Ejemplo n.º 1
0
    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
Ejemplo n.º 2
0
    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
Ejemplo n.º 3
0
    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
Ejemplo n.º 4
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    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
Ejemplo n.º 5
0
    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
Ejemplo n.º 6
0
    def test_projection_tri_quad(self):
        from sfepy.fem.projections import make_l2_projection

        source = FieldVariable('us', 'unknown', self.field)

        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)

        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
Ejemplo n.º 7
0
    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
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)
pb.time_update(ebcs=Conditions([u_bottom, u_top]))
Ejemplo n.º 9
0
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)
Ejemplo n.º 10
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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)
Ejemplo n.º 11
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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)
Ejemplo n.º 12
0
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)