def make_h1_projection_data(target, eval_data):
"""
Project scalar data given by a material-like `eval_data()` function to a
scalar `target` field variable using the :math:`H^1` dot product.
"""
order = target.field.approx_order * 2
integral = Integral('i', order=order)
un = target.name
v = FieldVariable('v', 'test', target.field, primary_var_name=un)
lhs1 = Term.new('dw_volume_dot(v, %s)' % un,
integral,
target.field.region,
v=v,
**{un: target})
lhs2 = Term.new('dw_laplace(v, %s)' % un,
integral,
target.field.region,
v=v,
**{un: target})
def _eval_data(ts, coors, mode, **kwargs):
if mode == 'qp':
val = eval_data(ts, coors, mode, 'val', **kwargs)
gval = eval_data(ts, coors, mode, 'grad', **kwargs)
return {'val': val, 'gval': gval}
m = Material('m', function=_eval_data)
rhs1 = Term.new('dw_volume_lvf(m.val, v)',
integral,
target.field.region,
m=m,
v=v)
rhs2 = Term.new('dw_diffusion_r(m.gval, v)',
integral,
target.field.region,
m=m,
v=v)
eq = Equation('projection', lhs1 + lhs2 - rhs1 - rhs2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('aux', equations=eqs, nls=nls, ls=ls)
pb.time_update()
# This sets the target variable with the projection solution.
pb.solve()
if nls_status.condition != 0:
output('H1 projection: solver did not converge!')
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)
## pb.save_regions_as_groups('regions')
pb.set_bcs(ebcs=Conditions([fix_u, shift_u]))
pb.set_solver(nls)
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 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({})
pb = Problem('laplace', equations=eqs, auto_solvers=None)
pb.time_update(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))
ev = pb.get_evaluator()
nls = Newton({}, lin_solver=ls,
fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)
pb.set_solver(nls)
state = pb.solve()
return pb, state
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 make_h1_projection_data(target, eval_data):
"""
Project scalar data given by a material-like `eval_data()` function to a
scalar `target` field variable using the :math:`H^1` dot product.
"""
order = target.field.approx_order * 2
integral = Integral('i', order=order)
un = target.name
v = FieldVariable('v', 'test', target.field, primary_var_name=un)
lhs1 = Term.new('dw_volume_dot(v, %s)' % un, integral,
target.field.region, v=v, **{un : target})
lhs2 = Term.new('dw_laplace(v, %s)' % un, integral,
target.field.region, v=v, **{un : target})
def _eval_data(ts, coors, mode, **kwargs):
if mode == 'qp':
val = eval_data(ts, coors, mode, 'val', **kwargs)
gval = eval_data(ts, coors, mode, 'grad', **kwargs)
return {'val' : val, 'gval' : gval}
m = Material('m', function=_eval_data)
rhs1 = Term.new('dw_volume_lvf(m.val, v)', integral, target.field.region,
m=m, v=v)
rhs2 = Term.new('dw_diffusion_r(m.gval, v)', integral, target.field.region,
m=m, v=v)
eq = Equation('projection', lhs1 + lhs2 - rhs1 - rhs2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('aux', equations=eqs, nls=nls, ls=ls)
pb.time_update()
# This sets the target variable with the projection solution.
pb.solve()
if nls_status.condition != 0:
output('H1 projection: solver did not converge!')
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 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 = Domain("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", 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_iso(m.lam, m.mu, 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 solve_problem(shape, dims, young, poisson, force, transform=None):
domain = make_domain(dims[:2], shape, transform=transform)
omega = domain.regions['Omega']
gamma1 = domain.regions['Gamma1']
gamma2 = domain.regions['Gamma2']
field = Field.from_args('fu', nm.float64, 6, omega, approx_order=1,
poly_space_base='shell10x')
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
thickness = dims[2]
if transform is None:
pload = [[0.0, 0.0, force / shape[1], 0.0, 0.0, 0.0]] * shape[1]
elif transform == 'bend':
pload = [[force / shape[1], 0.0, 0.0, 0.0, 0.0, 0.0]] * shape[1]
elif transform == 'twist':
pload = [[0.0, force / shape[1], 0.0, 0.0, 0.0, 0.0]] * shape[1]
m = Material('m', D=sh.create_elastic_tensor(young=young, poisson=poisson),
values={'.drill' : 1e-7})
load = Material('load', values={'.val' : pload})
aux = Integral('i', order=3)
qp_coors, qp_weights = aux.get_qp('3_8')
qp_coors[:, 2] = thickness * (qp_coors[:, 2] - 0.5)
qp_weights *= thickness
integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom')
t1 = Term.new('dw_shell10x(m.D, m.drill, v, u)',
integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_point_load(load.val, v)',
integral, gamma2, load=load, v=v)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity with shell10x', equations=eqs)
pb.set_bcs(ebcs=Conditions([fix_u]))
pb.set_solver(nls)
state = pb.solve()
return pb, state, u, gamma2
def solve_problem(shape, dims, young, poisson, force, transform=None):
domain = make_domain(dims[:2], shape, transform=transform)
omega = domain.regions['Omega']
gamma1 = domain.regions['Gamma1']
gamma2 = domain.regions['Gamma2']
field = Field.from_args('fu', nm.float64, 6, omega, approx_order=1,
poly_space_base='shell10x')
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
thickness = dims[2]
if transform is None:
pload = [[0.0, 0.0, force / shape[1], 0.0, 0.0, 0.0]] * shape[1]
elif transform == 'bend':
pload = [[force / shape[1], 0.0, 0.0, 0.0, 0.0, 0.0]] * shape[1]
elif transform == 'twist':
pload = [[0.0, force / shape[1], 0.0, 0.0, 0.0, 0.0]] * shape[1]
m = Material('m', D=sh.create_elastic_tensor(young=young, poisson=poisson),
values={'.drill' : 1e-7})
load = Material('load', values={'.val' : pload})
aux = Integral('i', order=3)
qp_coors, qp_weights = aux.get_qp('3_8')
qp_coors[:, 2] = thickness * (qp_coors[:, 2] - 0.5)
qp_weights *= thickness
integral = Integral('i', coors=qp_coors, weights=qp_weights, order='custom')
t1 = Term.new('dw_shell10x(m.D, m.drill, v, u)',
integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_point_load(load.val, v)',
integral, gamma2, load=load, v=v)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity with shell10x', equations=eqs, nls=nls, ls=ls)
pb.time_update(ebcs=Conditions([fix_u]))
state = pb.solve()
return pb, state, u, gamma2
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({})
pb = Problem("laplace", equations=eqs, auto_solvers=None)
pb.time_update(ebcs=Conditions([fix1, fix2]), lcbcs=Conditions([sper]))
ev = pb.get_evaluator()
nls = Newton({}, lin_solver=ls, fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)
pb.set_solver(nls)
state = pb.solve()
return pb, state
def linear_projection(pb, cval):
from sfepy.discrete import (FieldVariable, Material, Integral, Equation,
Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.base.base import IndexedStruct
mesh = Mesh.from_file(pb.conf.filename_mesh)
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('scf', nm.float64, 'scalar', omega, approx_order=1)
g = FieldVariable('g', 'unknown', field)
f = FieldVariable('f', 'test', field, primary_var_name='g')
integral = Integral('i', order=2)
m = Material('m', function=set_grad)
t1 = Term.new('dw_volume_dot(f, g)', integral, omega, f=f, g=g)
t2 = Term.new('dw_volume_lvf(m.cs, f)', integral, omega, m=m, f=f)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'eps_a': 1e-15}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs)
pb.set_solver(nls)
out = nm.empty((g.n_dof, cval.shape[2]), dtype=nm.float64)
for ii in range(cval.shape[2]):
pb.data = nm.ascontiguousarray(cval[:, :, ii, :])
pb.time_update()
state = pb.solve()
out[:, ii] = state.get_parts()['g']
return out
# ------------------
# | 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}")
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('--young', metavar='float', type=float,
action='store', dest='young',
default=2000.0, help=helps['young'])
parser.add_option('--poisson', metavar='float', type=float,
action='store', dest='poisson',
default=0.4, help=helps['poisson'])
parser.add_option('--load', metavar='float', type=float,
action='store', dest='load',
default=-1000.0, help=helps['load'])
parser.add_option('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_option('-r', '--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_option('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
parser.add_option('-p', '--probe',
action="store_true", dest='probe',
default=False, help=helps['probe'])
options, args = parser.parse_args()
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' vertical load:', options.load)
output('uniform mesh refinement level:', options.refine)
# Build the problem definition.
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.mesh')
domain = FEDomain('domain', mesh)
if options.refine > 0:
for ii in range(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 < 0.001', 'facet')
bottom = domain.create_region('Bottom',
'vertices in y < 0.001', 'facet')
top = domain.create_region('Top', 'vertex 2', 'vertex')
field = Field.from_args('fu', nm.float64, 'vector', omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
D = stiffness_from_youngpoisson(2, options.young, options.poisson)
asphalt = Material('Asphalt', D=D)
load = Material('Load', values={'.val' : [0.0, options.load]})
integral = Integral('i', order=2*options.order)
integral0 = Integral('i', order=0)
t1 = Term.new('dw_lin_elastic(Asphalt.D, v, u)',
integral, omega, Asphalt=asphalt, v=v, u=u)
t2 = Term.new('dw_point_load(Load.val, v)',
integral0, top, Load=load, v=v)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
xsym = EssentialBC('XSym', bottom, {'u.1' : 0.0})
ysym = EssentialBC('YSym', left, {'u.0' : 0.0})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.time_update(ebcs=Conditions([xsym, ysym]))
# Solve the problem.
state = pb.solve()
output(nls_status)
# Postprocess the solution.
out = state.create_output_dict()
out = stress_strain(out, pb, state, extend=True)
pb.save_state('its2D_interactive.vtk', out=out)
gdata = geometry_data['2_3']
nc = len(gdata.coors)
integral_vn = Integral('ivn', coors=gdata.coors,
weights=[gdata.volume / nc] * nc)
nodal_stress(out, pb, state, integrals=Integrals([integral_vn]))
if options.probe:
# Probe the solution.
probes, labels = gen_lines(pb)
sfield = Field.from_args('sym_tensor', nm.float64, 3, omega,
approx_order=options.order - 1)
stress = FieldVariable('stress', 'parameter', sfield,
primary_var_name='(set-to-None)')
strain = FieldVariable('strain', 'parameter', sfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('component', nm.float64, 1, omega,
approx_order=options.order - 1)
component = FieldVariable('component', 'parameter', cfield,
primary_var_name='(set-to-None)')
ev = pb.evaluate
order = 2 * (options.order - 1)
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Asphalt.D, u)' % order,
mode='qp', copy_materials=False)
project_by_component(strain, strain_qp, component, order)
project_by_component(stress, stress_qp, component, order)
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results(u, strain, stress, probe, labels[ii])
fig.savefig('its2D_interactive_probe_%d.png' % ii)
all_results.append(results)
for ii, results in enumerate(all_results):
output('probe %d:' % ii)
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
if options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
view = Viewer('its2D_interactive.vtk')
view(vector_mode='warp_norm', rel_scaling=1,
is_scalar_bar=True, is_wireframe=True)
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 make_l2_projection_data(target,
eval_data,
order=None,
ls=None,
nls_options=None):
"""
Project scalar data to a scalar `target` field variable using the
:math:`L^2` dot product.
Parameters
----------
target : FieldVariable instance
The target variable.
eval_data : callable or array
Either a material-like function `eval_data()`, or an array of values in
quadrature points that has to be reshapable to the shape required by
`order`.
order : int, optional
The quadrature order. If not given, it is set to
`2 * target.field.approx_order`.
"""
if order is None:
order = 2 * target.field.approx_order
integral = Integral('i', order=order)
un = FieldVariable('u', 'unknown', target.field)
v = FieldVariable('v', 'test', un.field, primary_var_name=un.name)
lhs = Term.new('dw_volume_dot(v, %s)' % un.name,
integral,
un.field.region,
v=v,
**{un.name: un})
def _eval_data(ts, coors, mode, **kwargs):
if mode == 'qp':
if callable(eval_data):
val = eval_data(ts, coors, mode, **kwargs)
else:
val = eval_data.reshape((coors.shape[0], 1, 1))
return {'val': val}
m = Material('m', function=_eval_data)
rhs = Term.new('dw_volume_lvf(m.val, v)',
integral,
un.field.region,
m=m,
v=v)
eq = Equation('projection', lhs - rhs)
eqs = Equations([eq])
if ls is None:
ls = ScipyDirect({})
if nls_options is None:
nls_options = {}
nls_status = IndexedStruct()
nls = Newton(nls_options, lin_solver=ls, status=nls_status)
pb = Problem('aux', equations=eqs, nls=nls, ls=ls)
pb.time_update()
# This sets the un variable with the projection solution.
pb.solve()
# Copy the projection solution to target.
target.set_data(un())
if nls_status.condition != 0:
output('L2 projection: solver did not converge!')
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()
options_probe = True
folder = str(uuid.uuid4())
os.mkdir(folder)
os.chdir(folder)
file = open('README.txt', 'w')
file.write('DIMENSIONS\n')
file.write('Lx = '+str(dims[0])+' Ly = '+str(dims[1])+' Lz = '+str(dims[2])+'\n')
file.write('DISCRETIZATION (NX, NY, NZ)\n')
file.write(str(NX)+' '+str(NY)+' '+str(NZ)+'\n')
file.write('MATERIALS\n')
file.write(str(E_f)+' '+str(nu_f)+' '+str(E_m)+' '+str(nu_m)+'\n')
#mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
mesh = mesh_generators.gen_block_mesh(dims,shape,centre,name='block')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
min_y, max_y = domain.get_mesh_bounding_box()[:,1]
min_z, max_z = domain.get_mesh_bounding_box()[:,2]
eps = 1e-8 * (max_x - min_x)
print min_x, max_x
print min_y, max_y
print min_z, max_z
R1 = domain.create_region('Ym',
'vertices in z < %.10f' % (max_z/2))
R2 = domain.create_region('Yf',
'vertices in z >= %.10f' % (min_z/2))
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Left',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Right',
'vertices in x > %.10f' % (max_x - eps),
'facet')
gamma3 = domain.create_region('Front',
'vertices in y < %.10f' % (min_y + eps),
'facet')
gamma4 = domain.create_region('Back',
'vertices in y > %.10f' % (max_y - eps),
'facet')
gamma5 = domain.create_region('Bottom',
'vertices in z < %.10f' % (min_z + eps),
'facet')
gamma6 = domain.create_region('Top',
'vertices in z > %.10f' % (max_z - 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')
mu=1.1
lam=1.0
m = Material('m', lam=lam, mu=mu)
f = Material('f', val=[[0.0], [0.0],[-1.0]])
load = Material('Load',val=[[0.0],[0.0],[-Load]])
D = stiffness_from_lame(3,lam, mu)
mat = Material('Mat', D=D)
get_mat = Function('get_mat1',get_mat1)
get_mat_f = Function('get_mat_f',get_mat1)
integral = Integral('i', order=3)
s_integral = Integral('is',order=2)
t1 = Term.new('dw_lin_elastic(Mat.D, v, u)',
integral, omega, Mat=mat, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
#t3 = Term.new('DotProductSurfaceTerm(Load.val, v)',s_integral,gamma5,Load=load,v=v)
t3 = Term.new('dw_surface_ltr( Load.val, v )',s_integral,gamma6,Load=load,v=v)
eq = Equation('balance', t1 + t2 + t3)
eqs = Equations([eq])
fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})
left_bc = EssentialBC('Left', gamma1, {'u.0' : 0.0})
right_bc = EssentialBC('Right', gamma2, {'u.0' : 0.0})
back_bc = EssentialBC('Front', gamma3, {'u.1' : 0.0})
front_bc = EssentialBC('Back', gamma4, {'u.1' : 0.0})
bottom_bc = EssentialBC('Bottom', gamma5, {'u.all' : 0.0})
top_bc = EssentialBC('Top', gamma6, {'u.2' : 0.2})
bc=[left_bc,right_bc,back_bc,front_bc,bottom_bc]
#bc=[bottom_bc,top_bc]
##############################
# ##### SOLVER SECTION #####
##############################
conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
i_max=10000, eps_a=1e-50, eps_r=1e-10, eps_d=1e4,
verbose=True)
ls = PETScKrylovSolver(conf)
file.write(str(ls.name)+' '+str(ls.conf.method)+' '+str(ls.conf.precond)+' '+str(ls.conf.eps_r)+' '+str(ls.conf.i_max)+'\n' )
nls_status = IndexedStruct()
nls = Newton({'i_max':1,'eps_a':1e-10}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
dd=pb.get_materials()['Mat']
dd.set_function(get_mat1)
#xload = pb.get_materials()['f']
#xload.set_function(get_mat_f)
pb.save_regions_as_groups('regions')
pb.time_update(ebcs=Conditions(bc))
vec = pb.solve()
print nls_status
file.write('TIME TO SOLVE\n')
file.write(str(nls.status.time_stats['solve'])+'\n')
file.write('TIME TO CREATE MATRIX\n')
file.write(str(nls.status.time_stats['matrix'])+'\n')
ev = pb.evaluate
out = vec.create_output_dict()
strain = ev('ev_cauchy_strain.3.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.3.Omega(Mat.D, u)', mode='el_avg',
copy_materials=False)
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
pb.save_state('strain.vtk', out=out)
print nls_status
file.close()
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()
options_probe = True
folder = str(uuid.uuid4())
os.mkdir(folder)
os.chdir(folder)
file = open('README.txt', 'w')
file.write('DIMENSIONS\n')
file.write('Lx = '+str(dims[0])+' Ly = '+str(dims[1])+' Lz = '+str(dims[2])+'\n')
file.write('DISCRETIZATION (NX, NY, NZ)\n')
file.write(str(NX)+' '+str(NY)+' '+str(NZ)+'\n')
file.write('MATERIALS\n')
file.write(str(E_f)+' '+str(nu_f)+' '+str(E_m)+' '+str(nu_m)+'\n')
#mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
mesh = mesh_generators.gen_block_mesh(dims,shape,centre,name='block')
domain = FEDomain('domain', mesh)
min_x, max_x = domain.get_mesh_bounding_box()[:,0]
min_y, max_y = domain.get_mesh_bounding_box()[:,1]
min_z, max_z = domain.get_mesh_bounding_box()[:,2]
eps = 1e-8 * (max_x - min_x)
print min_x, max_x
print min_y, max_y
print min_z, max_z
R1 = domain.create_region('Ym',
'vertices in z < %.10f' % (max_z/2))
R2 = domain.create_region('Yf',
'vertices in z >= %.10f' % (min_z/2))
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Left',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Right',
'vertices in x > %.10f' % (max_x - eps),
'facet')
gamma3 = domain.create_region('Front',
'vertices in y < %.10f' % (min_y + eps),
'facet')
gamma4 = domain.create_region('Back',
'vertices in y > %.10f' % (max_y - eps),
'facet')
gamma5 = domain.create_region('Bottom',
'vertices in z < %.10f' % (min_z + eps),
'facet')
gamma6 = domain.create_region('Top',
'vertices in z > %.10f' % (max_z - 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')
mu=1.1
lam=1.0
m = Material('m', lam=lam, mu=mu)
f = Material('f', val=[[0.0], [0.0],[0.0]])
#mu,lam=m.get_constants_mu_lam()
#print mu.lam
D = stiffness_from_lame(3,lam, mu)
mat = Material('Mat', D=D)
#D = stiffness_from_youngpoisson(2, options.young, options.poisson)
get_mat = Function('get_mat1',get_mat1)
#get_mat1=Function('get_mat', (lambda ts, coors, mode=None, problem=None, **kwargs:
# get_mat(coors, mode, problem)))
#mat = Material('Mat', function=Function('get_mat1',get_mat1))
#mat = Material('Mat', 'get_mat')
integral = Integral('i', order=3)
t1 = Term.new('dw_lin_elastic(Mat.D, v, u)',
integral, omega, Mat=mat, 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})
left_bc = EssentialBC('Left', gamma1, {'u.0' : 0.0})
right_bc = EssentialBC('Right', gamma2, {'u.0' : 0.0})
back_bc = EssentialBC('Front', gamma3, {'u.1' : 0.0})
front_bc = EssentialBC('Back', gamma4, {'u.1' : 0.0})
bottom_bc = EssentialBC('Bottom', gamma5, {'u.all' : 0.0})
top_bc = EssentialBC('Top', gamma6, {'u.2' : 0.2})
bc=[left_bc,right_bc,back_bc,front_bc,bottom_bc,top_bc]
#bc=[bottom_bc,top_bc]
bc_fun = Function('shift_u_fun', shift_u_fun, extra_args={'shift' : 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0' : bc_fun})
#get_mat = Function('get_mat1',get_mat1)
#mat = Material('Mat', function=Function('get_mat1',get_mat1))
#ls = ScipyDirect({'method':'umfpack'})
##############################
# ##### SOLVER SECTION #####
##############################
# GET MATRIX FOR PRECONTITIONER #
#ls = ScipyIterative({'method':'bicgstab','i_max':5000,'eps_r':1e-10})
#ls = ScipyIterative({})
#ls = PyAMGSolver({'i_max':5000,'eps_r':1e-10})
#conf = Struct(method='cg', precond='gamg', sub_precond=None,i_max=10000, eps_a=1e-50, eps_r=1e-5, eps_d=1e4, verbose=True)
#ls = PETScKrylovSolver({'method' : 'cg', 'precond' : 'icc', 'eps_r' : 1e-10, 'i_max' : 5000})
conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
i_max=10000, eps_a=1e-50, eps_r=1e-10, eps_d=1e4,
verbose=True)
#conf = Struct(method = 'cg', precond = 'icc', eps_r = 1e-10, i_max = 5000)
ls = PETScKrylovSolver(conf)
#if hasattr(ls.name,'ls.scipy_iterative'):
file.write(str(ls.name)+' '+str(ls.conf.method)+' '+str(ls.conf.precond)+' '+str(ls.conf.eps_r)+' '+str(ls.conf.i_max)+'\n' )
# else:
#file.write(str(ls.name)+' '+str(ls.conf.method)+'\n')
# conf = Struct(method='bcgsl', precond='jacobi', sub_precond=None,
# i_max=10000, eps_a=1e-50, eps_r=1e-8, eps_d=1e4,
# verbose=True)
#ls = PETScKrylovSolver(conf)
#ls = ScipyIterative({'method':'bicgstab','i_max':100,'eps_r':1e-10})
nls_status = IndexedStruct()
nls = Newton({'i_max':1,'eps_a':1e-10}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
dd=pb.get_materials()['Mat']
dd.set_function(get_mat1)
pb.save_regions_as_groups('regions')
#pb.time_update(ebcs=Conditions([fix_u, shift_u]))
pb.time_update(ebcs=Conditions(bc))
pb.save_regions_as_groups('regions')
#ls = ScipyIterative({'method':'bicgstab','i_max':100,'eps_r':1e-10})
# A = pb.mtx_a
# M = spilu(A,fill_factor = 1)
#conf = Struct(solvers ='ScipyIterative',method='bcgsl', sub_precond=None,
# i_max=1000, eps_r=1e-8)
#pb.set_conf_solvers(conf)
vec = pb.solve()
print nls_status
file.write('TIME TO SOLVE\n')
file.write(str(nls.status.time_stats['solve'])+'\n')
file.write('TIME TO CREATE MATRIX\n')
file.write(str(nls.status.time_stats['matrix'])+'\n')
#out = post_process(out, pb, state, extend=False)
ev = pb.evaluate
out = vec.create_output_dict()
strain = ev('ev_cauchy_strain.3.Omega(u)', mode='el_avg')
stress = ev('ev_cauchy_stress.3.Omega(Mat.D, u)', mode='el_avg',
copy_materials=False)
out['cauchy_strain'] = Struct(name='output_data', mode='cell',
data=strain, dofs=None)
out['cauchy_stress'] = Struct(name='output_data', mode='cell',
data=stress, dofs=None)
# Postprocess the solution.
#out = vec.create_output_dict()
#out = stress_strain(out, pb, vec,lam,mu, extend=True)
#pb.save_state('its2D_interactive.vtk', out=out)
#print 'aqui estoy'
pb.save_state('strain.vtk', out=out)
#pb.save_state('disp.vtk', out=vec)
#print 'ahora estoy aqui'
#out = stress_strain(out, pb, vec, extend=True)
#pb.save_state('out.vtk', out=out)
print nls_status
order = 3
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Mat.D, u)' % order,
mode='qp', copy_materials=False)
file.close()
options_probe=False
if options_probe:
# Probe the solution.
probes, labels = gen_lines(pb)
nls_options = {'eps_a':1e-8,'i_max':1}
ls = ScipyDirect({})
ls2 = ScipyIterative({'method':'bicgstab','i_max':5000,'eps_r':1e-20})
order = 5
sfield = Field.from_args('sym_tensor', nm.float64, (3,), omega,
approx_order=order-1)
stress = FieldVariable('stress', 'parameter', sfield,
primary_var_name='(set-to-None)')
strain = FieldVariable('strain', 'parameter', sfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('component', nm.float64, 1, omega,
approx_order=order-1)
component = FieldVariable('component', 'parameter', cfield,
primary_var_name='(set-to-None)')
ev = pb.evaluate
order = 2*(order - 1) #2 * (2- 1)
print "before strain_qp"
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Mat.D, u)' % order,
mode='qp', copy_materials=False)
print "before projections"
print stress
project_by_component(strain, strain_qp, component, order,ls2,nls_options)
#print 'strain done'
project_by_component(stress, stress_qp, component, order,ls2,nls_options)
print "after projections"
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results2(u, strain, stress, probe, labels[ii])
fig.savefig('test_probe_%d.png' % ii)
all_results.append(results)
for ii, results in enumerate(all_results):
output('probe %d:' % ii)
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 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 make_l2_projection_data(target, eval_data, order=None,
ls=None, nls_options=None):
"""
Project scalar data to a scalar `target` field variable using the
:math:`L^2` dot product.
Parameters
----------
target : FieldVariable instance
The target variable.
eval_data : callable or array
Either a material-like function `eval_data()`, or an array of values in
quadrature points that has to be reshapable to the shape required by
`order`.
order : int, optional
The quadrature order. If not given, it is set to
`2 * target.field.approx_order`.
"""
if order is None:
order = 2 * target.field.approx_order
integral = Integral('i', order=order)
un = FieldVariable('u', 'unknown', target.field)
v = FieldVariable('v', 'test', un.field, primary_var_name=un.name)
lhs = Term.new('dw_volume_dot(v, %s)' % un.name, integral,
un.field.region, v=v, **{un.name : un})
def _eval_data(ts, coors, mode, **kwargs):
if mode == 'qp':
if callable(eval_data):
val = eval_data(ts, coors, mode, **kwargs)
else:
val = eval_data.reshape((coors.shape[0], 1, 1))
return {'val' : val}
m = Material('m', function=_eval_data)
rhs = Term.new('dw_volume_lvf(m.val, v)', integral, un.field.region,
m=m, v=v)
eq = Equation('projection', lhs - rhs)
eqs = Equations([eq])
if ls is None:
ls = ScipyDirect({})
if nls_options is None:
nls_options = {}
nls_status = IndexedStruct()
nls = Newton(nls_options, lin_solver=ls, status=nls_status)
pb = Problem('aux', equations=eqs, nls=nls, ls=ls)
pb.time_update()
# This sets the un variable with the projection solution.
pb.solve()
# Copy the projection solution to target.
target.set_data(un())
if nls_status.condition != 0:
output('L2 projection: solver did not converge!')
nls_status = IndexedStruct()
nls = Newton({'i_max': 20}, 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)
show = True
if show:
view = Viewer('voronoi_foam_%f.vtk' % z_displacement)
view(vector_mode='warp_norm',
rel_scaling=1,
is_scalar_bar=True,
is_wireframe=True)
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
# 'i_max': 1, 'eps_a': 1e-10
pb = Problem('elasticity', equations=eqs)
pb.save_regions_as_groups('regions')
pb.set_bcs(ebcs=Conditions([fix_bot, fix_top]))
pb.set_solver(nls)
status = IndexedStruct()
state = pb.solve(status=status)
strain = pb.evaluate('ev_cauchy_strain.2.Omega(u)', u=u, mode='el_avg')
stress = pb.evaluate('ev_cauchy_stress.2.Omega(m.D, u)',
m=m,
u=u,
mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
np.savetxt('tmp_vms.dat', vms)
vms = np.loadtxt('tmp_vms.dat')
vol = mesh.cmesh.get_volumes(3)
np.savetxt('tmp_vol.dat', vol)
vol = np.loadtxt('tmp_vol.dat')
vm_stresses[i, 0] = np.sum(vms * vol) / np.sum(vol)
def main():
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = 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 _solve(self, property_array):
"""
Solve the Sfepy problem for one sample.
Args:
property_array: array of shape (n_x, n_y, 2) where the last
index is for Lame's parameter and shear modulus,
respectively.
Returns:
the strain field of shape (n_x, n_y, 2) where the last
index represents the x and y displacements
"""
shape = property_array.shape[:-1]
mesh = self._get_mesh(shape)
domain = Domain('domain', mesh)
region_all = domain.create_region('region_all', 'all')
field = Field.from_args('fu', np.float64, 'vector', region_all, # pylint: disable=no-member
approx_order=2)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
m = self._get_material(property_array, domain)
integral = Integral('i', order=4)
t1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral, region_all, m=m, v=v, u=u)
eq = Equation('balance_of_forces', t1)
eqs = Equations([eq])
epbcs, functions = self._get_periodicBCs(domain)
ebcs = self._get_displacementBCs(domain)
lcbcs = self._get_linear_combinationBCs(domain)
ls = ScipyDirect({})
pb = Problem('elasticity', equations=eqs, auto_solvers=None)
pb.time_update(
ebcs=ebcs, epbcs=epbcs, lcbcs=lcbcs, functions=functions)
ev = pb.get_evaluator()
nls = Newton({}, lin_solver=ls,
fun=ev.eval_residual, fun_grad=ev.eval_tangent_matrix)
try:
pb.set_solvers_instances(ls, nls)
except AttributeError:
pb.set_solver(nls)
vec = pb.solve()
u = vec.create_output_dict()['u'].data
u_reshape = np.reshape(u, (tuple(x + 1 for x in shape) + u.shape[-1:]))
dims = domain.get_mesh_bounding_box().shape[1]
strain = np.squeeze(
pb.evaluate(
'ev_cauchy_strain.{dim}.region_all(u)'.format(
dim=dims),
mode='el_avg',
copy_materials=False))
strain_reshape = np.reshape(strain, (shape + strain.shape[-1:]))
stress = np.squeeze(
pb.evaluate(
'ev_cauchy_stress.{dim}.region_all(m.D, u)'.format(
dim=dims),
mode='el_avg',
copy_materials=False))
stress_reshape = np.reshape(stress, (shape + stress.shape[-1:]))
return strain_reshape, u_reshape, stress_reshape
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('-o',
'--output-dir',
default='.',
help=helps['output_dir'])
parser.add_argument('--R1',
metavar='R1',
action='store',
dest='R1',
default='0.5',
help=helps['R1'])
parser.add_argument('--R2',
metavar='R2',
action='store',
dest='R2',
default='1.0',
help=helps['R2'])
parser.add_argument('--C1',
metavar='C1',
action='store',
dest='C1',
default='0.0,0.0',
help=helps['C1'])
parser.add_argument('--C2',
metavar='C2',
action='store',
dest='C2',
default='0.0,0.0',
help=helps['C2'])
parser.add_argument('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=2,
help=helps['order'])
parser.add_argument('-v',
'--viewpatch',
action='store_true',
dest='viewpatch',
default=False,
help=helps['viewpatch'])
options = parser.parse_args()
# Creation of the NURBS-patch with igakit
R1 = eval(options.R1)
R2 = eval(options.R2)
C1 = list(eval(options.C1))
C2 = list(eval(options.C2))
order = options.order
viewpatch = options.viewpatch
create_patch(R1, R2, C1, C2, order=order, viewpatch=viewpatch)
# Setting a Domain instance
filename_domain = data_dir + '/meshes/iga/concentric_circles.iga'
domain = IGDomain.from_file(filename_domain)
# Sub-domains
omega = domain.create_region('Omega', 'all')
Gamma_out = domain.create_region('Gamma_out',
'vertices of set xi01',
kind='facet')
Gamma_in = domain.create_region('Gamma_in',
'vertices of set xi00',
kind='facet')
# Field (featuring order elevation)
order_increase = order - domain.nurbs.degrees[0]
order_increase *= int(order_increase > 0)
field = Field.from_args('fu',
nm.float64,
'scalar',
omega,
approx_order='iga',
space='H1',
poly_space_base='iga')
# Variables
u = FieldVariable('u', 'unknown', field) # unknown function
v = FieldVariable('v', 'test', field,
primary_var_name='u') # test function
# Integral
integral = Integral('i', order=2 * field.approx_order)
# Term
t = Term.new('dw_laplace( v, u )', integral, omega, v=v, u=u)
# Equation
eq = Equation('laplace', t)
eqs = Equations([eq])
# Boundary Conditions
u_in = EssentialBC('u_in', Gamma_in, {'u.all': 7.0})
u_out = EssentialBC('u_out', Gamma_out, {'u.all': 3.0})
# solvers
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
# problem instance
pb = Problem('potential', equations=eqs, active_only=True)
# Set boundary conditions
pb.set_bcs(ebcs=Conditions([u_in, u_out]))
# solving
pb.set_solver(nls)
status = IndexedStruct()
state = pb.solve(status=status, save_results=True, verbose=True)
# Saving the results to a classic VTK file
filename = os.path.join(options.output_dir, 'concentric_circles.vtk')
ensure_path(filename)
pb.save_state(filename, state)
def main():
from sfepy import data_dir
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('--young',
metavar='float',
type=float,
action='store',
dest='young',
default=2000.0,
help=helps['young'])
parser.add_option('--poisson',
metavar='float',
type=float,
action='store',
dest='poisson',
default=0.4,
help=helps['poisson'])
parser.add_option('--load',
metavar='float',
type=float,
action='store',
dest='load',
default=-1000.0,
help=helps['load'])
parser.add_option('--order',
metavar='int',
type=int,
action='store',
dest='order',
default=1,
help=helps['order'])
parser.add_option('-r',
'--refine',
metavar='int',
type=int,
action='store',
dest='refine',
default=0,
help=helps['refine'])
parser.add_option('-s',
'--show',
action="store_true",
dest='show',
default=False,
help=helps['show'])
parser.add_option('-p',
'--probe',
action="store_true",
dest='probe',
default=False,
help=helps['probe'])
options, args = parser.parse_args()
assert_((0.0 < options.poisson < 0.5),
"Poisson's ratio must be in ]0, 0.5[!")
assert_((0 < options.order),
'displacement approximation order must be at least 1!')
output('using values:')
output(" Young's modulus:", options.young)
output(" Poisson's ratio:", options.poisson)
output(' vertical load:', options.load)
output('uniform mesh refinement level:', options.refine)
# Build the problem definition.
mesh = Mesh.from_file(data_dir + '/meshes/2d/its2D.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 < 0.001', 'facet')
bottom = domain.create_region('Bottom', 'vertices in y < 0.001', 'facet')
top = domain.create_region('Top', 'vertex 2', 'vertex')
field = Field.from_args('fu',
nm.float64,
'vector',
omega,
approx_order=options.order)
u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')
D = stiffness_from_youngpoisson(2, options.young, options.poisson)
asphalt = Material('Asphalt', D=D)
load = Material('Load', values={'.val': [0.0, options.load]})
integral = Integral('i', order=2 * options.order)
integral0 = Integral('i', order=0)
t1 = Term.new('dw_lin_elastic(Asphalt.D, v, u)',
integral,
omega,
Asphalt=asphalt,
v=v,
u=u)
t2 = Term.new('dw_point_load(Load.val, v)', integral0, top, Load=load, v=v)
eq = Equation('balance', t1 - t2)
eqs = Equations([eq])
xsym = EssentialBC('XSym', bottom, {'u.1': 0.0})
ysym = EssentialBC('YSym', left, {'u.0': 0.0})
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)
pb = Problem('elasticity', equations=eqs, nls=nls, ls=ls)
pb.time_update(ebcs=Conditions([xsym, ysym]))
# Solve the problem.
state = pb.solve()
output(nls_status)
# Postprocess the solution.
out = state.create_output_dict()
out = stress_strain(out, pb, state, extend=True)
pb.save_state('its2D_interactive.vtk', out=out)
gdata = geometry_data['2_3']
nc = len(gdata.coors)
integral_vn = Integral('ivn',
coors=gdata.coors,
weights=[gdata.volume / nc] * nc)
nodal_stress(out, pb, state, integrals=Integrals([integral_vn]))
if options.probe:
# Probe the solution.
probes, labels = gen_lines(pb)
sfield = Field.from_args('sym_tensor',
nm.float64,
3,
omega,
approx_order=options.order - 1)
stress = FieldVariable('stress',
'parameter',
sfield,
primary_var_name='(set-to-None)')
strain = FieldVariable('strain',
'parameter',
sfield,
primary_var_name='(set-to-None)')
cfield = Field.from_args('component',
nm.float64,
1,
omega,
approx_order=options.order - 1)
component = FieldVariable('component',
'parameter',
cfield,
primary_var_name='(set-to-None)')
ev = pb.evaluate
order = 2 * (options.order - 1)
strain_qp = ev('ev_cauchy_strain.%d.Omega(u)' % order, mode='qp')
stress_qp = ev('ev_cauchy_stress.%d.Omega(Asphalt.D, u)' % order,
mode='qp',
copy_materials=False)
project_by_component(strain, strain_qp, component, order)
project_by_component(stress, stress_qp, component, order)
all_results = []
for ii, probe in enumerate(probes):
fig, results = probe_results(u, strain, stress, probe, labels[ii])
fig.savefig('its2D_interactive_probe_%d.png' % ii)
all_results.append(results)
for ii, results in enumerate(all_results):
output('probe %d:' % ii)
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
if options.show:
# Show the solution. If the approximation order is greater than 1, the
# extra DOFs are simply thrown away.
from sfepy.postprocess.viewer import Viewer
view = Viewer('its2D_interactive.vtk')
view(vector_mode='warp_norm',
rel_scaling=1,
is_scalar_bar=True,
is_wireframe=True)
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')
# pb.time_update(ebcs=Conditions([fix_u, t1, t2]))
pb.time_update(ebcs=Conditions([bc1, bc2, bc3, bc4]))
vec = pb.solve()
print nls_status
pb.save_state('customCylinder.vtk', vec)
# if options.show:
# view = Viewer('customCylinder.vtk')
# view(vector_mode='warp_norm', rel_scaling=2,
# is_scalar_bar=True, is_wireframe=True)
solutionData = vec.vec.reshape(100, 100)
xGrid = mesh.coors[:, 0].reshape(100, 100)
yGrid = mesh.coors[:, 1].reshape(100, 100)
analyticSolution = np.sin(xGrid / np.pi) * np.sin(yGrid / np.pi)
errorData = 100 * (solutionData - analyticSolution) / analyticSolution
