sfepy.discrete.fem.fields_base module¶
Notes¶
Important attributes of continuous (order > 0) Field
and
SurfaceField
instances:
- vertex_remap : econn[:, :n_vertex] = vertex_remap[conn]
- vertex_remap_i : conn = vertex_remap_i[econn[:, :n_vertex]]
where conn is the mesh vertex connectivity, econn is the region-local field connectivity.
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class
sfepy.discrete.fem.fields_base.
FEField
(name, dtype, shape, region, approx_order=1)[source]¶ Base class for finite element fields.
Notes
- interps and hence node_descs are per region (must have single geometry!)
Field shape information:
shape
- the shape of the base functions in a pointn_components
- the number of DOFs per FE nodeval_shape
- the shape of field value (the product of DOFs and base functions) in a point
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create_mapping
(region, integral, integration, return_mapping=True)[source]¶ Create a new reference mapping.
Compute jacobians, element volumes and base function derivatives for Volume-type geometries (volume mappings), and jacobians, normals and base function derivatives for Surface-type geometries (surface mappings).
Notes
- surface mappings are defined on the surface region
- surface mappings require field order to be > 0
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create_mesh
(extra_nodes=True)[source]¶ Create a mesh from the field region, optionally including the field extra nodes.
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create_output
(dofs, var_name, dof_names=None, key=None, extend=True, fill_value=None, linearization=None)[source]¶ Convert the DOFs corresponding to the field to a dictionary of output data usable by Mesh.write().
Parameters: dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds to one component.
var_name : str
The variable name corresponding to dofs.
dof_names : tuple of str
The names of DOF components.
key : str, optional
The key to be used in the output dictionary instead of the variable name.
extend : bool
Extend the DOF values to cover the whole domain.
fill_value : float or complex
The value used to fill the missing DOF values if extend is True.
linearization : Struct or None
The linearization configuration for higher order approximations.
Returns: out : dict
The output dictionary.
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extend_dofs
(dofs, fill_value=None)[source]¶ Extend DOFs to the whole domain using the fill_value, or the smallest value in dofs if fill_value is None.
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get_connectivity
(region, integration, is_trace=False)[source]¶ Convenience alias to Field.get_econn(), that is used in some terms.
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get_coor
(nods=None)[source]¶ Get coordinates of the field nodes.
Parameters: nods : array, optional
The indices of the required nodes. If not given, the coordinates of all the nodes are returned.
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get_data_shape
(integral, integration='volume', region_name=None)[source]¶ Get element data dimensions.
Parameters: integral : Integral instance
The integral describing used numerical quadrature.
integration : ‘volume’, ‘surface’, ‘surface_extra’, ‘point’ or ‘custom’
The term integration type.
region_name : str
The name of the region of the integral.
Returns: data_shape : 4 ints
The (n_el, n_qp, dim, n_en) for volume shape kind, (n_fa, n_qp, dim, n_fn) for surface shape kind and (n_nod, 0, 0, 1) for point shape kind.
Notes
- n_el, n_fa = number of elements/facets
- n_qp = number of quadrature points per element/facet
- dim = spatial dimension
- n_en, n_fn = number of element/facet nodes
- n_nod = number of element nodes
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get_dofs_in_region
(region, merge=True)[source]¶ Return indices of DOFs that belong to the given region and group.
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get_evaluate_cache
(cache=None, share_geometry=False, verbose=False)[source]¶ Get the evaluate cache for
Variable.evaluate_at()
.Parameters: cache : Struct instance, optional
Optionally, use the provided instance to store the cache data.
share_geometry : bool
Set to True to indicate that all the evaluations will work on the same region. Certain data are then computed only for the first probe and cached.
verbose : bool
If False, reduce verbosity.
Returns: cache : Struct instance
The evaluate cache.
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get_qp
(key, integral)[source]¶ Get quadrature points and weights corresponding to the given key and integral. The key is ‘v’ or ‘s#’, where # is the number of face vertices.
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get_true_order
()[source]¶ Get the true approximation order depending on the reference element geometry.
For example, for P1 (linear) approximation the true order is 1, while for Q1 (bilinear) approximation in 2D the true order is 2.
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interp_to_qp
(dofs)[source]¶ Interpolate DOFs into quadrature points.
The quadrature order is given by the field approximation order.
Parameters: dofs : array
The array of DOF values of shape (n_nod, n_component).
Returns: data_qp : array
The values interpolated into the quadrature points.
integral : Integral
The corresponding integral defining the quadrature points.
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linearize
(dofs, min_level=0, max_level=1, eps=0.0001)[source]¶ Linearize the solution for post-processing.
Parameters: dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns: mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of mesh.
levels : array of ints
The refinement level used for each element group.
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class
sfepy.discrete.fem.fields_base.
H1Mixin
(**kwargs)[source]¶ Methods of fields specific to H1 space.
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class
sfepy.discrete.fem.fields_base.
SurfaceField
(name, dtype, shape, region, approx_order=1)[source]¶ Finite element field base class over surface (element dimension is one less than space dimension).
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average_qp_to_vertices
(data_qp, integral)[source]¶ Average data given in quadrature points in region elements into region vertices.
u_n = \sum_e (u_{e,avg} * area_e) / \sum_e area_e = \sum_e \int_{area_e} u / \sum area_e
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class
sfepy.discrete.fem.fields_base.
VolumeField
(name, dtype, shape, region, approx_order=1)[source]¶ Finite element field base class over volume elements (element dimension equals space dimension).
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average_qp_to_vertices
(data_qp, integral)[source]¶ Average data given in quadrature points in region elements into region vertices.
u_n = \sum_e (u_{e,avg} * volume_e) / \sum_e volume_e = \sum_e \int_{volume_e} u / \sum volume_e
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sfepy.discrete.fem.fields_base.
create_expression_output
(expression, name, primary_field_name, fields, materials, variables, functions=None, mode='eval', term_mode=None, extra_args=None, verbose=True, kwargs=None, min_level=0, max_level=1, eps=0.0001)[source]¶ Create output mesh and data for the expression using the adaptive linearizer.
Parameters: expression : str
The expression to evaluate.
name : str
The name of the data.
primary_field_name : str
The name of field that defines the element groups and polynomial spaces.
fields : dict
The dictionary of fields used in variables.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
functions : Functions instance, optional
The user functions for materials etc.
mode : one of ‘eval’, ‘el_avg’, ‘qp’
The evaluation mode - ‘qp’ requests the values in quadrature points, ‘el_avg’ element averages and ‘eval’ means integration over each term region.
term_mode : str
The term call mode - some terms support different call modes and depending on the call mode different values are returned.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable instance)) to be used in the expression.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns: out : dict
The output dictionary.
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sfepy.discrete.fem.fields_base.
eval_nodal_coors
(coors, mesh_coors, region, poly_space, geom_poly_space, econn, only_extra=True)[source]¶ Compute coordinates of nodes corresponding to poly_space, given mesh coordinates and geom_poly_space.