showLater=True, ax=ax1)
plt.figure()
plt.semilogy(pCNorm, label='norm')
plt.legend()
plt.ioff()
plt.show()
"""
This yields:
.. lastcout::
Now we know the gimli name space and can start creating a first mesh. A mesh is a collection of nodes, cells and boundaries, i.e, geometrical entities.
.. note::
A regular spaced mesh consisting of rectangles or hexahedrons is usually called grid. However, internal grids are just special meshes.
Gimli provides a collection of tools for mesh import and generation. Easy grid generation is built-in but we also provide wrappers for unstructured mesh generations. e.g. :term:`triangle` and :term:`tetgen`. Incorporation of other generators should be straightforward, e.g., :py:mod:`pygimli.meshtools`
"""
import numpy as np
grid = pg.createGrid(x=np.linspace(-1.0, 1.0, 3), y=-np.linspace(-1.0, 1.0, 3))
#grid = pg.createGrid(x=[-1.0, 0.0, 1.0, 4.0], y=[-1.0, 0.0, 1.0, 4.0])
"""
``grid`` is an instance of :gimliapi:`GIMLI::Mesh` and provides various methods for modification and io-operations.
"""
print(grid)
"""
yields:
.. lastcout::
For instance, you can iterate through all elements of the general type :gimliapi:`GIMLI::Cell`, which in turn also provides a lot of methods:
#!/usr/bin/env python
import numpy as np
import pygimli as pg
# Dummy data container
data = pg.DataContainer()
data.createSensor([0.0, 0.0])
data.createSensor([1.0, 2.0])
data.resize(1)
data.set("s", pg.RVector(1, 1.0))
data.set("g", pg.RVector(1, 2.0))
data.registerSensorIndex("s")
data.registerSensorIndex("g")
# Without secondary nodes
mesh = pg.createGrid([0,1,2],[0,1,2])
# Slowness
slo = [1,2,1,4]
def test_withoutSecNodes():
fop = pg.TravelTimeDijkstraModelling(mesh, data)
t_normal = fop.response(slo)
np.testing.assert_allclose(t_normal, 1 + np.sqrt(2))
def test_withSecNodes():
mesh2 = mesh.createMeshWithSecondaryNodes(n=3)
fop = pg.TravelTimeDijkstraModelling(mesh2, data)
t_refined = fop.response(slo)
np.testing.assert_allclose(t_refined, np.sqrt(5)) # only works if n_secNodes is odd number
Again, we first import numpy and pygimli, the solver and post processing
functionality.
"""
import numpy as np
import pygimli as pg
from pygimli.solver import solve
from pygimli.viewer import show
from pygimli.mplviewer import drawStreams
###############################################################################
# We create a 50x50 node grid to solve on.
grid = pg.createGrid(x=np.linspace(-1.0, 1.0, 21),
y=np.linspace(-1.0, 1.0, 21))
###############################################################################
# We start considering inhomogeneous Dirchlet boundary conditions (BC).
# There are different ways of specifying BCs. They can be maps from markers to
# values, explicit functions or implicit (lambda) functions.
#
# The boundary 1 (top) and 2 (left) are directly mapped to the values 1 and 2.
# On side 3 (bottom) a lambda function 3+x is used (p is the boundary position
# and p[0] its x coordinate. On side 4 (right) a function uDirichlet is used
# that simply returns 4 in this example but can compute anything as a function
# of the individual boundaries b.
###############################################################################
# Short test: setting single node dirichlet BC
u = solve(grid, f=1., uB=[grid.node(2), 0.])
import pygimli as pg
import pygimli.solver as solver
import matplotlib.pyplot as plt
import numpy as np
dx = 0.005
x = np.arange(0, 1., dx )
"""
Start modelling code
"""
h = 1./20.
grid = pg.createGrid(x=np.arange(-1.0, 1.0+h, h))
#grid = grid.createP2()
times = np.arange(0, 2., (h)*0.5)
print(grid)
dirichletBC = [[1, 0], # top
[2, 0]] #bottom
u = np.zeros((len(times), grid.nodeCount()))
v = np.zeros((len(times), grid.nodeCount()))
k = times[1]-times[0]
u[0,0] = 0.0
v[0,0] = 0.0
e = np.zeros(len(times))
A = solver.createStiffnessMatrix(grid)
import pygimli as pg
import pygimli.solver as solver
import matplotlib.pyplot as plt
import numpy as np
dx = 0.005
x = np.arange(0, 1., dx )
"""
Start modelling code
"""
h = 1./20.
grid = pg.createGrid(x=np.arange(-1.0, 1.0+h, h))
#grid = grid.createP2()
times = np.arange(0, 2., (h)*0.5)
print(grid)
dirichletBC = [[1, 0], # top
[2, 0]] #bottom
u = np.zeros((len(times), grid.nodeCount()))
v = np.zeros((len(times), grid.nodeCount()))
k = times[1]-times[0]
u[0,0] = 0.0
v[0,0] = 0.0
e = np.zeros(len(times))
A = solver.createStiffnessMatrix(grid)
from pygimli.mplviewer import drawMesh, drawModel, drawField, drawStreams
from pygimli.meshtools import createMesh
from solverFVM import solveFiniteVolume, createFVPostProzessMesh, diffusionConvectionKernel
import matplotlib.pyplot as plt
import numpy as np
swatch = pg.Stopwatch(True)
x = np.linspace(-1.0, 1.0, 41)
y = np.linspace( 0.0, 1.0, 21)
dx = x[1] - x[0]
dy = y[1] - y[0]
print(dx,dy)
grid = pg.createGrid(x=x, y=y)
# force vector per cell
f = pg.RVector(grid.cellCount(), 0.0)
#f[grid.findCell([-0.85, 0.55]).id()]=10.0
# velocity per cell [x-direction, y-direction]
vC = np.array(list(map(lambda p_: [ (2.*p_[1] *(1.0 -p_[0]**2)),
(-2.*p_[0] *(1.0 -p_[1]**2))],
grid.cellCenters())))
vB = np.array(list(map(lambda p_: [ (2.*p_[1] *(1.0 -p_[0]**2)),
(-2.*p_[0] *(1.0 -p_[1]**2))],
grid.boundaryCenters())))
ud0=10
poly = pg.Mesh(2)
nodes = [poly.createNode(b) for b in boundary]
poly.createEdge(nodes[0], nodes[1], 1) # dirichlet (inflow)
poly.createEdge(nodes[1], nodes[2], 3) # hom neumann (outflow)
poly.createEdge(nodes[2], nodes[3], 2) # hom dirichlet (isolation)
poly.createEdge(nodes[3], nodes[0], 4) # hom dirichlet (isolation)
mesh = createMesh(poly, quality=34, area=0.05, smooth=[0,10])
return mesh
dx = 0.2
x = np.arange(-20, 20., dx)
y = np.arange(-20, 0.0, dx)[::-1]
mesh = pg.createGrid(x=x, y=y)
mesh = createMesh2()
print(mesh)
h = pg.median(mesh.boundarySizes())
v1 = 1000
v2 = 3000
tmax = 10.1/v1
z = 2.
f0 = 1000.0 # A low wavelength of 50 Hz
velocities = pg.RVector(mesh.cellCount(), v1)
for c in mesh.cells():
S[1, 1] += aE
S[N + 1, N + 1] += 1.0
S[N, N + 1] += -aW
S[N, N] += aW
rhs[0] += uDir[0]
rhs[N + 1] += uDir[1]
return S, rhs
x = np.linspace(0.0, 1.0, 11)
dx = x[1] - x[0]
grid = pg.createGrid(x=x)
N = grid.cellCount()
# force vector per cell
f = pg.RVector(grid.cellCount(), 0.0)
# diffusions coefficient
a = pg.RVector(grid.cellCount(), 2.1)
# velocity per cell [x-direction]
v = pg.RVector(grid.cellCount(), 20.1)
print("Peclet-number:", v[0] / (a[0] / dx))
ud0 = 0
udN = 1
We use the preceding example (Poisson equation on the unit square) but want to specify different boundary conditions on the four sides.
Again, we first import numpy and pyplot, pygimli, the solver and some plotting functions.
Then we create a 50x50 node grid to solve on.
"""
import numpy as np
import matplotlib.pyplot as plt
import pygimli as pg
from pygimli.solver import solvePoisson
from pygimli.viewer import showMesh
from pygimli.mplviewer import drawMesh, drawStreamLines
grid = pg.createGrid(x=np.linspace(-1.0, 1.0, 50), y=np.linspace(-1.0, 1.0, 50))
"""
We start considering inhomogeneous Dichlet boundary conditions (BC).
There are different ways of specifying BCs.
They can be maps from markers to values, explicit functions or implicit (lambda) functions as exemplified in the next example.
The boundary 1 (top) and 2 (left) are directly mapped to the values 1.0 and 2.0.
On side 3 (bottom) a lambda function 3+x is used (p is the boundary position and p[0] its x coordinate.
On side 4 (right) a function uDirichlet is used that simply returns 4.0 in this example but can compute everything as a function of the individual boundaries b.
"""
def uDirichlet(b):
'''
Return a solution value for coordinate p.
'''
#!/usr/bin/env python
import numpy as np
import pygimli as pg
# Dummy data container
data = pg.DataContainer()
data.createSensor([0.0, 0.0])
data.createSensor([1.0, 2.0])
data.resize(1)
data.set("s", pg.RVector(1, 1.0))
data.set("g", pg.RVector(1, 2.0))
data.registerSensorIndex("s")
data.registerSensorIndex("g")
# Without secondary nodes
mesh = pg.createGrid([0, 1, 2], [0, 1, 2])
# Slowness
slo = [1, 2, 1, 4]
def test_withoutSecNodes():
fop = pg.TravelTimeDijkstraModelling(mesh, data)
t_normal = fop.response(slo)
np.testing.assert_allclose(t_normal, 1 + np.sqrt(2))
def test_withSecNodes():
mesh2 = mesh.createMeshWithSecondaryNodes(n=3)
fop = pg.TravelTimeDijkstraModelling(mesh2, data)
t_refined = fop.response(slo)
nu = .1
dt = .001
u = np.zeros((ny, nx))
v = np.zeros((ny, nx))
p = np.zeros((ny, nx))
b = np.zeros((ny, nx))
nt = 200
u, v, p = cavityFlow(nt, u, v, dt, dx, dy, p, rho, nu)
# fig = plt.figure(figsize=(11,7), dpi=100)
# ax1 = fig.add_subplot(1,3,1)
# ax2 = fig.add_subplot(1,3,2)
# ax3 = fig.add_subplot(1,3,3)
grid = pg.createGrid(x, y)
fig = plt.figure()
ax1 = fig.add_subplot(1, 3, 1)
ax2 = fig.add_subplot(1, 3, 2)
ax3 = fig.add_subplot(1, 3, 3)
pl = pg.logTransDropTol(np.array((p.T).flat), 1e-2)
ul = pg.logTransDropTol(np.array((u.T).flat), 1e-2)
vl = pg.logTransDropTol(np.array((v.T).flat), 1e-2)
pg.show(grid, pl, logScale=False, showLater=True, colorBar=True, axes=ax1,
cmap='b2r')
pg.show(grid, ul, logScale=False, showLater=True, colorBar=True, axes=ax2)
pg.show(grid, vl, logScale=False, showLater=True, colorBar=True, axes=ax3)
vel = np.vstack([np.array((u.T).flat), np.array((v.T).flat)]).T
###############################################################################
#
# Define function for the current source term
# :math:`\delta(x-pos), \int f(x) \delta(x-pos)=f(pos)=N(pos)`
# Right hand side entries will be shape functions(pos)
#
def pointSource(cell, f, userData):
sourcePos = userData['sourcePos']
if cell.shape().isInside(sourcePos):
f.setVal(cell.N(cell.shape().rst(sourcePos)), cell.ids())
grid = pg.createGrid(x=np.linspace(-10.0, 10.0, 21), y=np.linspace(-15.0, .0, 16))
#grid = grid.createH2()
grid = grid.createP2()
sourcePosA = [-5.0, -4.0]
sourcePosB = [ 5.0, -4.0]
neumannBC = [[1, mixedBC], #left boundary
[2, mixedBC], #right boundary
[4, mixedBC]] #bottom boundary
k = 1e-3
u = solve(grid, a=1, b=k*k, f=pointSource,
duB=neumannBC,
userData={'sourcePos': sourcePosA, 'k': k},
See: :py:mod:`pygimli.viewer`
Discussion: FEM is less suited for problems with piece-wise (element) constant
solutions, because linear shape functions demand twice differentiable solution.
For diffusion and wave equation with partially starting gradients = 0 you can
obtain numeric undulations (acausal overshoots) caused by the shape functions.
"""
import pygimli as pg
import pygimli.solver as solver
import matplotlib.pyplot as plt
import numpy as np
grid = pg.createGrid(x=np.linspace(0.0, 1.0, 100))
times = np.arange(0, 1.0, 0.04)
dirichletBC = [[1, 0], # top
[2, 0]] # bottom
probeID = int(grid.nodeCount() / 2)
###############################################################################
# For this case we have an analytical solution:
#
# .. math::
#
# u(t,x) = \e^{-\pi^2 t} \sin(\pi x)
#
#
break
if verbose:
print(str(i) + ": " + str(preCNorm[-1]))
return velocity, pressure, preCNorm, divVNorm
if __name__ == '__main__':
N = 21 # 21 reference
maxIter = 11 # 11 reference
Nx = N
Ny = N
x = np.linspace(-1.0, 1.0, Nx + 1)
y = np.linspace(-1.0, 1.0, Ny + 1)
grid = pg.createGrid(x=x, y=y)
a = pg.RVector(grid.cellCount(), 1.0)
b7 = grid.findBoundaryByMarker(1)[0]
for b in grid.findBoundaryByMarker(1):
if b.center()[1] < b.center()[1]:
b7 = b
b7.setMarker(7)
swatch = pg.Stopwatch(True)
velBoundary = [[1, [0.0, 0.0]],
[2, [0.0, 0.0]],
[3, [1.0, 0.0]],
[4, [0.0, 0.0]],
[7, [0.0, 0.0]]]
def createFopWithParaDomain(paraRefine=0, ncpu=6):
"""Create Forward operator and synthetic data."""
tMax = 345600 * 3
satSteps = 800 * 2
ertSteps = 10
synthPath = 'synth/'
synthArea = 0.1
paraArea = 0.1
simulateSynth(model=[1e-8, 5e-3, 1e-4, 8e-4],
tMax=tMax,
satSteps=satSteps,
ertSteps=ertSteps,
area=synthArea,
synthPath=synthPath)
fop = HydroGeophysicalModelling(mesh=None, tMax=tMax,
satSteps=satSteps,
ertSteps=ertSteps,
verbose=1)
rhoaR = np.load(synthPath + 'synthRhoaRatio.npy')
err = np.load(synthPath + 'synthErr.npy')
fop.setVerbose(True)
fop.setMultiThreadJacobian(ncpu)
paraMesh = pg.createGrid(x=[-20, -10, 0, 10, 20], y=[-16, -8, -2, 0])
# top Boundary Marker
for i, b in enumerate(paraMesh.findBoundaryByMarker(4)):
b.setMarker(8)
# right Boundary Marker
for i, b in enumerate(paraMesh.findBoundaryByMarker(2)):
b.setMarker(7 - i)
# bottom Boundary Marker
for i, b in enumerate(paraMesh.findBoundaryByMarker(3)):
b.setMarker(4)
# left boundary Marker
for i, b in enumerate(paraMesh.findBoundaryByMarker(1)):
b.setMarker(3-i)
# ax, _ = pg.show(paraMesh)
# pg.mplviewer.drawMeshBoundaries(ax=ax, mesh=paraMesh)
# pg.wait()
paraMesh.cell(0).setMarker(0) # bottom
paraMesh.cell(1).setMarker(0) # bottom
paraMesh.cell(2).setMarker(0) # bottom
paraMesh.cell(3).setMarker(0) # bottom
paraMesh.cell(4).setMarker(2) # center
paraMesh.cell(5).setMarker(2) # center
paraMesh.cell(6).setMarker(2) # center
paraMesh.cell(7).setMarker(2) # center
paraMesh.cell(8).setMarker(1) # top
paraMesh.cell(9).setMarker(1) # top
paraMesh.cell(10).setMarker(1) # top
paraMesh.cell(11).setMarker(1) # top
if paraRefine:
for i in range(paraRefine):
paraMesh = paraMesh.createH2()
paraCount = 2
for c in paraMesh.cells():
if c.marker() > 1:
c.setMarker(paraCount)
paraCount += 1
fop.setMesh(paraMesh)
for i in range(fop.regionManager().regionCount()):
fop.regionManager().region(i).setSingle(1)
else:
fop.setMesh(paraMesh)
fop.createRefinedForwardMesh(refine=False, pRefine=False)
fopMesh = pg.meshtools.createMesh(fop.regionManager().paraDomain(),
area=paraArea, smooth=[1, 10])
fop.setVerbose(True)
fop.setMesh(fopMesh, ignoreRegionManager=False)
for i in range(fop.regionManager().regionCount()):
fop.regionManager().region(i).setSingle(1)
return fop, rhoaR, err, paraMesh
b = pg.findBoundary(c.boundaryNodes(bi))
# print(b.norm(c).dot(F[b.id()]))
ret += b.norm(c).dot(F[b.id()]) * b.size()
return ret
def divergence(mesh, F):
div = pg.RVector(mesh.cellCount())
for c in mesh.cells():
div[c.id()] = divergenceCell(c, F)
return div
grid = pg.createGrid(x=np.arange(3. + 1), y=np.arange(2. + 1))
pot = np.arange(3. * 2)
print(grid, pot)
plt.ion()
show(grid, pot)
pN = pg.cellDataToPointData(grid, pot)
ax, cbar = show(grid, pN)
ax, cbar = show(grid, axes=ax)
vF = np.zeros((grid.boundaryCount(), 2))
cellGrad = cellDataToCellGrad(grid, pot)
print(cellGrad)
cellGrad = cellDataToCellGrad2(grid, pot)
def test_MeshStr(self):
mesh = pg.createGrid(2, 2, 2)
print(mesh.node(0))
def calc(out, mesh, density, viscosity):
print(mesh)
velBoundary=[
[1, [0.0, 'nan']],
[2, [0.0, 'nan']],
[3, ['nan', 0.0]],
[4, ['nan', 0.0]]
]
preBoundary=[[1, 0.0],
[2, 0.0],
[3, 0.0],
[4, 0.0],
]
densMatrix = pg.RMatrix()
vels = []
swatch = pg.Stopwatch(True)
class WS():
pass
wsfv = WS()
ax,_ = pg.show(mesh, density)
v = 1
nSteps = 3000
dt = 0.1 * v
dtSteps = 20
meshC = pg.createGrid(x=np.linspace(-10, 10, 21),
y=np.linspace(0, 20, 21))
vel=None
pre=None
for i in range(nSteps):
print(i, 'dens', min(density), max(density), "t:", dt*i)
densMatrix.push_back(density)
if v > 1:
viscosity=1.0 * density #v3
elif v < 1:
viscosity=1.0 / density #v3
else:
viscosity=1.0
vel, pre, pCNorm, divVNorm = solver.solveStokes(mesh,
velBoundary=velBoundary,
preBoundary=preBoundary,
viscosity=viscosity,
density=density,
pre0 = pre,
vel0 = vel,
f=[density*0, (density-1.0)*-9.81],
maxIter=1000,
tol=1e-6,
verbose=1,
vRelax=0.1,
pRelax=0.1,
ws=wsfv)
vels.append(vel)
print("stokes:" , swatch.duration(True), "div V: ", divVNorm[-1])
dens2 = solver.solveFiniteVolume(mesh, a=1./500, b=0.0, u0=density, vel=vel,
times=np.linspace(0, dt, dtSteps),
#uBoundary=[4, 0],
scheme='PS', verbose=0)
print("Convekt:" , swatch.duration(True))
density=dens2[-1]
ax.clear()
pg.show(mesh, density, axes=ax)
pg.show(mesh, vel, coarseMesh=meshC, axes=ax, color='white')
mesh.save(out)
meshC.save(out + 'C')
densMatrix.save(out + 'density.bmat')
np.save(out+'velo.bmat', vels)
from matplotlib.patheffects import withStroke
def circle(x, y, text=None, radius=0.15, c="blue"):
circle = Circle((x, y), radius, clip_on=False, zorder=10, linewidth=1,
edgecolor='black', facecolor=(0, 0, 0, .0125),
path_effects=[withStroke(linewidth=5, foreground='w')])
ax.add_artist(circle)
ax.plot(x, y, color=c, marker=".")
ax.text(x, y - (radius + 0.05), text, backgroundcolor="white",
ha='center', va='top', weight='bold', color=c)
################################################################################
# We now import pygimli and create simple grid/mesh with 3x3 cells.
import pygimli as pg
m = pg.createGrid(4,4)
################################################################################
# The following code creates the main plot and shows how the different mesh
# entities can be called.
# Create matplotlib figure and set size
fig, ax = plt.subplots(figsize=(8,8), dpi=90)
ax.set_title("The anatomy of a pyGIMLi mesh", fontweight="bold")
# Visualize mesh with the generic pg.show command
pg.show(m, ax=ax)
# Number all cells
for cell in m.cells():
node = cell.allNodes()[2]
def test_Dirichlet(self):
"""
"""
def _testP1_(mesh, show=False):
""" Laplace u = 0 solves u = x for u(r=0)=0 and u(r=1)=1
Test for u == exact x for P1 base functions
"""
u = pg.solve(mesh, a=1, b=0, f=0,
bc={'Dirichlet': [[1, 0], [2, 1]]})
if show:
if mesh.dim()==1:
pg.plt.plot(pg.x(mesh), u)
pg.wait()
elif mesh.dim()==2:
pg.show(mesh, u, label='u')
pg.wait()
xMin = mesh.xmin()
xSpan = (mesh.xmax() - xMin)
np.testing.assert_allclose(u, (pg.x(mesh)-xMin)/ xSpan)
return u
def _testP2_(mesh, show=False):
""" Laplace u = 2 solves u = x² for u(r=0)=0 and u(r=1)=1
Test for u == exact x² for P2 base functions
"""
meshp2 = mesh.createP2()
u = pg.solve(meshp2, f=-2, bc={'Dirichlet': [[1, 0], [2, 1]]})
# find test pos different from node pos
meshTests = mesh.createH2()
meshTests = meshTests.createH2()
c = [c.center() for c in meshTests.cells()]
startPos = meshTests.node(0).pos()
if mesh.dim() == 2:
c = [b.center() for b in meshTests.boundaries(meshTests.boundaryMarkers()==4)]
c.sort(key=lambda c_: c_.distance(startPos))
ui = pg.interpolate(meshp2, u, c)
xi = pg.utils.cumDist(c) + startPos.distance(c[0])
if show:
pg.plt.plot(xi, ui)
pg.plt.plot(xi, xi**2)
pg.wait()
np.testing.assert_allclose(ui, xi**2)
_testP1_(pg.createGrid(x=np.linspace(0, 1, 11)), show=False) #1D
_testP1_(pg.createGrid(x=np.linspace(-2, 1, 11), y=np.linspace(0, 1, 11))) #2D reg quad
_testP1_(pg.createGrid(x=np.linspace(-0.04, 0.01, 11), y=np.linspace(-0.4, 0, 11))) #2D scaled
_testP1_(pg.createGrid(x=np.linspace(-2, 1, 11), y=np.linspace( 0, 1, 11),
z=np.linspace( 0, 1, 11))) #3D
mesh = pg.meshtools.createMesh(pg.meshtools.createWorld(start=[4, -4], end=[6, -6], worldMarker=0), area=0.1)
mesh.setBoundaryMarkers(np.array([0,1,3,2,4])[mesh.boundaryMarkers()])
_testP1_(mesh, show=False) #2D tri
grid = pg.createGrid(x=np.linspace(-2, 2, 11), y=np.linspace(0, 1, 11))
grid.rotate([0, 0, np.pi/4])
#can't find proper test for this rotated case
#v = _testP1_(grid, show=False) #2D reg - rotated
# P2 tests
mesh = pg.meshtools.createMesh(pg.meshtools.createWorld(start=[0, -4], end=[1, -6], worldMarker=0), area=0.1)
mesh.setBoundaryMarkers(np.array([0,1,3,2,4])[mesh.boundaryMarkers()])
_testP2_(mesh, show=False) #2D tri
_testP2_(pg.createGrid(x=np.linspace(0, 1, 11)), show=0) #1D
_testP2_(pg.createGrid(x=np.linspace(0, 1, 11), y=np.linspace(0, 1, 11)), show=0) #2D reg quad
grid = pg.createGrid(x=np.linspace(0, 1, 11), y=np.linspace(0, 1, 11))
grid.rotate([0, 0, np.pi/4])
v = _testP2_(grid, show=False) #2D reg - rotated
(r2A * r1A * (r1A + r2A))
elif r1A > 1e-12 and r2A > 1e-12:
return k * ((r1.dot(n)) / r1A * pg.math.besselK1(r1A * k) +
(r2.dot(n)) / r2A * pg.math.besselK1(r2A * k)) / \
(pg.math.besselK0(r1A * k) + pg.math.besselK0(r2A * k))
else:
return 0.
def pointSource(cell, f, userData):
sourcePos = userData['sourcePos']
if cell.shape().isInside(sourcePos):
f.setVal(cell.N(cell.shape().rst(sourcePos)), cell.ids())
grid = pg.createGrid(x=np.linspace(-10.0, 10.0, 50.),
y=np.linspace(-15.0, .0, 50.))
#a = pg.Vector(grid.cellCount(),1)
a = np.ones(grid.cellCount())
for c in grid.cells():
if c.center()[1] < -5:
a[c.id()] = 0.1
#grid = grid.createH2()
#grid = grid.createP2()
sourcePosA = [-5.0, -4.0]
sourcePosB = [ 5.0, -4.0]
neumannBC = [[1, mixedBC], #left boundary
[2, mixedBC], #right boundary
a2.legend(loc='best')
fig = pg.plt.figure(figsize=(8,8))
ax = [fig.add_subplot(2, 2, i) for i in range(1, 5)]
# Horizontal cylinder
ga = gradUCylinderHoriz(pnts, radius, rho, pos=pos)
gza = gradGZCylinderHoriz(pnts, radius, rho, pos=pos)
circ = createCircle([0, -depth], radius=radius, marker=2, area=0.1,
segments=32)
g, gz = solveGravimetry(circ, rho, pnts, complete=True)
plot(x, ax[0], ga, gza, ax[1], g, gz)
# Half plate
thickness = 0.1
# mesh = pg.createGrid(x=[-2,2], y=[-2,2], z=[-3,-7])
mesh = pg.createGrid(x=np.linspace(0, 5000, 2),
y=[-depth-thickness/2.0, -depth+thickness/2.0])
ga = gradUHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
gza = gradGZHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
g, gz = solveGravimetry(mesh, rho, pnts, complete=True)
plot(x, ax[2], ga, gza, ax[3], g, gz)
