Exemple #1
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    def from_conf(conf, options):
        import sfepy
        from sfepy.fem import Mesh, Domain, H1NodalVolumeField
        mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = Domain('domain', mesh)
        dim = domain.shape.dim

        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 = H1NodalVolumeField('fu', nm.float64, 'vector', omega,
                                   approx_order=2)

        test = Test(conf=conf, options=options, dim=dim,
                    omega=omega, gamma1=gamma1, gamma2=gamma2,
                    field=field)
        return test
Exemple #2
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    def from_conf(conf, options):
        import sfepy
        from sfepy.fem import Mesh, Domain, H1NodalVolumeField
        mesh = Mesh.from_file('meshes/2d/rectangle_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = Domain('domain', mesh)
        dim = domain.shape.dim

        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 = H1NodalVolumeField('fu',
                                   nm.float64,
                                   'vector',
                                   omega,
                                   approx_order=2)

        test = Test(conf=conf,
                    options=options,
                    dim=dim,
                    omega=omega,
                    gamma1=gamma1,
                    gamma2=gamma2,
                    field=field)
        return test
Exemple #3
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    def test_interpolation_two_meshes(self):
        from sfepy import data_dir
        from sfepy.fem import Mesh, Domain, H1NodalVolumeField, Variables

        m1 = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')

        m2 = Mesh('target mesh',
                  data_dir + '/meshes/3d/cube_medium_tetra.mesh')
        m2.coors *= 2.0

        bbox = m1.get_bounding_box()
        dd = bbox[1, :] - bbox[0, :]
        data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])

        variables1 = {
            'u': ('unknown field', 'scalar_tp', 0),
            'v': ('test field', 'scalar_tp', 'u'),
        }

        variables2 = {
            'u': ('unknown field', 'scalar_si', 0),
            'v': ('test field', 'scalar_si', 'u'),
        }

        d1 = Domain('d1', m1)
        omega1 = d1.create_region('Omega', 'all')
        field1 = H1NodalVolumeField('scalar_tp',
                                    nm.float64, (1, 1),
                                    omega1,
                                    approx_order=1)
        ff1 = {field1.name: field1}

        d2 = Domain('d2', m2)
        omega2 = d2.create_region('Omega', 'all')
        field2 = H1NodalVolumeField('scalar_si',
                                    nm.float64, (1, 1),
                                    omega2,
                                    approx_order=0)
        ff2 = {field2.name: field2}

        vv1 = Variables.from_conf(transform_variables(variables1), ff1)
        u1 = vv1['u']
        u1.set_from_mesh_vertices(data)

        vv2 = Variables.from_conf(transform_variables(variables2), ff2)
        u2 = vv2['u']

        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)

        fname = in_dir(self.options.out_dir)
        u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
        u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))

        return True
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 = Field("fu", nm.float64, "vector", omega, space="H1", poly_space_base="lagrange", 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 test_interpolation_two_meshes(self):
        from sfepy import data_dir
        from sfepy.fem import Mesh, Domain, H1NodalVolumeField, Variables

        m1 = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')

        m2 = Mesh('target mesh', data_dir + '/meshes/3d/cube_medium_tetra.mesh')
        m2.coors *= 2.0

        bbox = m1.get_bounding_box()
        dd = bbox[1,:] - bbox[0,:]
        data = nm.sin(4.0 * nm.pi * m1.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * m1.coors[:,1:2] / dd[1])

        variables1 = {
            'u'       : ('unknown field', 'scalar_tp', 0),
            'v'       : ('test field',    'scalar_tp', 'u'),
        }

        variables2 = {
            'u'       : ('unknown field', 'scalar_si', 0),
            'v'       : ('test field',    'scalar_si', 'u'),
        }

        d1 = Domain('d1', m1)
        omega1 = d1.create_region('Omega', 'all')
        field1 = H1NodalVolumeField('scalar_tp', nm.float64, (1,1), omega1,
                                    approx_order=1)
        ff1 = {field1.name : field1}

        d2 = Domain('d2', m2)
        omega2 = d2.create_region('Omega', 'all')
        field2 = H1NodalVolumeField('scalar_si', nm.float64, (1,1), omega2,
                                    approx_order=0)
        ff2 = {field2.name : field2}

        vv1 = Variables.from_conf(transform_variables(variables1), ff1)
        u1 = vv1['u']
        u1.set_from_mesh_vertices(data)

        vv2 = Variables.from_conf(transform_variables(variables2), ff2)
        u2 = vv2['u']

        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.1)

        fname = in_dir(self.options.out_dir)
        u1.save_as_mesh(fname('test_mesh_interp_block_scalar.vtk'))
        u2.save_as_mesh(fname('test_mesh_interp_cube_scalar.vtk'))

        return True
Exemple #6
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def do_interpolation(m2, m1, data, field_name, force=False):
    """Interpolate data from m1 to m2. """
    from sfepy.fem import Domain, H1NodalVolumeField, Variables

    fields = {
        'scalar_si': ((1, 1), 'Omega', 2),
        'vector_si': ((3, 1), 'Omega', 2),
        'scalar_tp': ((1, 1), 'Omega', 1),
        'vector_tp': ((3, 1), 'Omega', 1),
    }

    d1 = Domain('d1', m1)

    omega1 = d1.create_region('Omega', 'all')

    f = fields[field_name]

    field1 = H1NodalVolumeField('f',
                                nm.float64,
                                f[0],
                                d1.regions[f[1]],
                                approx_order=f[2])
    ff = {field1.name: field1}

    vv = Variables.from_conf(transform_variables(variables), ff)
    u1 = vv['u']
    u1.set_from_mesh_vertices(data)

    d2 = Domain('d2', m2)
    omega2 = d2.create_region('Omega', 'all')

    field2 = H1NodalVolumeField('f',
                                nm.float64,
                                f[0],
                                d2.regions[f[1]],
                                approx_order=f[2])
    ff2 = {field2.name: field2}

    vv2 = Variables.from_conf(transform_variables(variables), ff2)
    u2 = vv2['u']

    if not force:
        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)

    else:
        coors = u2.field.get_coor()
        vals = u1.evaluate_at(coors, close_limit=0.5)
        u2.set_data(vals)

    return u1, u2
Exemple #7
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def main():
    parser = OptionParser(usage=usage, version="%prog")

    options, args = parser.parse_args()

    if (len(args) == 1):
        mesh_filename = args[0];
    else:
        parser.print_help(),
        return

    mesh = Mesh('mesh', mesh_filename)
    print mesh

    domain = Domain('domain', mesh)
    print domain

    reg = domain.create_region('Surface',
                               'nodes of surface',
                               {'can_cells' : True})

    dual_mesh = DualMesh(reg)
    dual_mesh.save('dual_mesh.mesh',)
    dual_mesh.save_axes('axes.vtk',)

    print dual_mesh
def main():
    parser = OptionParser(usage=usage, version="%prog")

    options, args = parser.parse_args()

    if (len(args) == 1):
        mesh_filename = args[0];
    else:
        parser.print_help(),
        return

    mesh = Mesh('mesh', mesh_filename)
    print mesh

    domain = Domain('domain', mesh)
    print domain

    reg = domain.create_region('Surface',
                               'nodes of surface',
                               {'can_cells' : True})

    dual_mesh = DualMesh(reg)
    dual_mesh.save('dual_mesh.mesh',)
    dual_mesh.save_axes('axes.vtk',)

    print dual_mesh
def do_interpolation(m2, m1, data, field_name, force=False):
    """Interpolate data from m1 to m2. """
    from sfepy.fem import Domain, H1NodalVolumeField, Variables

    fields = {
        'scalar_si' : ((1,1), 'Omega', 2),
        'vector_si' : ((3,1), 'Omega', 2),
        'scalar_tp' : ((1,1), 'Omega', 1),
        'vector_tp' : ((3,1), 'Omega', 1),
    }

    d1 = Domain('d1', m1)

    omega1 = d1.create_region('Omega', 'all')

    f = fields[field_name]

    field1 = H1NodalVolumeField('f', nm.float64, f[0], d1.regions[f[1]],
                                approx_order=f[2])
    ff = {field1.name : field1}

    vv = Variables.from_conf(transform_variables(variables), ff)
    u1 = vv['u']
    u1.set_from_mesh_vertices(data)

    d2 = Domain('d2', m2)
    omega2 = d2.create_region('Omega', 'all')

    field2 = H1NodalVolumeField('f', nm.float64, f[0], d2.regions[f[1]],
                                approx_order=f[2])
    ff2 = {field2.name : field2}

    vv2 = Variables.from_conf(transform_variables(variables), ff2)
    u2 = vv2['u']

    if not force:
        # Performs interpolation, if other field differs from self.field
        # or, in particular, is defined on a different mesh.
        u2.set_from_other(u1, strategy='interpolation', close_limit=0.5)

    else:
        coors = u2.field.get_coor()
        vals = u1.evaluate_at(coors, close_limit=0.5)
        u2.set_data(vals)

    return u1, u2
    def from_conf(conf, options):
        from sfepy.fem import Mesh, Domain, Integral

        domains = []
        for filename in filename_meshes:
            mesh = Mesh.from_file(filename)
            domain = Domain('domain_%s' % mesh.name.replace(data_dir, ''),
                            mesh)
            domain.create_region('Omega', 'all')
            domain.create_region('Gamma', 'vertices of surface', 'facet')

            domains.append(domain)

        integral = Integral('i', order=3)

        test = Test(domains=domains, integral=integral,
                    conf=conf, options=options)
        return test
Exemple #11
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    def from_conf(conf, options):
        mesh = Mesh.from_file("meshes/2d/square_unit_tri.mesh", prefix_dir=sfepy.data_dir)
        domain = Domain("domain", mesh)

        omega = domain.create_region("Omega", "all")

        field = H1NodalVolumeField("linear", nm.float64, "scalar", omega, approx_order=1)

        test = Test(conf=conf, options=options, omega=omega, field=field)
        return test
Exemple #12
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    def from_conf(conf, options):
        from sfepy.fem import Mesh, Domain, Integral

        domains = []
        for filename in filename_meshes:
            mesh = Mesh.from_file(filename)
            domain = Domain('domain_%s' % mesh.name.replace(data_dir, ''),
                            mesh)
            domain.create_region('Omega', 'all')
            domain.create_region('Gamma', 'nodes of surface')

            domains.append(domain)

        integrals = {'Omega' : Integral('iv', kind='v', order=3),
                     'Gamma' : Integral('is', kind='s', order=3)}

        test = Test(domains=domains, integrals=integrals,
                    conf=conf, options=options)
        return test
    def from_conf(conf, options):
        from sfepy.fem import Mesh, Domain, Integral

        domains = []
        for filename in filename_meshes:
            mesh = Mesh.from_file(filename)
            domain = Domain('domain_%s' % mesh.name.replace(data_dir, ''),
                            mesh)
            domain.create_region('Omega', 'all')
            domain.create_region('Gamma', 'vertices of surface', 'facet')

            domains.append(domain)

        integral = Integral('i', order=3)

        test = Test(domains=domains,
                    integral=integral,
                    conf=conf,
                    options=options)
        return test
    def from_conf(conf, options):
        mesh = Mesh.from_file('meshes/2d/square_unit_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = Domain('domain', mesh)

        omega = domain.create_region('Omega', 'all')

        field = Field('linear', nm.float64, 'scalar', omega,
                      space='H1', poly_space_base='lagrange', approx_order=1)

        test = Test(conf=conf, options=options, omega=omega, field=field)
        return test
Exemple #15
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    def from_conf(conf, options):
        mesh = Mesh.from_file('meshes/2d/square_unit_tri.mesh',
                              prefix_dir=sfepy.data_dir)
        domain = Domain('domain', mesh)

        omega = domain.create_region('Omega', 'all')

        field = H1NodalVolumeField('linear', nm.float64, 'scalar', omega,
                                   approx_order=1)

        test = Test(conf=conf, options=options, omega=omega, field=field)
        return test
Exemple #16
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    def test_normals(self):
        """
        Check orientations of surface normals on the reference elements.
        """
        import sfepy
        from sfepy.fem import Mesh, Domain, Integral
        from sfepy.fem.poly_spaces import PolySpace
        from sfepy.fem.mappings import SurfaceMapping
        from sfepy.linalg import normalize_vectors

        ok = True

        for geom in ['2_3', '2_4', '3_4', '3_8']:
            mesh = Mesh.from_file('meshes/elements/%s_1.mesh' % geom,
                                  prefix_dir=sfepy.data_dir)
            domain = Domain('domain', mesh)
            surface = domain.create_region('Surface', 'vertices of surface',
                                           'facet')
            domain.create_surface_group(surface)

            sd = domain.surface_groups[0][surface.name]

            coors = domain.get_mesh_coors()
            gel = domain.geom_els[geom].surface_facet
            ps = PolySpace.any_from_args('aux', gel, 1)

            mapping = SurfaceMapping(coors, sd.get_connectivity(), ps)

            integral = Integral('i', order=1)
            vals, weights = integral.get_qp(gel.name)

            # Evaluate just in the first quadrature point...
            geo = mapping.get_mapping(vals[:1], weights[:1])

            expected = expected_normals[geom].copy()
            normalize_vectors(expected)

            _ok = nm.allclose(expected,
                              geo.normal[:, 0, :, 0],
                              rtol=0.0,
                              atol=1e-14)
            self.report('%s: %s' % (geom, _ok))

            if not _ok:
                self.report('expected:')
                self.report(expected)
                self.report('actual:')
                self.report(geo.normal[:, 0, :, 0])

            ok = ok and _ok

        return ok
Exemple #17
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    def test_normals(self):
        """
        Check orientations of surface normals on the reference elements.
        """
        import sfepy
        from sfepy.fem import Mesh, Domain, Integral
        from sfepy.fem.poly_spaces import PolySpace
        from sfepy.fem.mappings import SurfaceMapping
        from sfepy.linalg import normalize_vectors

        ok = True

        for geom in ['2_3', '2_4', '3_4', '3_8']:
            mesh = Mesh.from_file('meshes/elements/%s_1.mesh' % geom,
                                  prefix_dir=sfepy.data_dir)
            domain = Domain('domain', mesh)
            surface = domain.create_region('Surface', 'nodes of surface')
            domain.create_surface_group(surface)

            sd = domain.surface_groups[0][surface.name]

            coors = domain.get_mesh_coors()
            gel = domain.geom_els[geom].surface_facet
            ps = PolySpace.any_from_args('aux', gel, 1)

            mapping = SurfaceMapping(coors, sd.get_connectivity(), ps)

            integral = Integral('i', order=1)
            vals, weights = integral.get_qp(gel.name)

            # Evaluate just in the first quadrature point...
            geo = mapping.get_mapping(vals[:1], weights[:1])

            expected = expected_normals[geom].copy()
            normalize_vectors(expected)

            _ok = nm.allclose(expected, geo.normal[:, 0, :, 0],
                              rtol=0.0, atol=1e-14)
            self.report('%s: %s' % (geom, _ok))

            if not _ok:
                self.report('expected:')
                self.report(expected)
                self.report('actual:')
                self.report(geo.normal[:, 0, :, 0])

            ok = ok and _ok

        return ok
Exemple #18
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    def test_invariance_qp(self):
        from sfepy import data_dir
        from sfepy.fem import (Mesh, Domain, H1NodalVolumeField, Variables,
                               Integral)
        from sfepy.terms import Term
        from sfepy.fem.mappings import get_physical_qps

        mesh = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')

        bbox = mesh.get_bounding_box()
        dd = bbox[1, :] - bbox[0, :]
        data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])

        variables = {
            'u': ('unknown field', 'scalar_tp', 0),
            'v': ('test field', 'scalar_tp', 'u'),
        }

        domain = Domain('domain', mesh)
        omega = domain.create_region('Omega', 'all')
        field = H1NodalVolumeField('scalar_tp',
                                   nm.float64,
                                   1,
                                   omega,
                                   approx_order=1)
        ff = {field.name: field}

        vv = Variables.from_conf(transform_variables(variables), ff)
        u = vv['u']
        u.set_from_mesh_vertices(data)

        integral = Integral('i', order=2)
        term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
        term.setup()
        val1, _ = term.evaluate(mode='qp')
        val1 = val1.ravel()

        qps = get_physical_qps(omega, integral)
        coors = qps.get_merged_values()

        val2 = u.evaluate_at(coors).ravel()

        self.report('max. difference:', nm.abs(val1 - val2).max())
        ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
        self.report('invariance in qp: %s' % ok)

        return ok
Exemple #19
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    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 test_invariance_qp(self):
        from sfepy import data_dir
        from sfepy.fem import (Mesh, Domain, H1NodalVolumeField,
                               Variables, Integral)
        from sfepy.terms import Term
        from sfepy.fem.mappings import get_physical_qps

        mesh = Mesh('source mesh', data_dir + '/meshes/3d/block.mesh')

        bbox = mesh.get_bounding_box()
        dd = bbox[1,:] - bbox[0,:]
        data = nm.sin(4.0 * nm.pi * mesh.coors[:,0:1] / dd[0]) \
               * nm.cos(4.0 * nm.pi * mesh.coors[:,1:2] / dd[1])

        variables = {
            'u'       : ('unknown field', 'scalar_tp', 0),
            'v'       : ('test field',    'scalar_tp', 'u'),
        }

        domain = Domain('domain', mesh)
        omega = domain.create_region('Omega', 'all')
        field = H1NodalVolumeField('scalar_tp', nm.float64, 1, omega,
                                   approx_order=1)
        ff = {field.name : field}

        vv = Variables.from_conf(transform_variables(variables), ff)
        u = vv['u']
        u.set_from_mesh_vertices(data)

        integral = Integral('i', order=2)
        term = Term.new('ev_volume_integrate(u)', integral, omega, u=u)
        term.setup()
        val1, _ = term.evaluate(mode='qp')
        val1 = val1.ravel()

        qps = get_physical_qps(omega, integral)
        coors = qps.get_merged_values()

        val2 = u.evaluate_at(coors).ravel()

        self.report('max. difference:', nm.abs(val1 - val2).max())
        ok = nm.allclose(val1, val2, rtol=0.0, atol=1e-12)
        self.report('invariance in qp: %s' % ok)

        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
Exemple #22
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    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
from sfepy.fem import (Mesh, Domain, Field,
                       FieldVariable,
                       Material, Integral,
                       Equation, Equations,
                       ProblemDefinition)
from sfepy.terms import Term
from sfepy.fem.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess import Viewer

mesh = Mesh.from_file('meshes/2d/square_tri2.mesh')
domain = Domain('domain', mesh)

omega = domain.create_region('Omega', 'all')
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')
Exemple #24
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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)
Exemple #25
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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)
            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)
Exemple #26
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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 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',
                                  'nodes in x < %.10f' % (min_x + eps))
    gamma2 = domain.create_region('Gamma2',
                                  'nodes in x > %.10f' % (max_x - eps))

    field = Field('fu', nm.float64, 'vector', omega,
                  space='H1', poly_space_base='lagrange', 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('-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()
Exemple #30
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)
Exemple #31
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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)
Exemple #32
0
    def test_linearization(self):
        from sfepy.base.base import Struct
        from sfepy.fem import Mesh, Domain, H1NodalVolumeField
        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 = H1NodalVolumeField('fu',
                                               nm.float64,
                                               dpn,
                                               omega,
                                               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 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
Exemple #34
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)
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()
Exemple #36
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)