def test_surface_evaluate(self):
from sfepy.fem import FieldVariable
problem = self.problem
us = problem.get_variables()['us']
vec = nm.empty(us.n_dof, dtype=us.dtype)
vec[:] = 1.0
us.set_data(vec)
expr = 'ev_surface_integrate.isurf.Left( us )'
val = problem.evaluate(expr, us=us)
ok1 = nm.abs(val - 1.0) < 1e-15
self.report('with unknown: %s, value: %s, ok: %s' % (expr, val, ok1))
ps1 = FieldVariable('ps1',
'parameter',
us.get_field(),
1,
primary_var_name='(set-to-None)')
ps1.set_data(vec)
expr = 'ev_surface_integrate.isurf.Left( ps1 )'
val = problem.evaluate(expr, ps1=ps1)
ok2 = nm.abs(val - 1.0) < 1e-15
self.report('with parameter: %s, value: %s, ok: %s' % (expr, val, ok2))
ok2 = True
return ok1 and ok2
def test_surface_evaluate(self):
from sfepy.fem import FieldVariable
problem = self.problem
us = problem.get_variables()['us']
vec = nm.empty(us.n_dof, dtype=us.dtype)
vec[:] = 1.0
us.data_from_any(vec)
expr = 'di_surface_integrate.isurf.Left( us )'
val = problem.evaluate(expr, us=us)
ok1 = nm.abs(val - 1.0) < 1e-15
self.report('with unknown: %s, value: %s, ok: %s'
% (expr, val, ok1))
ps1 = FieldVariable('ps1', 'parameter', us.get_field(), 1,
primary_var_name='(set-to-None)')
ps1.data_from_any(vec)
expr = 'di_surface_integrate.isurf.Left( ps1 )'
val = problem.evaluate(expr, ps1=ps1)
ok2 = nm.abs(val - 1.0) < 1e-15
self.report('with parameter: %s, value: %s, ok: %s'
% (expr, val, ok2))
ok2 = True
return ok1 and ok2
def nodal_stress(out, pb, state, extend=False):
'''
Calculate stresses at nodal points.
'''
# Point load.
mat = pb.get_materials()['Load']
P = 2.0 * mat.get_data('special', None, 'val')[1]
# Calculate nodal stress.
pb.time_update()
stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp')
sfield = H1NodalVolumeField('stress', nm.float64, (3,),
pb.domain.regions['Omega'])
svar = FieldVariable('sigma', 'parameter', sfield,
primary_var_name='(set-to-None)')
svar.set_data_from_qp(stress, pb.integrals['ivn'])
print '\n=================================================================='
print 'Given load = %.2f N' % -P
print '\nAnalytical solution'
print '==================='
print 'Horizontal tensile stress = %.5e MPa/mm' % (-2.*P/(nm.pi*150.))
print 'Vertical compressive stress = %.5e MPa/mm' % (-6.*P/(nm.pi*150.))
print '\nFEM solution'
print '============'
print 'Horizontal tensile stress = %.5e MPa/mm' % (svar()[0][0])
print 'Vertical compressive stress = %.5e MPa/mm' % (-svar()[0][1])
print '=================================================================='
return out
def test_surface_evaluate(self):
from sfepy.fem import FieldVariable
problem = self.problem
p = problem.get_variables()['p']
vec = nm.empty(p.n_dof, dtype=p.dtype)
vec[:] = 1.0
p.data_from_any(vec)
expr = 'd_surface_integrate.isurf.Left( p )'
val = problem.evaluate(expr, p=p)
ok1 = nm.abs(val - 1.0) < 1e-15
self.report('with unknown: %s, value: %s, ok: %s' \
% (expr, val, ok1))
r = FieldVariable('r', 'parameter', p.get_field(), 1,
primary_var_name='(set-to-None)')
r.data_from_any(vec)
expr = 'd_surface_integrate.isurf.Left( r )'
val = problem.evaluate(expr, r=r)
ok2 = nm.abs(val - 1.0) < 1e-15
self.report('with parameter: %s, value: %s, ok: %s' \
% (expr, val, ok2))
ok2 = True
return ok1 and ok2
def test_surface_evaluate(self):
from sfepy.fem import FieldVariable
problem = self.problem
us = problem.get_variables()["us"]
vec = nm.empty(us.n_dof, dtype=us.dtype)
vec[:] = 1.0
us.set_data(vec)
expr = "ev_surface_integrate.i.Left( us )"
val = problem.evaluate(expr, us=us)
ok1 = nm.abs(val - 1.0) < 1e-15
self.report("with unknown: %s, value: %s, ok: %s" % (expr, val, ok1))
ps1 = FieldVariable("ps1", "parameter", us.get_field(), primary_var_name="(set-to-None)")
ps1.set_data(vec)
expr = "ev_surface_integrate.i.Left( ps1 )"
val = problem.evaluate(expr, ps1=ps1)
ok2 = nm.abs(val - 1.0) < 1e-15
self.report("with parameter: %s, value: %s, ok: %s" % (expr, val, ok2))
ok2 = True
return ok1 and ok2
def test_solving(self):
from sfepy.base.base import IndexedStruct
from sfepy.fem \
import FieldVariable, Material, ProblemDefinition, \
Function, Equation, Equations, Integral
from sfepy.fem.conditions import Conditions, EssentialBC
from sfepy.terms import Term
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
u = FieldVariable('u', 'unknown', self.field, self.dim)
v = FieldVariable('v', 'test', self.field, self.dim,
primary_var_name='u')
m = Material('m', lam=1.0, mu=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_iso(m.lam, m.mu, 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 = ProblemDefinition('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 create_subequations(self, var_names, known_var_names=None):
"""
Create sub-equations containing only terms with the given virtual
variables.
Parameters
----------
var_names : list
The list of names of virtual variables.
known_var_names : list
The list of names of (already) known state variables.
Returns
-------
subequations : Equations instance
The sub-equations.
"""
from sfepy.fem import FieldVariable
known_var_names = get_default(known_var_names, [])
objs = []
for iv, var_name in enumerate(var_names):
terms = [
term.copy(name=term.name) for eq in self for term in eq.terms
if term.get_virtual_name() == var_name
]
# Make parameter variables from known state variables in terms
# arguments.
for known_name in known_var_names:
for term in terms:
if known_name in term.arg_names:
ii = term.arg_names.index(known_name)
state = self.variables[known_name]
par = FieldVariable(known_name,
'parameter',
state.field,
state.n_components,
primary_var_name='(set-to-None)')
term.args[ii] = par
term._kwargs[known_name] = par
par.set_data(state())
new_terms = Terms(terms)
objs.append(Equation('eq_%d' % iv, new_terms))
subequations = Equations(objs)
return subequations
def test_term_arithmetics(self):
from sfepy.fem import FieldVariable, Integral
from sfepy.terms.terms import Term
integral = Integral('i', order=3)
integral_s = Integral('i', kind='s', order=3)
u = FieldVariable('u', 'parameter', self.field, self.dim,
primary_var_name='(set-to-None)')
t1 = Term.new('d_volume(u)', integral, self.omega, u=u)
t2 = Term.new('d_surface(u)', integral_s, self.gamma1, u=u)
expr = 2.2j * (t1 * 5.5 - 3j * t2) * 0.25
ok = len(expr) == 2
if not ok:
self.report('wrong expression length!')
_ok = nm.allclose(expr[0].sign, 3.025j, rtol=1e-15, atol=0)
if not _ok:
self.report('wrong sign of the first term!')
ok = ok and _ok
_ok = nm.allclose(expr[1].sign, 1.65, rtol=1e-15, atol=0)
if not _ok:
self.report('wrong sign of the second term!')
ok = ok and _ok
return ok
def test_term_evaluation(self):
from sfepy.fem import Integral, FieldVariable
from sfepy.terms.terms import Term
integral = Integral('i', order=3)
u = FieldVariable('u', 'parameter', self.field, self.dim,
primary_var_name='(set-to-None)')
term = Term.new('d_volume(u)', integral, self.omega, u=u)
term *= 10.0
term.setup()
vol = term.evaluate()
self.report('volume: %.8f == 2000.0' % vol)
ok = nm.allclose(vol, 2000.0, rtol=1e-15, atol=0)
## vec = t1.evaluate() # Returns vector.
## vec = t1.evaluate(u=u_vec) # Returns the same vector.
## mtx = t1.evaluate(diff_var='u') # Returns matrix.
## val = t1.evaluate(v=u_vec, u=u_vec) # Forbidden - virtual variable
## # cannot have value.
return ok
def test_volume( self ):
from sfepy.fem import FieldVariable
ok = True
field_map = {'u' : 'vector', 'p' : 'scalar'}
volumes = {}
avg = 0.0
for key, term in expressions.items():
var_name = key[-1]
field = self.problem.fields[field_map[var_name]]
var = FieldVariable(var_name, 'parameter', field, 1,
primary_var_name='(set-to-None)')
val = self.problem.evaluate(term, **{var_name : var})
volumes[key] = val
avg += val
avg /= len(volumes)
for key, val in volumes.items():
err = nm.abs( avg - val ) / nm.abs( avg )
_ok = err < 1e-12
self.report('"'"%s"'" - volume: %e' % (key, val))
self.report('"'"%s"'" - relative volume difference: %e -> %s'\
% (key, err, _ok) )
ok = ok and _ok
return ok
def create_subequations(self, var_names, known_var_names=None):
"""
Create sub-equations containing only terms with the given virtual
variables.
Parameters
----------
var_names : list
The list of names of virtual variables.
known_var_names : list
The list of names of (already) known state variables.
Returns
-------
subequations : Equations instance
The sub-equations.
"""
from sfepy.fem import FieldVariable
known_var_names = get_default(known_var_names, [])
objs = []
for iv, var_name in enumerate(var_names):
terms = [term.copy(name=term.name)
for eq in self for term in eq.terms
if term.get_virtual_name() == var_name]
# Make parameter variables from known state variables in terms
# arguments.
for known_name in known_var_names:
for term in terms:
if known_name in term.arg_names:
ii = term.arg_names.index(known_name)
state = self.variables[known_name]
par = FieldVariable(known_name, 'parameter',
state.field, state.n_components,
primary_var_name='(set-to-None)')
term.args[ii] = par
term._kwargs[known_name] = par
par.set_data(state())
new_terms = Terms(terms)
objs.append(Equation('eq_%d' % iv, new_terms))
subequations = Equations(objs)
return subequations
def test_variables(self):
from sfepy.fem import FieldVariable
u = FieldVariable('u', 'parameter', self.field, self.dim,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
ok = nm.allclose(vec, 1.0)
## print u()
## print u.get_vector() # Coefficient vector w.r.t. the field space basis.
## print u(gamma1)
## print u.get_vector(gamma2)
return ok
def test_variables(self):
from sfepy.fem import FieldVariable
u = FieldVariable('u', 'parameter', self.field,
primary_var_name='(set-to-None)')
u.set_constant(1.0)
vec = u() # Nodal values.
ok = nm.allclose(vec, 1.0)
## print u()
## print u.get_vector() # Coefficient vector w.r.t. the field space basis.
## print u(gamma1)
## print u.get_vector(gamma2)
return ok
def test_projection_tri_quad(self):
from sfepy.fem.projections import make_l2_projection
source = FieldVariable('us', 'unknown', self.field, 1)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:,0] * coors[:,1])
source.data_from_any(vals)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_source.vtk')
source.save_as_mesh(name)
mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
prefix_dir=sfepy.data_dir)
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field('bilinear', nm.float64, 'scalar', omega,
space='H1', poly_space_base='lagrange', approx_order=1)
target = FieldVariable('ut', 'unknown', field, 1)
make_l2_projection(target, source)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_target.vtk')
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
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, 1, 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 = ProblemDefinition('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_projection_tri_quad(self):
from sfepy.fem.projections import make_l2_projection
source = FieldVariable("us", "unknown", self.field, 1)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:, 0] * coors[:, 1])
source.data_from_any(vals)
name = op.join(self.options.out_dir, "test_projection_tri_quad_source.vtk")
source.save_as_mesh(name)
mesh = Mesh.from_file("meshes/2d/square_quad.mesh", prefix_dir=sfepy.data_dir)
domain = Domain("domain", mesh)
omega = domain.create_region("Omega", "all")
field = H1NodalVolumeField("bilinear", nm.float64, "scalar", omega, approx_order=1)
target = FieldVariable("ut", "unknown", field, 1)
make_l2_projection(target, source)
name = op.join(self.options.out_dir, "test_projection_tri_quad_target.vtk")
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
return ok
def create_mass_matrix(field):
"""
Create scalar mass matrix corresponding to the given field.
Returns
-------
mtx : csr_matrix
The mass matrix in CSR format.
"""
u = FieldVariable('u', 'unknown', field, 1)
v = FieldVariable('v', 'test', field, 1, primary_var_name='u')
integral = Integral('i', order=field.approx_order * 2)
term = Term.new('dw_volume_dot(v, u)', integral, field.region, v=v, u=u)
eq = Equation('aux', term)
eqs = Equations([eq])
eqs.time_update(None)
dummy = eqs.create_state_vector()
mtx = eqs.create_matrix_graph()
mtx = eqs.eval_tangent_matrices(dummy, mtx)
return mtx
def nodal_stress(out, pb, state, extend=False):
'''
Calculate stresses at nodal points.
'''
# Point load.
mat = pb.get_materials()['Load']
P = 2.0 * mat.get_data('special', None, 'val')[1]
# Calculate nodal stress.
pb.time_update()
stress = pb.evaluate('ev_cauchy_stress.ivn.Omega(Asphalt.D, u)', mode='qp')
sfield = H1NodalVolumeField('stress', nm.float64, (3, ),
pb.domain.regions['Omega'])
svar = FieldVariable('sigma',
'parameter',
sfield,
3,
primary_var_name='(set-to-None)')
svar.set_data_from_qp(stress, pb.integrals['ivn'])
print '\n=================================================================='
print 'Given load = %.2f N' % -P
print '\nAnalytical solution'
print '==================='
print 'Horizontal tensile stress = %.5e MPa/mm' % (-2. * P /
(nm.pi * 150.))
print 'Vertical compressive stress = %.5e MPa/mm' % (-6. * P /
(nm.pi * 150.))
print '\nFEM solution'
print '============'
print 'Horizontal tensile stress = %.5e MPa/mm' % (svar()[0][0])
print 'Vertical compressive stress = %.5e MPa/mm' % (-svar()[0][1])
print '=================================================================='
return out
def get_volume(problem, field_name, region_name, quad_order=1):
"""
Get volume of a given region using integration defined by a given
field. Both the region and the field have to be defined in
`problem`.
"""
from sfepy.fem import FieldVariable
field = problem.fields[field_name]
var = FieldVariable('u',
'parameter',
field,
1,
primary_var_name='(set-to-None)')
vol = problem.evaluate('d_volume.%d.%s( u )' % (quad_order, region_name),
u=var)
return vol
field_u = Field.from_args('displacement', np.float64,
'vector', omega, 1)
u = FieldVariable('u', 'unknown', field_u, mesh.dim)
v = FieldVariable('v', 'test', field_u, mesh.dim,
primary_var_name='u')
lam = 10.0 # Lame parameters.
mu = 5.0
te = 0.5 # Thermal expansion coefficient.
T0 = 20.0 # Background temperature.
eye_sym = np.array([[1], [1], [0]],
dtype=np.float64)
m = Material('m', lam=lam, mu=mu,
alpha=te * eye_sym)
t2 = FieldVariable('t', 'parameter', field_t, 1,
primary_var_name='(set-to-None)')
t2.set_data(t() - T0)
term1 = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral, omega, m=m, v=v, u=u)
term2 = Term.new('dw_biot(m.alpha, v, t)',
integral, omega, m=m, v=v, t=t2)
eq = Equation('temperature', term1 - term2)
eqs = Equations([eq])
u_bottom = EssentialBC('u_bottom',
bottom, {'u.all' : 0.0})
u_top = EssentialBC('u_top',
top, {'u.[0]' : 0.0})
pb.set_equations_instance(eqs, keep_solvers=True)
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain):
from sfepy.base.base import basestr
from sfepy.fem import Field, FieldVariable, Material, Variables, Materials
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 5
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh), )
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii,
nm.float64,
shape,
omega,
approx_order=1)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field, shape)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v',
'test',
field,
shape,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field, shape)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii,
'parameter',
field,
shape,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
# Array.
values = {
'%sc%d' % (prefix, ii): nm.ones(shape, dtype=nm.float64)
}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii: 1.0}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
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',
'nodes in x < %.10f' % (min_x + eps))
gamma2 = domain.create_region('Gamma2',
'nodes in x > %.10f' % (max_x - eps))
field = H1NodalVolumeField('fu',
nm.float64,
'vector',
omega,
approx_order=2)
u = FieldVariable('u', 'unknown', field, mesh.dim)
v = FieldVariable('v', 'test', field, mesh.dim, 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 = ProblemDefinition('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 = OptionParser(usage=usage, version='%prog')
parser.add_option('-b', '--basis', metavar='name',
action='store', dest='basis',
default='lagrange', help=help['basis'])
parser.add_option('-d', '--derivative', metavar='d', type=int,
action='store', dest='derivative',
default=0, help=help['derivative'])
parser.add_option('-n', '--max-order', metavar='order', type=int,
action='store', dest='max_order',
default=2, help=help['max_order'])
parser.add_option('-g', '--geometry', metavar='name',
action='store', dest='geometry',
default='2_4', help=help['geometry'])
parser.add_option('-m', '--mesh', metavar='mesh',
action='store', dest='mesh',
default=None, help=help['mesh'])
parser.add_option('', '--permutations', metavar='permutations',
action='store', dest='permutations',
default=None, help=help['permutations'])
parser.add_option('', '--dofs', metavar='dofs',
action='store', dest='dofs',
default=None, help=help['dofs'])
parser.add_option('-l', '--lin-options', metavar='options',
action='store', dest='lin_options',
default='min_level=2,max_level=5,eps=1e-3',
help=help['lin_options'])
parser.add_option('', '--plot-dofs',
action='store_true', dest='plot_dofs',
default=False, help=help['plot_dofs'])
options, args = parser.parse_args()
if len(args) == 1:
output_dir = args[0]
else:
parser.print_help(),
return
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
lin = Struct(kind='adaptive', min_level=2, max_level=5, eps=1e-3)
for opt in options.lin_options.split(','):
key, val = opt.split('=')
setattr(lin, key, eval(val))
if options.mesh is None:
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
gel = GeometryElement(options.geometry)
gps = PolySpace.any_from_args(None, gel, 1,
base=options.basis)
ps = PolySpace.any_from_args(None, gel, options.max_order,
base=options.basis)
n_digit, _format = get_print_info(ps.n_nod, fill='0')
name_template = os.path.join(output_dir, 'bf_%s.vtk' % _format)
for ip in get_dofs(options.dofs, ps.n_nod):
output('shape function %d...' % ip)
def eval_dofs(iels, rx):
if options.derivative == 0:
bf = ps.eval_base(rx).squeeze()
rvals = bf[None, :, ip:ip+1]
else:
bfg = ps.eval_base(rx, diff=True)
rvals = bfg[None, ..., ip]
return rvals
def eval_coors(iels, rx):
bf = gps.eval_base(rx).squeeze()
coors = nm.dot(bf, gel.coors)[None, ...]
return coors
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors, 1,
ps, min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
out = {
'bf' : Struct(name='output_data',
mode='vertex', data=vdofs,
var_name='bf', dofs=None)
}
mesh = Mesh.from_data('bf_mesh', coors, None, [conn], [mat_ids],
[options.geometry])
name = name_template % ip
mesh.write(name, out=out)
output('...done (%s)' % name)
else:
mesh = Mesh.from_file(options.mesh)
output('mesh geometry:')
output(' dimension: %d, vertices: %d, elements: %d'
% (mesh.dim, mesh.n_nod, mesh.n_el))
domain = Domain('domain', mesh)
if options.permutations:
permutations = [int(ii) for ii in options.permutations.split(',')]
output('using connectivity permutations:', permutations)
for group in domain.iter_groups():
perms = group.gel.get_conn_permutations()[permutations]
offsets = nm.arange(group.shape.n_el) * group.shape.n_ep
group.conn[:] = group.conn.take(perms + offsets[:, None])
domain.setup_facets()
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f', nm.float64, shape=1, region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir, 'dof_%s.vtk' % _format)
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.data_from_any(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u', 'f', {'f' : field}, None,
Variables([var]),
mode='qp', verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def save_basis_on_mesh(mesh,
options,
output_dir,
lin,
permutations=None,
suffix=''):
if permutations is not None:
mesh = mesh.copy()
for ig, conn in enumerate(mesh.conns):
gel = GeometryElement(mesh.descs[ig])
perms = gel.get_conn_permutations()[permutations]
n_el, n_ep = conn.shape
offsets = nm.arange(n_el) * n_ep
conn[:] = conn.take(perms + offsets[:, None])
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.aps[0].econn,
field.aps[0].interp.poly_spaces['v'].nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u',
'f', {'f': field},
None,
Variables([var]),
mode='qp',
verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain):
from sfepy.base.base import basestr
from sfepy.fem import Field, FieldVariable, Material, Variables, Materials
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 5
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
# Array.
values = {'%sc%d' % (prefix, ii)
: nm.ones(shape, dtype=nm.float64)}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : 1.0}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
def save_basis_on_mesh(mesh, options, output_dir, lin,
permutations=None, suffix=''):
if permutations is not None:
mesh = mesh.copy()
for ig, conn in enumerate(mesh.conns):
gel = GeometryElement(mesh.descs[ig])
perms = gel.get_conn_permutations()[permutations]
n_el, n_ep = conn.shape
offsets = nm.arange(n_el) * n_ep
conn[:] = conn.take(perms + offsets[:, None])
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f', nm.float64, shape=1, region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.aps[0].econn,
field.aps[0].interp.poly_spaces['v'].nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u', 'f', {'f' : field}, None,
Variables([var]),
mode='qp', verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def _gen_common_data(orders, gels, report):
import sfepy
from sfepy.base.base import Struct
from sfepy.linalg import combine
from sfepy.fem import Mesh, Domain, Field, FieldVariable, Integral
from sfepy.fem.global_interp import get_ref_coors
bases = ([ii for ii in combine([['2_4', '3_8'],
['lagrange', 'lobatto']])]
+ [ii for ii in combine([['2_3', '3_4'],
['lagrange']])])
for geom, poly_space_base in bases:
report('geometry: %s, base: %s' % (geom, poly_space_base))
order = orders[geom]
integral = Integral('i', order=order)
aux = '' if geom in ['2_4', '3_8'] else 'z'
mesh0 = Mesh.from_file('meshes/elements/%s_2%s.mesh' % (geom, aux),
prefix_dir=sfepy.data_dir)
gel = gels[geom]
perms = gel.get_conn_permutations()
qps, qp_weights = integral.get_qp(gel.surface_facet.name)
zz = nm.zeros_like(qps[:, :1])
qps = nm.hstack(([qps] + [zz]))
shift = shifts[geom]
rcoors = nm.ascontiguousarray(qps
+ shift[:1, :] - shift[1:, :])
ccoors = nm.ascontiguousarray(qps
+ shift[:1, :] + shift[1:, :])
for ir, pr in enumerate(perms):
for ic, pc in enumerate(perms):
report('ir: %d, ic: %d' % (ir, ic))
report('pr: %s, pc: %s' % (pr, pc))
mesh = mesh0.copy()
conn = mesh.conns[0]
conn[0, :] = conn[0, pr]
conn[1, :] = conn[1, pc]
cache = Struct(mesh=mesh)
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
region = domain.create_region('Facet', rsels[geom], 'facet')
field = Field.from_args('f', nm.float64, shape=1,
region=omega, approx_order=order,
poly_space_base=poly_space_base)
var = FieldVariable('u', 'unknown', field, 1)
report('# dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
ap = field.aps[0]
ps = ap.interp.poly_spaces['v']
dofs = field.get_dofs_in_region_group(region, 0,
merge=False)
edofs, fdofs = nm.unique(dofs[1]), nm.unique(dofs[2])
rrc, rcells, rstatus = get_ref_coors(field, rcoors,
cache=cache)
crc, ccells, cstatus = get_ref_coors(field, ccoors,
cache=cache)
assert_((rstatus == 0).all() and (cstatus == 0).all())
yield (geom, poly_space_base, qp_weights, mesh, ir, ic,
ap, ps, rrc, rcells[0, 1], crc, ccells[0, 1],
vec, edofs, fdofs)
def test_projection_tri_quad(self):
from sfepy.fem.projections import make_l2_projection
source = FieldVariable('us', 'unknown', self.field, 1)
coors = self.field.get_coor()
vals = nm.sin(2.0 * nm.pi * coors[:,0] * coors[:,1])
source.set_data(vals)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_source.vtk')
source.save_as_mesh(name)
mesh = Mesh.from_file('meshes/2d/square_quad.mesh',
prefix_dir=sfepy.data_dir)
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = H1NodalVolumeField('bilinear', nm.float64, 'scalar', omega,
approx_order=1)
target = FieldVariable('ut', 'unknown', field, 1)
make_l2_projection(target, source)
name = op.join(self.options.out_dir,
'test_projection_tri_quad_target.vtk')
target.save_as_mesh(name)
bbox = self.field.domain.get_mesh_bounding_box()
x = nm.linspace(bbox[0, 0] + 0.001, bbox[1, 0] - 0.001, 20)
y = nm.linspace(bbox[0, 1] + 0.001, bbox[1, 1] - 0.001, 20)
xx, yy = nm.meshgrid(x, y)
test_coors = nm.c_[xx.ravel(), yy.ravel()].copy()
vec1 = source.evaluate_at(test_coors)
vec2 = target.evaluate_at(test_coors)
ok = (nm.abs(vec1 - vec2) < 0.01).all()
return ok
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-b',
'--basis',
metavar='name',
action='store',
dest='basis',
default='lagrange',
help=help['basis'])
parser.add_option('-d',
'--derivative',
metavar='d',
type=int,
action='store',
dest='derivative',
default=0,
help=help['derivative'])
parser.add_option('-n',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=2,
help=help['max_order'])
parser.add_option('-g',
'--geometry',
metavar='name',
action='store',
dest='geometry',
default='2_4',
help=help['geometry'])
parser.add_option('-m',
'--mesh',
metavar='mesh',
action='store',
dest='mesh',
default=None,
help=help['mesh'])
parser.add_option('',
'--permutations',
metavar='permutations',
action='store',
dest='permutations',
default=None,
help=help['permutations'])
parser.add_option('',
'--dofs',
metavar='dofs',
action='store',
dest='dofs',
default=None,
help=help['dofs'])
parser.add_option('-l',
'--lin-options',
metavar='options',
action='store',
dest='lin_options',
default='min_level=2,max_level=5,eps=1e-3',
help=help['lin_options'])
parser.add_option('',
'--plot-dofs',
action='store_true',
dest='plot_dofs',
default=False,
help=help['plot_dofs'])
options, args = parser.parse_args()
if len(args) == 1:
output_dir = args[0]
else:
parser.print_help(),
return
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
lin = Struct(kind='adaptive', min_level=2, max_level=5, eps=1e-3)
for opt in options.lin_options.split(','):
key, val = opt.split('=')
setattr(lin, key, eval(val))
if options.mesh is None:
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
gel = GeometryElement(options.geometry)
gps = PolySpace.any_from_args(None, gel, 1, base=options.basis)
ps = PolySpace.any_from_args(None,
gel,
options.max_order,
base=options.basis)
n_digit, _format = get_print_info(ps.n_nod, fill='0')
name_template = os.path.join(output_dir, 'bf_%s.vtk' % _format)
for ip in get_dofs(options.dofs, ps.n_nod):
output('shape function %d...' % ip)
def eval_dofs(iels, rx):
if options.derivative == 0:
bf = ps.eval_base(rx).squeeze()
rvals = bf[None, :, ip:ip + 1]
else:
bfg = ps.eval_base(rx, diff=True)
rvals = bfg[None, ..., ip]
return rvals
def eval_coors(iels, rx):
bf = gps.eval_base(rx).squeeze()
coors = nm.dot(bf, gel.coors)[None, ...]
return coors
(level, coors, conn, vdofs,
mat_ids) = create_output(eval_dofs,
eval_coors,
1,
ps,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
out = {
'bf':
Struct(name='output_data',
mode='vertex',
data=vdofs,
var_name='bf',
dofs=None)
}
mesh = Mesh.from_data('bf_mesh', coors, None, [conn], [mat_ids],
[options.geometry])
name = name_template % ip
mesh.write(name, out=out)
output('...done (%s)' % name)
else:
mesh = Mesh.from_file(options.mesh)
output('mesh geometry:')
output(' dimension: %d, vertices: %d, elements: %d' %
(mesh.dim, mesh.n_nod, mesh.n_el))
domain = Domain('domain', mesh)
if options.permutations:
permutations = [int(ii) for ii in options.permutations.split(',')]
output('using connectivity permutations:', permutations)
for group in domain.iter_groups():
perms = group.gel.get_conn_permutations()[permutations]
offsets = nm.arange(group.shape.n_el) * group.shape.n_ep
group.conn[:] = group.conn.take(perms + offsets[:, None])
domain.setup_facets()
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field, 1)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
group = domain.groups[0]
ax = pd.plot_mesh(None, mesh.coors, mesh.conns[0], group.gel.edges)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.aps[0].econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.aps[0].econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.aps[0].econn,
field.aps[0].interp.poly_spaces['v'].nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir, 'dof_%s.vtk' % _format)
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u',
'f', {'f': field},
None,
Variables([var]),
mode='qp',
verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-b',
'--basis',
metavar='name',
action='store',
dest='basis',
default='lagrange',
help=help['basis'])
parser.add_option('-n',
'--max-order',
metavar='order',
type=int,
action='store',
dest='max_order',
default=10,
help=help['max_order'])
parser.add_option('-m',
'--matrix',
metavar='type',
action='store',
dest='matrix_type',
default='laplace',
help=help['matrix_type'])
parser.add_option('-g',
'--geometry',
metavar='name',
action='store',
dest='geometry',
default='2_4',
help=help['geometry'])
options, args = parser.parse_args()
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
n_c = {'laplace': 1, 'elasticity': dim}[options.matrix_type]
output('matrix type:', options.matrix_type)
output('number of variable components:', n_c)
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
mesh = Mesh.from_file(data_dir +
'/meshes/elements/%s_1.mesh' % options.geometry)
domain = Domain('domain', mesh)
omega = domain.create_region('Omega', 'all')
orders = nm.arange(1, options.max_order + 1, dtype=nm.int)
conds = []
order_fix = 0 if options.geometry in ['2_4', '3_8'] else 1
for order in orders:
output('order:', order, '...')
field = Field.from_args('fu',
nm.float64,
n_c,
omega,
approx_order=order,
space='H1',
poly_space_base=options.basis)
to = field.approx_order
quad_order = 2 * (max(to - order_fix, 0))
output('quadrature order:', quad_order)
integral = Integral('i', order=quad_order)
qp, _ = integral.get_qp(options.geometry)
output('number of quadrature points:', qp.shape[0])
u = FieldVariable('u', 'unknown', field, n_c)
v = FieldVariable('v', 'test', field, n_c, primary_var_name='u')
m = Material('m', lam=1.0, mu=1.0)
if options.matrix_type == 'laplace':
term = Term.new('dw_laplace(m.mu, v, u)',
integral,
omega,
m=m,
v=v,
u=u)
n_zero = 1
else:
assert_(options.matrix_type == 'elasticity')
term = Term.new('dw_lin_elastic_iso(m.lam, m.mu, v, u)',
integral,
omega,
m=m,
v=v,
u=u)
n_zero = (dim + 1) * dim / 2
term.setup()
output('assembling...')
tt = time.clock()
mtx, iels = term.evaluate(mode='weak', diff_var='u')
output('...done in %.2f s' % (time.clock() - tt))
mtx = mtx[0][0, 0]
try:
assert_(nm.max(nm.abs(mtx - mtx.T)) < 1e-10)
except:
from sfepy.base.base import debug
debug()
output('matrix shape:', mtx.shape)
eigs = eig(mtx, method='eig.sgscipy', eigenvectors=False)
eigs.sort()
# Zero 'true' zeros.
eigs[:n_zero] = 0.0
ii = nm.where(eigs < 0.0)[0]
if len(ii):
output('matrix is not positive semi-definite!')
ii = nm.where(eigs[n_zero:] < 1e-12)[0]
if len(ii):
output('matrix has more than %d zero eigenvalues!' % n_zero)
output('smallest eigs:\n', eigs[:10])
ii = nm.where(eigs > 0.0)[0]
emin, emax = eigs[ii[[0, -1]]]
output('min:', emin, 'max:', emax)
cond = emax / emin
conds.append(cond)
output('condition number:', cond)
output('...done')
plt.figure(1)
plt.semilogy(orders, conds)
plt.xticks(orders, orders)
plt.xlabel('polynomial order')
plt.ylabel('condition number')
plt.grid()
plt.figure(2)
plt.loglog(orders, conds)
plt.xticks(orders, orders)
plt.xlabel('polynomial order')
plt.ylabel('condition number')
plt.grid()
plt.show()
