def test_write_mesh():
os.system('cashocs-convert ./mesh/mesh.msh ./mesh/mesh.xdmf')
mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh(
'./mesh/mesh.xdmf')
cashocs.utils.write_out_mesh(mesh, './mesh/mesh.msh', './mesh/test.msh')
os.system('cashocs-convert ./mesh/test.msh ./mesh/test.xdmf')
test, _, _, _, _, _ = cashocs.import_mesh('./mesh/test.xdmf')
assert np.allclose(test.coordinates()[:, :], mesh.coordinates()[:, :])
os.system('rm ./mesh/test.msh')
os.system('rm ./mesh/test.xdmf')
os.system('rm ./mesh/test.h5')
os.system('rm ./mesh/test_subdomains.xdmf')
os.system('rm ./mesh/test_subdomains.h5')
os.system('rm ./mesh/test_boundaries.xdmf')
os.system('rm ./mesh/test_boundaries.h5')
os.system('rm ./mesh/mesh.xdmf')
os.system('rm ./mesh/mesh.h5')
os.system('rm ./mesh/mesh_subdomains.xdmf')
os.system('rm ./mesh/mesh_subdomains.h5')
os.system('rm ./mesh/mesh_boundaries.xdmf')
os.system('rm ./mesh/mesh_boundaries.h5')
def generate_references():
mesh, subdomains, boundaries, dx, ds, dS = import_mesh(
'./meshes/eit/reference.xdmf')
cg_elem = FiniteElement('CG', mesh.ufl_cell(), 1)
r_elem = FiniteElement('R', mesh.ufl_cell(), 0)
V = FunctionSpace(mesh, MixedElement([cg_elem, r_elem]))
u, c = TrialFunctions(V)
v, d = TestFunctions(V)
a = sigma_out * inner(grad(u), grad(v)) * dx(1) + sigma_in * inner(
grad(u), grad(v)) * dx(2) + u * d * ds + v * c * ds
L1 = Constant(1) * v * (ds(3) + ds(4)) + Constant(-1) * v * (ds(1) + ds(2))
L2 = Constant(1) * v * (ds(3) + ds(2)) + Constant(-1) * v * (ds(1) + ds(4))
L3 = Constant(1) * v * (ds(3) + ds(1)) + Constant(-1) * v * (ds(2) + ds(4))
reference1 = Function(V)
reference2 = Function(V)
reference3 = Function(V)
solve(a == L1, reference1)
solve(a == L2, reference2)
solve(a == L3, reference3)
ref1, _ = reference1.split(True)
ref2, _ = reference2.split(True)
ref3, _ = reference3.split(True)
return [ref1, ref2, ref3]
def test_mesh_import():
os.system('cashocs-convert ./mesh/mesh.msh ./mesh/mesh.xdmf')
mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh(
'./mesh/mesh.xdmf')
gmsh_coords = np.array([[0, 0], [1, 0], [1, 1], [0, 1],
[0.499999999998694, 0], [1, 0.499999999998694],
[0.5000000000020591, 1], [0, 0.5000000000020591],
[0.2500000000010297, 0.7500000000010296],
[0.3749999970924328, 0.3750000029075671],
[0.7187499979760099, 0.2812500030636815],
[0.6542968741702071, 0.6542968818888233]])
assert abs(fenics.assemble(1 * dx) - 1) < 1e-14
assert abs(fenics.assemble(1 * ds) - 4) < 1e-14
assert abs(fenics.assemble(1 * ds(1)) - 1) < 1e-14
assert abs(fenics.assemble(1 * ds(2)) - 1) < 1e-14
assert abs(fenics.assemble(1 * ds(3)) - 1) < 1e-14
assert abs(fenics.assemble(1 * ds(4)) - 1) < 1e-14
assert np.allclose(mesh.coordinates(), gmsh_coords)
os.system('rm ./mesh/mesh.xdmf')
os.system('rm ./mesh/mesh.h5')
os.system('rm ./mesh/mesh_subdomains.xdmf')
os.system('rm ./mesh/mesh_subdomains.h5')
os.system('rm ./mesh/mesh_boundaries.xdmf')
os.system('rm ./mesh/mesh_boundaries.h5')
def generate_measurements():
mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh(
'./mesh/reference.xdmf')
cg_elem = FiniteElement('CG', mesh.ufl_cell(), 1)
r_elem = FiniteElement('R', mesh.ufl_cell(), 0)
V = FunctionSpace(mesh, MixedElement([cg_elem, r_elem]))
u, c = TrialFunctions(V)
v, d = TestFunctions(V)
a = kappa_out * inner(grad(u), grad(v)) * dx(1) + kappa_in * inner(
grad(u), grad(v)) * dx(2) + u * d * ds + v * c * ds
L1 = Constant(1) * v * (ds(3) + ds(4)) + Constant(-1) * v * (ds(1) + ds(2))
L2 = Constant(1) * v * (ds(3) + ds(2)) + Constant(-1) * v * (ds(1) + ds(4))
L3 = Constant(1) * v * (ds(3) + ds(1)) + Constant(-1) * v * (ds(2) + ds(4))
meas1 = Function(V)
meas2 = Function(V)
meas3 = Function(V)
solve(a == L1, meas1)
solve(a == L2, meas2)
solve(a == L3, meas3)
m1, _ = meas1.split(True)
m2, _ = meas2.split(True)
m3, _ = meas3.split(True)
return [m1, m2, m3]
solve(a == L2, reference2)
solve(a == L3, reference3)
ref1, _ = reference1.split(True)
ref2, _ = reference2.split(True)
ref3, _ = reference3.split(True)
return [ref1, ref2, ref3]
config = configparser.ConfigParser()
config.read('./eit_config.ini')
config_list = generate_cg_benchmark_configs(config)
mesh, subdomains, boundaries, dx, ds, dS = import_mesh(
'./meshes/eit/mesh.xdmf')
coordinates = mesh.coordinates().copy()
cg_elem = FiniteElement('CG', mesh.ufl_cell(), 1)
r_elem = FiniteElement('R', mesh.ufl_cell(), 0)
V = FunctionSpace(mesh, MixedElement([cg_elem, r_elem]))
references = generate_references()
bcs = None
uc1 = Function(V)
u1, c1 = split(uc1)
pd1 = Function(V)
p1, d1 = split(pd1)
e1 = sigma_out*inner(grad(u1), grad(p1))*dx(1) + sigma_in*inner(grad(u1), grad(p1))*dx(2) \
+ u1*d1*ds + p1*c1*ds - Constant(1)*p1*(ds(3) + ds(4)) - Constant(-1)*p1*(ds(1) + ds(2))
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with CASHOCS. If not, see <https://www.gnu.org/licenses/>.
"""For the documentation of this demo see https://cashocs.readthedocs.io/en/latest/demos/shape_optimization/doc_shape_stokes.html.
"""
from fenics import *
import cashocs
config = cashocs.load_config('./config.ini')
mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh('./mesh/mesh.xdmf')
v_elem = VectorElement('CG', mesh.ufl_cell(), 2)
p_elem = FiniteElement('CG', mesh.ufl_cell(), 1)
V = FunctionSpace(mesh, MixedElement([v_elem, p_elem]))
up = Function(V)
u, p = split(up)
vq = Function(V)
v, q = split(vq)
e = inner(grad(u), grad(v))*dx - p*div(v)*dx - q*div(u)*dx
u_in = Expression(('-1.0/4.0*(x[1] - 2.0)*(x[1] + 2.0)', '0.0'), degree=2)
bc_in = DirichletBC(V.sub(0), u_in, boundaries, 1)
bc_no_slip = cashocs.create_bcs_list(V.sub(0), Constant((0,0)), boundaries, [2,4])
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with CASHOCS. If not, see <https://www.gnu.org/licenses/>.
"""For the documentation of this demo see https://cashocs.readthedocs.io/en/latest/demos/shape_optimization/doc_remeshing.html.
"""
from fenics import *
import cashocs
config = cashocs.load_config('./config.ini')
mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh(config)
V = FunctionSpace(mesh, 'CG', 1)
u = Function(V)
p = Function(V)
x = SpatialCoordinate(mesh)
f = 2.5 * pow(x[0] + 0.4 - pow(x[1], 2), 2) + pow(x[0], 2) + pow(x[1], 2) - 1
e = inner(grad(u), grad(p)) * dx - f * p * dx
bcs = DirichletBC(V, Constant(0), boundaries, 1)
J = u * dx
sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
sop.solve()