def _get_periodicBC_X(self, domain, dim):
dim_dict = {1: ('y', per.match_y_plane),
2: ('z', per.match_z_plane)}
dim_string = dim_dict[dim][0]
match_plane = dim_dict[dim][1]
min_, max_ = domain.get_mesh_bounding_box()[:, dim]
min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
plus_ = self._subdomain_func(max_x=max_x, **{dim_string: (max_,)})
minus_ = self._subdomain_func(max_x=max_x, **{dim_string: (min_,)})
plus_string = dim_string + 'plus'
minus_string = dim_string + 'minus'
plus = Function(plus_string, plus_)
minus = Function(minus_string, minus_)
region_plus = domain.create_region(
'region_{0}_plus'.format(dim_string),
'vertices by {0}'.format(
plus_string),
'facet',
functions=Functions([plus]))
region_minus = domain.create_region(
'region_{0}_minus'.format(dim_string),
'vertices by {0}'.format(
minus_string),
'facet',
functions=Functions([minus]))
match_plane = Function(
'match_{0}_plane'.format(dim_string), match_plane)
bc_dict = {'u.0': 'u.0'}
bc = PeriodicBC('periodic_{0}'.format(dim_string),
[region_plus, region_minus],
bc_dict,
match='match_{0}_plane'.format(dim_string))
return bc, match_plane
def run(domain, order):
omega = domain.create_region('Omega', 'all')
bbox = domain.get_mesh_bounding_box()
min_x, max_x = bbox[:, 0]
min_y, max_y = bbox[:, 1]
eps = 1e-8 * (max_x - min_x)
gamma1 = domain.create_region('Gamma1',
'vertices in (x < %.10f)' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in (x > %.10f)' % (max_x - eps),
'facet')
gamma3 = domain.create_region('Gamma3',
'vertices in y < %.10f' % (min_y + eps),
'facet')
gamma4 = domain.create_region('Gamma4',
'vertices in y > %.10f' % (max_y - eps),
'facet')
field = Field.from_args('fu', nm.float64, 1, omega, approx_order=order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
integral = Integral('i', order=2 * order)
t1 = Term.new('dw_laplace(v, u)', integral, omega, v=v, u=u)
eq = Equation('eq', t1)
eqs = Equations([eq])
fix1 = EssentialBC('fix1', gamma1, {'u.0': 0.4})
fix2 = EssentialBC('fix2', gamma2, {'u.0': 0.0})
def get_shift(ts, coors, region):
return nm.ones_like(coors[:, 0])
dof_map_fun = Function('dof_map_fun', per.match_x_line)
shift_fun = Function('shift_fun', get_shift)
sper = LinearCombinationBC('sper', [gamma3, gamma4], {'u.0': 'u.0'},
dof_map_fun,
'shifted_periodic',
arguments=(shift_fun, ))
ls = ScipyDirect({})
nls = Newton({}, lin_solver=ls)
pb = Problem('laplace', equations=eqs)
pb.set_bcs(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))
pb.set_solver(nls)
state = pb.solve()
return pb, state
def _get_fixed_displacementsBCs(self, domain):
"""
Fix the left top and bottom points in x, y and z
Args:
domain: an Sfepy domain
Returns:
the Sfepy boundary conditions
"""
min_xyz = domain.get_mesh_bounding_box()[0]
max_xyz = domain.get_mesh_bounding_box()[1]
kwargs = {}
fix_points_dict = {'u.0': 0.0, 'u.1': 0.0}
if len(min_xyz) == 3:
kwargs = {'z': (max_xyz[2], min_xyz[2])}
fix_points_dict['u.2'] = 0.0
fix_x_points_ = self._subdomain_func(x=(min_xyz[0],),
y=(max_xyz[1], min_xyz[1]),
**kwargs)
fix_x_points = Function('fix_x_points', fix_x_points_)
region_fix_points = domain.create_region(
'region_fix_points',
'vertices by fix_x_points',
'vertex',
functions=Functions([fix_x_points]))
return EssentialBC('fix_points_BC', region_fix_points, fix_points_dict)
def _get_shift_displacementsBCs(self, domain):
"""
Fix the right top and bottom points in x, y and z
Args:
domain: an Sfepy domain
Returns:
the Sfepy boundary conditions
"""
min_xyz = domain.get_mesh_bounding_box()[0]
max_xyz = domain.get_mesh_bounding_box()[1]
kwargs = {}
if len(min_xyz) == 3:
kwargs = {'z': (max_xyz[2], min_xyz[2])}
displacement = self.macro_strain * (max_xyz[0] - min_xyz[0])
shift_points_dict = {'u.0': displacement}
shift_x_points_ = self._subdomain_func(x=(max_xyz[0],),
y=(max_xyz[1], min_xyz[1]),
**kwargs)
shift_x_points = Function('shift_x_points', shift_x_points_)
region_shift_points = domain.create_region(
'region_shift_points',
'vertices by shift_x_points',
'vertex',
functions=Functions([shift_x_points]))
return EssentialBC('shift_points_BC',
region_shift_points, shift_points_dict)
def eval_force(region_name):
strain = problem.evaluate(
'ev_cauchy_strain.i.%s(u)' % region_name,
mode='qp',
verbose=False,
)
D = problem.evaluate(
'ev_integrate_mat.i.%s(solid.D, u)' % region_name,
mode='qp',
verbose=False,
)
normal = nm.array([1, 0, 0], dtype=nm.float64)
s2f = get_full_indices(len(normal))
stress = nm.einsum('cqij,cqjk->cqik', D, strain)
# Full (matrix) form of stress.
mstress = stress[..., s2f, 0]
# Force in normal direction.
force = nm.einsum('cqij,i,j->cq', mstress, normal, normal)
def get_force(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'force': force.reshape(coors.shape[0], 1, 1)}
aux = Material('aux', function=Function('get_force', get_force))
middle_force = -problem.evaluate(
'ev_integrate_mat.i.%s(aux.force, u)' % region_name,
aux=aux,
verbose=False,
)
output('%s section axial force:' % region_name, middle_force)
def get_bc(max_x_func, domain, dim, bc_dict_func):
"""Get the periodic boundary condition
Args:
max_x_func: function for finding the maximum value of x
domain: the Sfepy domain
dim: the x, y or z direction
bc_dict_func: function to generate the bc dict
Returns:
the boundary condition and the sfepy function
"""
dim_dict = lambda x: [
("x", per.match_x_plane),
("y", per.match_y_plane),
("z", per.match_z_plane),
][dim][x]
return pipe(
domain.get_mesh_bounding_box(),
lambda x: PeriodicBC(
"periodic_{0}".format(dim_dict(0)),
list(
map_(
get_region_func(max_x_func(x), dim_dict(0), domain),
zip(("plus", "minus"), x[:, dim][::-1]),
)
),
bc_dict_func(x),
match="match_{0}_plane".format(dim_dict(0)),
),
lambda x: (x, Function("match_{0}_plane".format(dim_dict(0)), dim_dict(1))),
)
def _get_material(self, property_array, domain):
"""
Creates an SfePy material from the material property fields for the
quadrature points.
Args:
property_array: array of the properties with shape (n_x, n_y, n_z, 2)
Returns:
an SfePy material
"""
min_xyz = domain.get_mesh_bounding_box()[0]
dims = domain.get_mesh_bounding_box().shape[1]
def _material_func_(ts, coors, mode=None, **kwargs):
if mode == 'qp':
ijk_out = np.empty_like(coors, dtype=int)
ijk = np.floor((coors - min_xyz[None]) / self.dx,
ijk_out, casting="unsafe")
ijk_tuple = tuple(ijk.swapaxes(0, 1))
property_array_qp = property_array[ijk_tuple]
lam = property_array_qp[..., 0]
mu = property_array_qp[..., 1]
lam = np.ascontiguousarray(lam.reshape((lam.shape[0], 1, 1)))
mu = np.ascontiguousarray(mu.reshape((mu.shape[0], 1, 1)))
from sfepy.mechanics.matcoefs import stiffness_from_lame
stiffness = stiffness_from_lame(dims, lam=lam, mu=mu)
return {'lam': lam, 'mu': mu, 'D': stiffness}
else:
return
material_func = Function('material_func', _material_func_)
return Material('m', function=material_func)
def solveLaplaceEquationTetrahedral(mesh, meshVTK, boundaryPoints,
boundaryConditions):
"""
mesh: path to a 3D mesh / sfepy mesh
"""
if isinstance(mesh, str):
mesh = Mesh.from_file(mesh)
#Set domains
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
boundary = domain.create_region(
'gamma',
'vertex %s' % ','.join(map(str, range(meshVTK.GetNumberOfPoints()))),
'facet')
#set fields
field = Field.from_args('fu', np.float64, 1, omega, approx_order=1)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', val=[1.])
#Define element integrals
integral = Integral('i', order=3)
#Equations defining
t1 = Term.new('dw_laplace( v, u )', integral, omega, v=v, u=u)
eq = Equation('balance', t1)
eqs = Equations([eq])
heatBoundary = boundaryConditions
points = boundaryPoints
#Boundary conditions
c = ClosestPointStupid(points, heatBoundary, meshVTK)
def u_fun(ts, coors, bc=None, problem=None, c=c):
c.distances = []
v = np.zeros(len(coors))
for i, p in enumerate(coors):
v[i] = c.interpolate(p)
#c.findClosestPoint(p)
return v
bc_fun = Function('u_fun', u_fun)
fix1 = EssentialBC('fix_u', boundary, {'u.all': bc_fun})
#Solve problem
ls = ScipyDirect({})
nls = Newton({}, lin_solver=ls)
pb = Problem('heat', equations=eqs)
pb.set_bcs(ebcs=Conditions([fix1]))
pb.set_solver(nls)
state = pb.solve(verbose=False, save_results=False)
u = state.get_parts()['u']
return u
def test_solving(self):
from sfepy.base.base import IndexedStruct
from sfepy.discrete import (FieldVariable, Material, Problem, Function,
Equation, Equations, Integral)
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.terms import Term
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.mechanics.matcoefs import stiffness_from_lame
u = FieldVariable('u', 'unknown', self.field)
v = FieldVariable('v', 'test', self.field, primary_var_name='u')
m = Material('m', D=stiffness_from_lame(self.dim, 1.0, 1.0))
f = Material('f', val=[[0.02], [0.01]])
bc_fun = Function('fix_u_fun', fix_u_fun,
extra_args={'extra_arg' : 'hello'})
fix_u = EssentialBC('fix_u', self.gamma1, {'u.all' : bc_fun})
shift_u = EssentialBC('shift_u', self.gamma2, {'u.0' : 0.1})
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(m.D, v, u)',
integral, self.omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, self.omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
## pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions([fix_u, shift_u]))
state = pb.solve()
name = op.join(self.options.out_dir, 'test_high_level_solving.vtk')
pb.save_state(name, state)
ok = nls_status.condition == 0
if not ok:
self.report('solver did not converge!')
_ok = state.has_ebc()
if not _ok:
self.report('EBCs violated!')
ok = ok and _ok
return ok
def func(min_xyz, max_xyz):
def shift_(_, coors, __):
return np.ones_like(coors[:, 0]) * macro_strain * (max_xyz[0] - min_xyz[0])
return pipe(
[("plus", max_xyz[0]), ("minus", min_xyz[0])],
map_(get_region_func(None, "x", domain)),
list,
lambda x: LinearCombinationBC(
"lcbc",
x,
{"u.0": "u.0"},
Function("match_x_plane", per.match_x_plane),
"shifted_periodic",
arguments=(Function("shift", shift_),),
),
lambda x: Conditions([x]),
)
def _get_linear_combinationBCs(self, domain):
"""
The right nodes are periodic with the left nodes but also displaced.
Args:
domain: an Sfepy domain
Returns:
the Sfepy boundary conditions
"""
min_xyz = domain.get_mesh_bounding_box()[0]
max_xyz = domain.get_mesh_bounding_box()[1]
xplus_ = self._subdomain_func(x=(max_xyz[0], ))
xminus_ = self._subdomain_func(x=(min_xyz[0], ))
xplus = Function('xplus', xplus_)
xminus = Function('xminus', xminus_)
region_x_plus = domain.create_region('region_x_plus',
'vertices by xplus',
'facet',
functions=Functions([xplus]))
region_x_minus = domain.create_region('region_x_minus',
'vertices by xminus',
'facet',
functions=Functions([xminus]))
match_x_plane = Function('match_x_plane', per.match_x_plane)
def shift_(ts, coors, region):
return np.ones_like(
coors[:, 0]) * self.macro_strain * (max_xyz[0] - min_xyz[0])
shift = Function('shift', shift_)
lcbc = LinearCombinationBC('lcbc', [region_x_plus, region_x_minus],
{'u.0': 'u.0'},
match_x_plane,
'shifted_periodic',
arguments=(shift, ))
return Conditions([lcbc])
def get_material(calc_stiffness, calc_prestress):
"""Get the material
Args:
calc_stiffness: the function for calculating the stiffness tensor
calc_prestress: the function for calculating the prestress
Returns:
the material
"""
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return dict(D=calc_stiffness(coors), stress=calc_prestress(coors))
return None
return Material("m", function=Function("material_func", _material_func_))
def func(min_xyz, max_xyz):
return pipe(
dict(z_points=(max_xyz[2], min_xyz[2])) if len(min_xyz) == 3 else dict(),
lambda x: subdomain_func(
x_points=x_points_f(min_xyz, max_xyz),
y_points=(max_xyz[1], min_xyz[1]),
**x,
),
lambda x: Function(f"{name}_x_points", x),
lambda x: domain.create_region(
f"region_{name}_points",
f"vertices by {name}_x_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC(
f"{name}_points_BC", x, points_dict_f(min_xyz, max_xyz)
),
)
def _get_material(property_array, domain, delta_x):
"""
Creates an SfePy material from the material property fields for the
quadrature points.
Args:
property_array: array of the properties with shape (n_x, n_y, n_z, 2)
domain: the Sfepy domain
delta_x: the grid spacing
Returns:
a SfePy material
"""
reshape = lambda x: np.ascontiguousarray(x.reshape((x.shape[0], 1, 1)))
def _material_func_(_, coors, mode=None, **__):
if mode == "qp":
return pipe(
np.empty_like(coors, dtype=int),
lambda x: np.floor(
(coors - domain.get_mesh_bounding_box()[0][None]) /
delta_x,
x,
casting="unsafe",
),
lambda x: x.swapaxes(0, 1),
tuple,
lambda x: property_array[x],
lambda x: dict(
lam=reshape(x[..., 0]),
mu=reshape(x[..., 1]),
D=stiffness_from_lame(
domain.get_mesh_bounding_box().shape[1],
lam=x[..., 0],
mu=x[..., 1],
),
),
)
return None
return Material("m", function=Function("material_func", _material_func_))
def get_region_func(max_x, dim_string, domain, name_minmax):
"""Generate the Sfepy region
Args:
max_x: max value in the x direction
dim_string: either "x", "y", or "z"
domain: the Sfepy domain
name_minmax: tuple of name and min / max
Returns:
the Sfepy region
"""
return pipe(
subdomain_func(max_x=max_x, **{dim_string + "_points": (name_minmax[1],)}),
lambda x: Function(dim_string + name_minmax[0], x),
lambda x: domain.create_region(
"region_{0}_{1}".format(dim_string, name_minmax[0]),
"vertices by {0}".format(x.name),
"facet",
functions=Functions([x]),
),
)
def get_bc(domain, delta_x, index, cond):
"""Make a displacement boundary condition
Args:
domain: the Sfepy domain
delta_x: the mesh spacing
index: the index (either 0 or 1) depends on direction of axes
cond: the BC dictionary
Returns:
the Sfepy boundary condition
"""
return pipe(
Function("fix_points", subdomain(index, domain, delta_x * 1e-3)),
lambda x: domain.create_region(
"region_fix_points",
"vertices by fix_points",
"vertex",
functions=Functions([x]),
),
lambda x: EssentialBC("fix_points_BC", x, cond),
)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-s',
'--show',
action="store_true",
dest='show',
default=False,
help=help['show'])
options, args = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:, 0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in x > %.10f' % (max_x - eps),
'facet')
field = Field.from_args('fu', nm.float64, 'vector', omega, approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = Material('m', D=stiffness_from_lame(dim=2, lam=1.0, mu=1.0))
f = Material('f', val=[[0.02], [0.01]])
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(m.D, v, u)', integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all': 0.0})
bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift': 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0': bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions([fix_u, shift_u]))
vec = pb.solve()
print(nls_status)
pb.save_state('linear_elasticity.vtk', vec)
if options.show:
view = Viewer('linear_elasticity.vtk')
view(vector_mode='warp_norm',
rel_scaling=2,
is_scalar_bar=True,
is_wireframe=True)
def main():
parser = ArgumentParser(description=__doc__.rstrip(),
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('output_dir', help=helps['output_dir'])
parser.add_argument('--dims', metavar='dims',
action='store', dest='dims',
default='1.0,1.0,1.0', help=helps['dims'])
parser.add_argument('--shape', metavar='shape',
action='store', dest='shape',
default='7,7,7', help=helps['shape'])
parser.add_argument('--centre', metavar='centre',
action='store', dest='centre',
default='0.0,0.0,0.0', help=helps['centre'])
parser.add_argument('-3', '--3d',
action='store_true', dest='is_3d',
default=False, help=helps['3d'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
options = parser.parse_args()
dim = 3 if options.is_3d else 2
dims = nm.array(eval(options.dims), dtype=nm.float64)[:dim]
shape = nm.array(eval(options.shape), dtype=nm.int32)[:dim]
centre = nm.array(eval(options.centre), dtype=nm.float64)[:dim]
output('dimensions:', dims)
output('shape: ', shape)
output('centre: ', centre)
mesh0 = gen_block_mesh(dims, shape, centre, name='block-fem',
verbose=True)
domain0 = FEDomain('d', mesh0)
bbox = domain0.get_mesh_bounding_box()
min_x, max_x = bbox[:, 0]
eps = 1e-8 * (max_x - min_x)
cnt = (shape[0] - 1) // 2
g0 = 0.5 * dims[0]
grading = nm.array([g0 / 2**ii for ii in range(cnt)]) + eps + centre[0] - g0
domain, subs = refine_towards_facet(domain0, grading, 'x <')
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in (x < %.10f)' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in (x > %.10f)' % (max_x - eps),
'facet')
field = Field.from_args('fu', nm.float64, 1, omega,
approx_order=options.order)
if subs is not None:
field.substitute_dofs(subs)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
integral = Integral('i', order=2*options.order)
t1 = Term.new('dw_laplace(v, u)',
integral, omega, v=v, u=u)
eq = Equation('eq', t1)
eqs = Equations([eq])
def u_fun(ts, coors, bc=None, problem=None):
"""
Define a displacement depending on the y coordinate.
"""
if coors.shape[1] == 2:
min_y, max_y = bbox[:, 1]
y = (coors[:, 1] - min_y) / (max_y - min_y)
val = (max_y - min_y) * nm.cos(3 * nm.pi * y)
else:
min_y, max_y = bbox[:, 1]
min_z, max_z = bbox[:, 2]
y = (coors[:, 1] - min_y) / (max_y - min_y)
z = (coors[:, 2] - min_z) / (max_z - min_z)
val = ((max_y - min_y) * (max_z - min_z)
* nm.cos(3 * nm.pi * y) * (1.0 + 3.0 * (z - 0.5)**2))
return val
bc_fun = Function('u_fun', u_fun)
fix1 = EssentialBC('shift_u', gamma1, {'u.0' : bc_fun})
fix2 = EssentialBC('fix2', gamma2, {'u.all' : 0.0})
ls = ScipyDirect({})
nls = Newton({}, lin_solver=ls)
pb = Problem('heat', equations=eqs, nls=nls, ls=ls)
pb.time_update(ebcs=Conditions([fix1, fix2]))
state = pb.solve()
if subs is not None:
field.restore_dofs()
filename = os.path.join(options.output_dir, 'hanging.vtk')
ensure_path(filename)
pb.save_state(filename, state)
if options.order > 1:
pb.save_state(filename, state, linearization=Struct(kind='adaptive',
min_level=0,
max_level=8,
eps=1e-3))
def main(argv=None):
options = parse_args(argv=argv)
# vvvvvvvvvvvvvvvv #
approx_order = 2
# ^^^^^^^^^^^^^^^^ #
# Setup output names
outputs_folder = options.output_dir
domain_name = "domain_1D"
problem_name = "iburgers_1D"
output_folder = pjoin(outputs_folder, problem_name, str(approx_order))
output_format = "vtk"
save_timestn = 100
clear_folder(pjoin(output_folder, "*." + output_format))
configure_output({
'output_screen':
True,
'output_log_name':
pjoin(output_folder, f"last_run_{problem_name}_{approx_order}.txt")
})
# ------------
# | Get mesh |
# ------------
X1 = 0.
XN = 1.
n_nod = 100
n_el = n_nod - 1
mesh = get_gen_1D_mesh_hook(X1, XN, n_nod).read(None)
# -----------------------------
# | Create problem components |
# -----------------------------
integral = Integral('i', order=approx_order * 2)
domain = FEDomain(domain_name, mesh)
omega = domain.create_region('Omega', 'all')
left = domain.create_region('Gamma1', 'vertices in x == %.10f' % X1,
'vertex')
right = domain.create_region('Gamma2', 'vertices in x == %.10f' % XN,
'vertex')
field = DGField('dgfu',
nm.float64,
'scalar',
omega,
approx_order=approx_order)
u = FieldVariable('u', 'unknown', field, history=1)
v = FieldVariable('v', 'test', field, primary_var_name='u')
MassT = Term.new('dw_dot(v, u)', integral, omega, u=u, v=v)
velo = nm.array(1.0)
def adv_fun(u):
vu = velo.T * u[..., None]
return vu
def adv_fun_d(u):
v1 = velo.T * nm.ones(u.shape + (1, ))
return v1
burg_velo = velo.T / nm.linalg.norm(velo)
def burg_fun(u):
vu = burg_velo * u[..., None]**2
return vu
def burg_fun_d(u):
v1 = 2 * burg_velo * u[..., None]
return v1
StiffT = Term.new('dw_ns_dot_grad_s(fun, fun_d, u[-1], v)',
integral,
omega,
u=u,
v=v,
fun=burg_fun,
fun_d=burg_fun_d)
# alpha = Material('alpha', val=[.0])
# FluxT = AdvectDGFluxTerm("adv_lf_flux(a.val, v, u)", "a.val, v, u[-1]",
# integral, omega, u=u, v=v, a=a, alpha=alpha)
FluxT = Term.new('dw_dg_nonlinear_laxfrie_flux(fun, fun_d, v, u[-1])',
integral,
omega,
u=u,
v=v,
fun=burg_fun,
fun_d=burg_fun_d)
eq = Equation('balance', MassT - StiffT + FluxT)
eqs = Equations([eq])
# ------------------------------
# | Create boundary conditions |
# ------------------------------
left_fix_u = EssentialBC('left_fix_u', left, {'u.all': 1.0})
right_fix_u = EssentialBC('right_fix_u', right, {'u.all': 0.0})
# ----------------------------
# | Create initial condition |
# ----------------------------
def ghump(x):
"""
Nice gaussian.
"""
return nm.exp(-200 * x**2)
def ic_wrap(x, ic=None):
return ghump(x - .3)
ic_fun = Function('ic_fun', ic_wrap)
ics = InitialCondition('ic', omega, {'u.0': ic_fun})
# ------------------
# | Create problem |
# ------------------
pb = Problem(problem_name,
equations=eqs,
conf=Struct(options={"save_times": save_timestn},
ics={},
ebcs={},
epbcs={},
lcbcs={},
materials={}),
active_only=False)
pb.setup_output(output_dir=output_folder, output_format=output_format)
pb.set_ics(Conditions([ics]))
# ------------------
# | Create limiter |
# ------------------
limiter = MomentLimiter1D
# ---------------------------
# | Set time discretization |
# ---------------------------
CFL = .2
max_velo = nm.max(nm.abs(velo))
t0 = 0
t1 = .2
dx = nm.min(mesh.cmesh.get_volumes(1))
dt = dx / max_velo * CFL / (2 * approx_order + 1)
tn = int(nm.ceil((t1 - t0) / dt))
dtdx = dt / dx
# ------------------
# | Create solver |
# ------------------
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'is_linear': True}, lin_solver=ls, status=nls_status)
tss_conf = {
't0': t0,
't1': t1,
'n_step': tn,
'limiters': {
"dgfu": limiter
}
}
tss = TVDRK3StepSolver(tss_conf, nls=nls, context=pb, verbose=True)
# ---------
# | Solve |
# ---------
pb.set_solver(tss)
state_end = pb.solve()
output("Solved equation \n\n\t\t u_t - div(f(u))) = 0\n")
output(f"With IC: {ic_fun.name}")
# output("and EBCs: {}".format(pb.ebcs.names))
# output("and EPBCS: {}".format(pb.epbcs.names))
output("-------------------------------------")
output(f"Approximation order is {approx_order}")
output(f"Space divided into {mesh.n_el} cells, " +
f"{len(mesh.coors)} steps, step size is {dx}")
output(f"Time divided into {tn - 1} nodes, {tn} steps, step size is {dt}")
output(f"CFL coefficient was {CFL} and " +
f"order correction {1 / (2 * approx_order + 1)}")
output(f"Courant number c = max(abs(u)) * dt/dx = {max_velo * dtdx}")
output("------------------------------------------")
output(f"Time stepping solver is {tss.name}")
output(f"Limiter used: {limiter.name}")
output("======================================")
# ----------
# | Plot 1D|
# ----------
if options.plot:
load_and_plot_fun(output_folder, domain_name, t0, t1,
min(tn, save_timestn), ic_fun)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('--diffusivity',
metavar='float',
type=float,
action='store',
dest='diffusivity',
default=1e-5,
help=helps['diffusivity'])
parser.add_option('--ic-max',
metavar='float',
type=float,
action='store',
dest='ic_max',
default=2.0,
help=helps['ic_max'])
parser.add_option('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=2,
help=helps['order'])
parser.add_option('-r',
'--refine',
metavar='int',
type=int,
action='store',
dest='refine',
default=0,
help=helps['refine'])
parser.add_option('-p',
'--probe',
action="store_true",
dest='probe',
default=False,
help=helps['probe'])
parser.add_option('-s',
'--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
options, args = parser.parse_args()
assert_((0 < options.order),
'temperature approximation order must be at least 1!')
output('using values:')
output(' diffusivity:', options.diffusivity)
output(' max. IC value:', options.ic_max)
output('uniform mesh refinement level:', options.refine)
mesh = Mesh.from_file(data_dir + '/meshes/3d/cylinder.mesh')
domain = FEDomain('domain', mesh)
if options.refine > 0:
for ii in xrange(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements' %
(domain.shape.n_nod, domain.shape.n_el))
omega = domain.create_region('Omega', 'all')
left = domain.create_region('Left', 'vertices in x < 0.00001', 'facet')
right = domain.create_region('Right', 'vertices in x > 0.099999', 'facet')
field = Field.from_args('fu',
nm.float64,
'scalar',
omega,
approx_order=options.order)
T = FieldVariable('T', 'unknown', field, history=1)
s = FieldVariable('s', 'test', field, primary_var_name='T')
m = Material('m', diffusivity=options.diffusivity * nm.eye(3))
integral = Integral('i', order=2 * options.order)
t1 = Term.new('dw_diffusion(m.diffusivity, s, T)',
integral,
omega,
m=m,
s=s,
T=T)
t2 = Term.new('dw_volume_dot(s, dT/dt)', integral, omega, s=s, T=T)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])
# Boundary conditions.
ebc1 = EssentialBC('T1', left, {'T.0': 2.0})
ebc2 = EssentialBC('T2', right, {'T.0': -2.0})
# Initial conditions.
def get_ic(coors, ic):
x, y, z = coors.T
return 2 - 40.0 * x + options.ic_max * nm.sin(4 * nm.pi * x / 0.1)
ic_fun = Function('ic_fun', get_ic)
ic = InitialCondition('ic', omega, {'T.0': ic_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'is_linear': True}, lin_solver=ls, status=nls_status)
pb = Problem('heat', equations=eqs, nls=nls, ls=ls)
pb.set_bcs(ebcs=Conditions([ebc1, ebc2]))
pb.set_ics(Conditions([ic]))
tss = SimpleTimeSteppingSolver({
't0': 0.0,
't1': 100.0,
'n_step': 11
},
problem=pb)
tss.init_time()
if options.probe:
# Prepare probe data.
probes, labels = gen_lines(pb)
ev = pb.evaluate
order = 2 * (options.order - 1)
gfield = Field.from_args('gu',
nm.float64,
'vector',
omega,
approx_order=options.order - 1)
dvel = FieldVariable('dvel',
'parameter',
gfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('gu',
nm.float64,
'scalar',
omega,
approx_order=options.order - 1)
component = FieldVariable('component',
'parameter',
cfield,
primary_var_name='(set-to-None)')
nls_options = {'eps_a': 1e-16, 'i_max': 1}
if options.show:
plt.ion()
# Solve the problem using the time stepping solver.
suffix = tss.ts.suffix
for step, time, state in tss():
if options.probe:
# Probe the solution.
dvel_qp = ev('ev_diffusion_velocity.%d.Omega(m.diffusivity, T)' %
order,
copy_materials=False,
mode='qp')
project_by_component(dvel,
dvel_qp,
component,
order,
nls_options=nls_options)
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results(ii, T, dvel, probe, labels[ii])
all_results.append(results)
plt.tight_layout()
fig.savefig('time_poisson_interactive_probe_%s.png' %
(suffix % step),
bbox_inches='tight')
if options.show:
plt.draw()
for ii, results in enumerate(all_results):
output('probe %d (%s):' % (ii, probes[ii].name))
output.level += 2
for key, res in ordered_iteritems(results):
output(key + ':')
val = res[1]
output(' min: %+.2e, mean: %+.2e, max: %+.2e' %
(val.min(), val.mean(), val.max()))
output.level -= 2
def create_local_problem(omega_gi, order):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)' %
(min_x + eps_x),
'facet',
allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)' %
(max_x - eps_x),
'facet',
allow_empty=True)
field_i = Field.from_args('fu', nm.float64, 1, omega_i, approx_order=order)
output('number of local field DOFs:', field_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field_i)
v_i = FieldVariable('v_i', 'test', field_i, primary_var_name='u_i')
integral = Integral('i', order=2 * order)
mat = Material('m', lam=10, mu=5)
t1 = Term.new('dw_laplace(m.lam, v_i, u_i)',
integral,
omega_i,
m=mat,
v_i=v_i,
u_i=u_i)
def _get_load(coors):
val = nm.ones_like(coors[:, 0])
for coor in coors.T:
val *= nm.sin(4 * nm.pi * coor)
return val
def get_load(ts, coors, mode=None, **kwargs):
if mode == 'qp':
return {'val': _get_load(coors).reshape(coors.shape[0], 1, 1)}
load = Material('load', function=Function('get_load', get_load))
t2 = Term.new('dw_volume_lvf(load.val, v_i)',
integral,
omega_i,
load=load,
v_i=v_i)
eq = Equation('balance', t1 - 100 * t2)
eqs = Equations([eq])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all': 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.all': 0.1})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2]))
pb.update_materials()
return pb
def main(cli_args):
dims = parse_argument_list(cli_args.dims, float)
shape = parse_argument_list(cli_args.shape, int)
centre = parse_argument_list(cli_args.centre, float)
material_parameters = parse_argument_list(cli_args.material_parameters,
float)
order = cli_args.order
ts_vals = cli_args.ts.split(',')
ts = {
't0': float(ts_vals[0]),
't1': float(ts_vals[1]),
'n_step': int(ts_vals[2])
}
do_plot = cli_args.plot
### Mesh and regions ###
mesh = gen_block_mesh(dims, shape, centre, name='block', verbose=False)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
lbn, rtf = domain.get_mesh_bounding_box()
box_regions = define_box_regions(3, lbn, rtf)
regions = dict(
[[r, domain.create_region(r, box_regions[r][0], box_regions[r][1])]
for r in box_regions])
### Fields ###
scalar_field = Field.from_args('fu',
np.float64,
'scalar',
omega,
approx_order=order - 1)
vector_field = Field.from_args('fv',
np.float64,
'vector',
omega,
approx_order=order)
u = FieldVariable('u', 'unknown', vector_field, history=1)
v = FieldVariable('v', 'test', vector_field, primary_var_name='u')
p = FieldVariable('p', 'unknown', scalar_field, history=1)
q = FieldVariable('q', 'test', scalar_field, primary_var_name='p')
### Material ###
c10, c01 = material_parameters
m = Material(
'm',
mu=2 * c10,
kappa=2 * c01,
)
### Boundary conditions ###
x_sym = EssentialBC('x_sym', regions['Left'], {'u.0': 0.0})
y_sym = EssentialBC('y_sym', regions['Near'], {'u.1': 0.0})
z_sym = EssentialBC('z_sym', regions['Bottom'], {'u.2': 0.0})
disp_fun = Function('disp_fun', get_displacement)
displacement = EssentialBC('displacement', regions['Right'],
{'u.0': disp_fun})
ebcs = Conditions([x_sym, y_sym, z_sym, displacement])
### Terms and equations ###
integral = Integral('i', order=2 * order)
term_neohook = Term.new('dw_tl_he_neohook(m.mu, v, u)',
integral,
omega,
m=m,
v=v,
u=u)
term_mooney = Term.new('dw_tl_he_mooney_rivlin(m.kappa, v, u)',
integral,
omega,
m=m,
v=v,
u=u)
term_pressure = Term.new('dw_tl_bulk_pressure(v, u, p)',
integral,
omega,
v=v,
u=u,
p=p)
term_volume_change = Term.new('dw_tl_volume(q, u)',
integral,
omega,
q=q,
u=u,
term_mode='volume')
term_volume = Term.new('dw_volume_integrate(q)', integral, omega, q=q)
eq_balance = Equation('balance',
term_neohook + term_mooney + term_pressure)
eq_volume = Equation('volume', term_volume_change - term_volume)
equations = Equations([eq_balance, eq_volume])
### Solvers ###
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'i_max': 5}, lin_solver=ls, status=nls_status)
### Problem ###
pb = Problem('hyper', equations=equations)
pb.set_bcs(ebcs=ebcs)
pb.set_ics(ics=Conditions([]))
tss = SimpleTimeSteppingSolver(ts, nls=nls, context=pb)
pb.set_solver(tss)
### Solution ###
axial_stress = []
axial_displacement = []
def stress_strain_fun(*args, **kwargs):
return stress_strain(*args,
order=order,
global_stress=axial_stress,
global_displacement=axial_displacement,
**kwargs)
pb.solve(save_results=True, post_process_hook=stress_strain_fun)
if do_plot:
plot_graphs(material_parameters,
axial_stress,
axial_displacement,
undeformed_length=dims[0])
def find_level_interface(domain, refine_flag):
"""
Find facets of the coarse mesh that are on the coarse-refined cell
boundary.
ids w.r.t. current mesh:
- facets: global, local w.r.t. cells[:, 0], local w.r.t. cells[:, 1]
- interface cells:
- cells[:, 0] - cells to refine
- cells[:, 1] - their facet sharing neighbors (w.r.t. both meshes)
- cells[:, 2] - facet kind: 0 = face, 1 = edge
"""
if not refine_flag.any():
facets = nm.zeros((0, 3), dtype=nm.uint32)
cells = nm.zeros((0, 3), dtype=nm.uint32)
return facets, cells, 0, None, None
def _get_refine(coors, domain=None):
return nm.nonzero(refine_flag)[0]
def _get_coarse(coors, domain=None):
return nm.nonzero(1 - refine_flag)[0]
get_refine = Function('get_refine', _get_refine)
get_coarse = Function('get_coarse', _get_coarse)
functions = Functions([get_refine, get_coarse])
region0 = domain.create_region('coarse',
'cells by get_coarse',
functions=functions,
add_to_regions=False,
allow_empty=True)
region1 = domain.create_region('refine',
'cells by get_refine',
functions=functions,
add_to_regions=False)
cmesh = domain.mesh.cmesh
dim = cmesh.dim
if dim == 2:
oe = 0
facets = nm.intersect1d(region0.facets, region1.facets)
cmesh.setup_connectivity(dim - 1, dim)
cells, offs = cmesh.get_incident(dim,
facets,
dim - 1,
ret_offsets=True)
assert_((nm.diff(offs) == 2).all())
ii = cmesh.get_local_ids(facets, dim - 1, cells, offs, dim)
ii = ii.reshape((-1, 2))
cells = cells.reshape((-1, 2))
ii = nm.where(refine_flag[cells], ii[:, :1], ii[:, 1:])
cells = nm.where(refine_flag[cells], cells[:, :1], cells[:, 1:])
facets = nm.c_[facets, ii]
cells = nm.c_[cells, nm.zeros_like(cells[:, 1])]
else: # if dim == 3:
gel = domain.geom_els['3_8']
epf = gel.get_edges_per_face()
cmesh.setup_connectivity(dim, dim)
fc, coffs = cmesh.get_incident(dim,
region1.cells,
dim,
ret_offsets=True)
cc = nm.repeat(region1.cells, nm.diff(coffs))
aux = nm.c_[cc, fc]
"""
nnn[:, 0] cells to refine, nnn[:, 1] non-refined neighbours, nnn[:, 2]
neighbour kind : 0 face, 1 edge.
"""
nn = aux[refine_flag[fc] == 0]
cf = nn[:, 0].copy().astype(nm.uint32)
cc = nn[:, 1].copy().astype(nm.uint32)
vc, vco = cmesh.get_incident(0, cc, dim, ret_offsets=True)
vf, vfo = cmesh.get_incident(0, cf, dim, ret_offsets=True)
vc = vc.reshape((-1, 8))
vf = vf.reshape((-1, 8))
nnn = []
oe = 0
ov = nn.shape[0]
for ii in range(vc.shape[0]):
aux = set(vc[ii]).intersection(vf[ii])
nc = len(aux)
if nc == 1:
nnn.append((0, 0, 2))
ov -= 1
elif nc == 4:
nnn.append((nn[ii, 0], nn[ii, 1], 0))
oe += 1
else:
nnn.append((nn[ii, 0], nn[ii, 1], 1))
nnn = nm.array(nnn)
if nnn.shape[0] == 0:
facets = nm.zeros((0, 3), dtype=nm.uint32)
cells = nm.zeros((0, 4), dtype=nm.uint32)
return facets, cells, 0, region0, region1
# Sort by neighbour kind, skip vertex-only neighbours.
ii = nm.argsort(nnn[:, 2])
nnn = nnn[ii][:ov]
cf = cf[ii][:ov]
cc = cc[ii][:ov]
ec, eco = cmesh.get_incident(1, cc, dim, ret_offsets=True)
ef, efo = cmesh.get_incident(1, cf, dim, ret_offsets=True)
ec = ec.reshape((-1, 12))
ef = ef.reshape((-1, 12))
fc, fco = cmesh.get_incident(2, cc, dim, ret_offsets=True)
ff, ffo = cmesh.get_incident(2, cf, dim, ret_offsets=True)
fc = fc.reshape((-1, 6))
ff = ff.reshape((-1, 6))
emask = nm.zeros((domain.shape.n_el, 12), dtype=nm.bool)
ffs = []
for ii in range(oe):
facet = nm.intersect1d(fc[ii], ff[ii])[0]
i1 = nm.where(ff[ii] == facet)[0][0]
i0 = nm.where(fc[ii] == facet)[0][0]
ffs.append((facet, i1, i0))
emask[nnn[ii, 0], epf[i1]] = True
for ii in range(oe, nnn.shape[0]):
facet = nm.intersect1d(ec[ii], ef[ii])[0]
i1 = nm.where(ef[ii] == facet)[0][0]
i0 = nm.where(ec[ii] == facet)[0][0]
ffs.append((facet, i1, i0))
ffs = nm.array(ffs)
ie = nm.where(nnn[:, 2] == 1)[0]
ennn = nnn[ie]
effs = ffs[ie]
omit = ie[emask[ennn[:, 0], effs[:, 1]]]
valid = nm.ones(nnn.shape[0], dtype=nm.bool)
valid[omit] = False
cells = nnn[valid]
facets = ffs[valid]
return facets, cells, oe, region0, region1
def set_bc_impl(ts, coors, bc=None, problem=None, **kwargs):
x = coors[:, 0]
y = coors[:, 1]
val = np.sin(x / np.pi) * np.sin(y / np.pi)
# val = 0*x
# val = 0.0001*np.ones(x.size)
return val
# fix_u = EssentialBC('fix_u', omega, {'u.all' : 0.0})
# bc1 = EssentialBC('Gamma_Left', gammaL, {'t.0' : -20.0})
# bc2 = EssentialBC('Gamma_Right', gammaR, {'t.0' : 20.0})
set_bc_fun = Function('set_bc_impl', set_bc_impl)
bc1 = EssentialBC('Gamma_Left', gammaL, {'t.0': set_bc_fun})
bc2 = EssentialBC('Gamma_Right', gammaR, {'t.0': set_bc_fun})
bc3 = EssentialBC('Gamma_Top', gammaT, {'t.0': set_bc_fun})
bc4 = EssentialBC('Gamma_Bottom', gammaB, {'t.0': set_bc_fun})
ls = ScipyDirect({})
nls_status = IndexedStruct()
newtonConfig = {'i_max': 10, 'eps_a': 1e-10, 'eps_r': 1}
nls = Newton(newtonConfig, lin_solver=ls, status=nls_status)
pb = Problem('Poisson', equations=eqs, nls=nls, ls=ls)
pb.save_regions_as_groups('regions')
def create_local_problem(omega_gi, orders):
"""
Local problem definition using a domain corresponding to the global region
`omega_gi`.
"""
order_u, order_p = orders
mesh = omega_gi.domain.mesh
# All tasks have the whole mesh.
bbox = mesh.get_bounding_box()
min_x, max_x = bbox[:, 0]
eps_x = 1e-8 * (max_x - min_x)
min_y, max_y = bbox[:, 1]
eps_y = 1e-8 * (max_y - min_y)
mesh_i = Mesh.from_region(omega_gi, mesh, localize=True)
domain_i = FEDomain('domain_i', mesh_i)
omega_i = domain_i.create_region('Omega', 'all')
gamma1_i = domain_i.create_region('Gamma1',
'vertices in (x < %.10f)'
% (min_x + eps_x),
'facet', allow_empty=True)
gamma2_i = domain_i.create_region('Gamma2',
'vertices in (x > %.10f)'
% (max_x - eps_x),
'facet', allow_empty=True)
gamma3_i = domain_i.create_region('Gamma3',
'vertices in (y < %.10f)'
% (min_y + eps_y),
'facet', allow_empty=True)
field1_i = Field.from_args('fu', nm.float64, mesh.dim, omega_i,
approx_order=order_u)
field2_i = Field.from_args('fp', nm.float64, 1, omega_i,
approx_order=order_p)
output('field 1: number of local DOFs:', field1_i.n_nod)
output('field 2: number of local DOFs:', field2_i.n_nod)
u_i = FieldVariable('u_i', 'unknown', field1_i, order=0)
v_i = FieldVariable('v_i', 'test', field1_i, primary_var_name='u_i')
p_i = FieldVariable('p_i', 'unknown', field2_i, order=1)
q_i = FieldVariable('q_i', 'test', field2_i, primary_var_name='p_i')
if mesh.dim == 2:
alpha = 1e2 * nm.array([[0.132], [0.132], [0.092]])
else:
alpha = 1e2 * nm.array([[0.132], [0.132], [0.132],
[0.092], [0.092], [0.092]])
mat = Material('m', D=stiffness_from_lame(mesh.dim, lam=10, mu=5),
k=1, alpha=alpha)
integral = Integral('i', order=2*(max(order_u, order_p)))
t11 = Term.new('dw_lin_elastic(m.D, v_i, u_i)',
integral, omega_i, m=mat, v_i=v_i, u_i=u_i)
t12 = Term.new('dw_biot(m.alpha, v_i, p_i)',
integral, omega_i, m=mat, v_i=v_i, p_i=p_i)
t21 = Term.new('dw_biot(m.alpha, u_i, q_i)',
integral, omega_i, m=mat, u_i=u_i, q_i=q_i)
t22 = Term.new('dw_laplace(m.k, q_i, p_i)',
integral, omega_i, m=mat, q_i=q_i, p_i=p_i)
eq1 = Equation('eq1', t11 - t12)
eq2 = Equation('eq1', t21 + t22)
eqs = Equations([eq1, eq2])
ebc1 = EssentialBC('ebc1', gamma1_i, {'u_i.all' : 0.0})
ebc2 = EssentialBC('ebc2', gamma2_i, {'u_i.0' : 0.05})
def bc_fun(ts, coors, **kwargs):
val = 0.3 * nm.sin(4 * nm.pi * (coors[:, 0] - min_x) / (max_x - min_x))
return val
fun = Function('bc_fun', bc_fun)
ebc3 = EssentialBC('ebc3', gamma3_i, {'p_i.all' : fun})
pb = Problem('problem_i', equations=eqs, active_only=False)
pb.time_update(ebcs=Conditions([ebc1, ebc2, ebc3]))
pb.update_materials()
return pb
# ------------------------------
# | Create bounrady conditions |
# ------------------------------
left_fix_u = EssentialBC('left_fix_u', left, {'u.all': 1.0})
right_fix_u = EssentialBC('right_fix_u', right, {'u.all': 0.0})
# ----------------------------
# | Create initial condition |
# ----------------------------
def ic_wrap(x, ic=None):
return ghump(x - .3)
ic_fun = Function('ic_fun', ic_wrap)
ics = InitialCondition('ic', omega, {'u.0': ic_fun})
# ------------------
# | Create problem |
# ------------------
pb = Problem(problem_name,
equations=eqs,
conf=Struct(options={"save_times": save_timestn},
ics={},
ebcs={},
epbcs={},
lcbcs={},
materials={}),
active_only=False)
pb.setup_output(output_dir=output_folder, output_format=output_format)
def test_epbcs(self):
from sfepy.discrete import Function, Functions
from sfepy.discrete.conditions import Conditions, PeriodicBC
from sfepy.discrete.common.dof_info import expand_nodes_to_equations
from sfepy.discrete.fem.periodic import match_y_line
variables = self.variables
regions = self.problem.domain.regions
match_y_line = Function('match_y_line', match_y_line)
pbc = PeriodicBC('pbc', [regions['LeftStrip'], regions['RightStrip']],
{'u.[1,0]': 'u.[0,1]'},
match='match_y_line')
functions = Functions([match_y_line])
epbcs = Conditions([pbc])
variables.equation_mapping(ebcs=None,
epbcs=epbcs,
ts=None,
functions=functions)
vec = init_vec(variables)
variables.apply_ebc(vec)
var = variables['u']
var_bcs = epbcs.group_by_variables()['u']
bc = var_bcs['pbc']
bc.canonize_dof_names(var.dofs)
nods0 = var.field.get_dofs_in_region(bc.regions[0])
nods1 = var.field.get_dofs_in_region(bc.regions[1])
coors0 = var.field.get_coor(nods0)
coors1 = var.field.get_coor(nods1)
i0, i1 = match_y_line(coors0, coors1)
eq0 = expand_nodes_to_equations(nods0[i0], bc.dofs[0], var.dofs)
eq1 = expand_nodes_to_equations(nods1[i1], bc.dofs[1], var.dofs)
ok = True
_ok = len(nm.setdiff1d(eq0, var.eq_map.master)) == 0
if not _ok:
self.report('master equations mismatch! (set(%s) == set(%s))' %
(eq0, var.eq_map.master))
ok = ok and _ok
_ok = len(nm.setdiff1d(eq1, var.eq_map.slave)) == 0
if not _ok:
self.report('slave equations mismatch! (set(%s) == set(%s))' %
(eq1, var.eq_map.slave))
ok = ok and _ok
off = variables.di.indx['u'].start
_ok = nm.allclose(vec[off + eq0], vec[off + eq1], atol=1e-14, rtol=0.0)
if not _ok:
self.report('periodicity test failed! (%s == %s)' %
(vec[off + eq0], vec[off + eq0]))
ok = ok and _ok
return ok