def _cooks(cls, **kwargs):
mesh = UnitSquareMesh(10, 5)
def cooks_domain(x, y):
return [48 * x, 44 * (x + y) - 18 * x * y]
mesh.coordinates()[:] = np.array(cooks_domain(mesh.coordinates()[:, 0], mesh.coordinates()[:, 1])).transpose()
# plot(mesh, interactive=True, axes=True)
maxx, minx, maxy, miny = 48, 0, 60, 0
# setup boundary parts
llc, lrc, tlc, trc = compile_subdomains(['near(x[0], 0.) && near(x[1], 0.)',
'near(x[0], 48.) && near(x[1], 0.)',
'near(x[0], 0.) && near(x[1], 60.)',
'near(x[0], 48.) && near(x[1], 60.)'])
top, bottom, left, right = compile_subdomains([ 'x[0] >= 0. && x[0] <= 48. && x[1] >= 44. && on_boundary',
'x[0] >= 0. && x[0] <= 48. && x[1] <= 44. && on_boundary',
'near(x[0], 0.) && on_boundary',
'near(x[0], 48.) && on_boundary'])
# the corners
llc.minx = minx
llc.miny = miny
lrc.maxx = maxx
lrc.miny = miny
tlc.minx = minx
tlc.maxy = maxy
trc.maxx = maxx
trc.maxy = maxy
# the edges
top.minx = minx
top.maxx = maxx
bottom.minx = minx
bottom.maxx = maxx
left.minx = minx
right.maxx = maxx
return mesh, {'top':top, 'bottom':bottom, 'left':left, 'right':right, 'llc':llc, 'lrc':lrc, 'tlc':tlc, 'trc':trc, 'all': DomainBoundary()}, 2
def _interval(cls, **kwargs):
N = kwargs['initial_mesh_N']
mesh0 = UnitInterval(N)
maxx, minx = 1, 0
# setup boundary parts
left, right = compile_subdomains(['near(x[0], 0.) && on_boundary',
'near(x[0], 1.) && on_boundary'])
left.minx = minx
right.maxx = maxx
return mesh0, {'left':left, 'right':right, 'all': DomainBoundary()}, 1
def _lshape(cls, **kwargs):
lshape_xml = os.path.join(os.path.dirname(__file__), 'lshape.xml')
mesh0 = Mesh(lshape_xml)
maxx, minx, maxy, miny = 1, -1, 1, -1
# setup boundary parts
top, bottom, left, right = compile_subdomains([ 'near(x[1], 1.) && on_boundary',
'near(x[1], -1.) && on_boundary',
'near(x[0], -1.) && on_boundary',
'x[0]>=0. && x[1]<=1. && x[1]>=-1. && on_boundary'])
top.maxy = maxy
bottom.miny = miny
left.minx = minx
return mesh0, {'top':top, 'bottom':bottom, 'left':left, 'right':right, 'all': DomainBoundary()}, 2
def _square(cls, **kwargs):
N = kwargs['initial_mesh_N']
mesh0 = UnitSquareMesh(N, N)
maxx, minx, maxy, miny = 1, 0, 1, 0
# setup boundary parts
top, bottom, left, right = compile_subdomains([ 'near(x[1], 1.) && on_boundary',
'near(x[1], 0.) && on_boundary',
'near(x[0], 0.) && on_boundary',
'near(x[0], 1.) && on_boundary'])
top.maxy = maxy
bottom.miny = miny
left.minx = minx
right.maxx = maxx
return mesh0, {'top':top, 'bottom':bottom, 'left':left, 'right':right, 'all': DomainBoundary()}, 2
def create_dirichlet_conditions(values, boundaries, function_space):
"""Create Dirichlet boundary conditions for given boundary values,
boundaries and function space."""
# Check that the size matches
if len(values) != len(boundaries):
error(
"The number of Dirichlet values does not match the number of Dirichlet boundaries."
)
info("Creating %d Dirichlet boundary condition(s)." % len(values))
# Create Dirichlet conditions
bcs = []
for (i, value) in enumerate(values):
# Get current boundary
boundary = boundaries[i]
# Case 0: boundary is a string
if isinstance(boundary, str):
boundary = compile_subdomains(boundary)
bc = DirichletBC(function_space, value, boundary)
# Case 1: boundary is a SubDomain
elif isinstance(boundary, SubDomain):
bc = DirichletBC(function_space, value, boundary)
# Case 2: boundary is defined by a MeshFunction
elif isinstance(boundary, tuple):
mesh_function, index = boundary
bc = DirichletBC(function_space, value, mesh_function, index)
# Unhandled case
else:
error(
"Unhandled boundary specification for boundary condition. "
"Expecting a string, a SubDomain or a (MeshFunction, int) tuple."
)
bcs.append(bc)
return bcs
def create_dirichlet_conditions(values, boundaries, function_space):
"""Create Dirichlet boundary conditions for given boundary values,
boundaries and function space."""
# Check that the size matches
if len(values) != len(boundaries):
error("The number of Dirichlet values does not match the number of Dirichlet boundaries.")
info("Creating %d Dirichlet boundary condition(s)." % len(values))
# Create Dirichlet conditions
bcs = []
for (i, value) in enumerate(values):
# Get current boundary
boundary = boundaries[i]
# Case 0: boundary is a string
if isinstance(boundary, str):
boundary = compile_subdomains(boundary)
bc = DirichletBC(function_space, value, boundary)
# Case 1: boundary is a SubDomain
elif isinstance(boundary, SubDomain):
bc = DirichletBC(function_space, value, boundary)
# Case 2: boundary is defined by a MeshFunction
elif isinstance(boundary, tuple):
mesh_function, index = boundary
bc = DirichletBC(function_space, value, mesh_function, index)
# Unhandled case
else:
error("Unhandled boundary specification for boundary condition. "
"Expecting a string, a SubDomain or a (MeshFunction, int) tuple.")
bcs.append(bc)
return bcs
# setup meshes
lshape = False
if lshape:
mesh0 = Mesh(lshape_xml)
maxx, minx, maxy, miny = 1, -1, 1, -1
else:
mesh0 = UnitSquareMesh(5, 5)
maxx, minx, maxy, miny = 1, 0, 1, 0
#meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=10, randref=(0.4, 0.3))
meshes = SampleProblem.setupMeshes(mesh0, len(mis), num_refine=0)
# setup boundary parts
top, bottom, left, right = compile_subdomains([ 'near(x[1], maxy) && on_boundary',
'near(x[1], miny) && on_boundary',
'near(x[0], minx) && on_boundary',
'near(x[0], maxx) && on_boundary'])
top.maxy = maxy
bottom.miny = miny
left.minx = minx
right.maxx = maxx
# define coefficient field
coeff_types = ("EF-square-cos", "EF-square-sin", "monomials")
gamma = 0.9
coeff_field = SampleProblem.setupCF(coeff_types[1], decayexp=4, gamma=gamma, freqscale=1, freqskip=10, rvtype="uniform", scale=1000)
# define RHS
f = Constant(1.0)
# define Dirichlet and Neumann boundaries
