def __init__(self, region):
"""
Assume a single GeometryElement type in all groups, linear
approximation.
Works for one group only for the moment.
"""
domain = region.domain
self.dim = domain.shape.dim
self.region = copy(region)
self.region.setup_face_indices()
self.mesh_coors = domain.mesh.coors
# add_to_regions=True due to Field implementation shortcomings.
omega = domain.create_region('Omega', 'all', add_to_regions=True)
self.field = Field('displacements', nm.float64, (3, ), omega, 1)
self.gel = domain.geom_els.values()[0]
self.sgel = self.gel.surface_facet
face_key = 's%d' % self.sgel.n_vertex
# Coordinate interpolation to face centres.
self.ps = self.gel.interp.poly_spaces[face_key]
centre = self.ps.node_coors.sum(axis=0) / self.ps.n_nod
self.bf = self.ps.eval_base(centre[None, :])
self.surfaces = surfaces = {}
self.dual_surfaces = dual_surfaces = {}
n_nod = n_fa = 0
for ig, conn in enumerate(domain.mesh.conns):
surface = FESurface(None, self.region, self.gel.faces, conn, ig)
surfaces[ig] = surface
dual_surface = self.describe_dual_surface(surface)
dual_surfaces[ig] = dual_surface
n_nod += dual_surface.n_nod
n_fa += dual_surface.n_fa
# Domain-like shape.
self.shape = Struct(n_nod=n_nod, n_el=n_fa, dim=self.dim)
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()
left = domain.create_region('Left',
'vertices in x < -0.999',
'facet')
right = domain.create_region('Right',
'vertices in x > 0.999',
'facet')
bottom = domain.create_region('Bottom',
'vertices in y < -0.999',
'facet')
top = domain.create_region('Top',
'vertices in y > 0.999',
'facet')
domain.save_regions_as_groups('regions.vtk')
field_t = Field.from_args('temperature', np.float64,
'scalar', omega, 2)
t = FieldVariable('t', 'unknown', field_t, 1)
s = FieldVariable('s', 'test', field_t, 1,
primary_var_name='t')
integral = Integral('i', order=2)
term = Term.new('dw_laplace(s, t)', integral, omega,
s=s, t=t)
eq = Equation('temperature', term)
eqs = Equations([eq])
t_left = EssentialBC('t_left',
left, {'t.0' : 10.0})
t_right = EssentialBC('t_right',
right, {'t.0' : 30.0})
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():
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 _gen_common_data(order, 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
integral = Integral('i', order=order)
for geom, poly_space_base in combine([['2_4', '3_8'],
['lagrange', 'lobatto']]):
report('geometry: %s, base: %s' % (geom, poly_space_base))
mesh0 = Mesh.from_file('meshes/elements/%s_2.mesh' % geom,
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]))
rot = rots[geom]
if rot is not None:
pass
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))
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])
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)
yield (geom, poly_space_base, qp_weights, mesh, ir, ic,
ap, ps, rrc, crc, vec, edofs, fdofs)
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_linearization(self):
from sfepy.base.base import Struct
from sfepy.fem import Mesh, Domain, Field
from sfepy import data_dir
geometries = ['2_3', '2_4', '3_4', '3_8']
approx_orders = [1, 2]
funs = [nm.cos, nm.sin, lambda x: x]
ok = True
for geometry in geometries:
name = os.path.join(data_dir,
'meshes/elements/%s_1.mesh' % geometry)
mesh = Mesh.from_file(name)
domain = Domain('', mesh)
domain = domain.refine()
domain.mesh.write(self.join('linearizer-%s-0.mesh' % geometry))
omega = domain.create_region('Omega', 'all')
for approx_order in approx_orders:
for dpn in [1, mesh.dim]:
self.report('geometry: %s, approx. order: %d, dpn: %d' %
(geometry, approx_order, dpn))
field = Field('fu', nm.float64, dpn, omega,
space='H1', poly_space_base='lagrange',
approx_order=approx_order)
cc = field.get_coor()
dofs = nm.zeros((field.n_nod, dpn), dtype=nm.float64)
for ic in range(dpn):
dofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))
vmesh, vdofs, levels = field.linearize(dofs,
min_level=0,
max_level=3,
eps=1e-2)
level = levels[0]
if approx_order == 1:
_ok = level == 0
else:
_ok = level > 0
self.report('max. refinement level: %d: %s' % (level, _ok))
ok = ok and _ok
rdofs = nm.zeros((vmesh.n_nod, dpn), dtype=nm.float64)
cc = vmesh.coors
for ic in range(dpn):
rdofs[:, ic] = funs[ic](3 * (cc[:, 0] * cc[:, 1]))
_ok = nm.allclose(rdofs, vdofs, rtol=0.0, atol=0.03)
self.report('interpolation: %s' % _ok)
ok = ok and _ok
out = {
'u' : Struct(name='output_data',
mode='vertex', data=vdofs,
var_name='u', dofs=None)
}
name = self.join('linearizer-%s-%d-%d'
% (geometry, approx_order, dpn))
vmesh.write(name + '.mesh')
vmesh.write(name + '.vtk', out=out)
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)
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)
integral = Integral('i', order=quad_order)
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()
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()
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 = 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)
