sfepy.discrete.variables module¶
Classes of variables for equations/terms.
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class
sfepy.discrete.variables.
FieldVariable
(name, kind, field, order=None, primary_var_name=None, special=None, flags=None, history=None, **kwargs)[source]¶ A finite element field variable.
field .. field description of variable (borrowed)
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apply_ebc
(vec, offset=0, force_values=None)[source]¶ Apply essential (Dirichlet) and periodic boundary conditions to vector vec, starting at offset.
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apply_ic
(vec, offset=0, force_values=None)[source]¶ Apply initial conditions conditions to vector vec, starting at offset.
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create_output
(vec=None, key=None, extend=True, fill_value=None, linearization=None)[source]¶ Convert the DOF vector to a dictionary of output data usable by Mesh.write().
Parameters: - vec : array, optional
An alternative DOF vector to be used instead of the variable DOF vector.
- 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.
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equation_mapping
(bcs, var_di, ts, functions, problem=None, warn=False)[source]¶ Create the mapping of active DOFs from/to all DOFs.
Sets n_adof.
Returns: - active_bcs : set
The set of boundary conditions active in the current time.
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evaluate
(mode=’val’, region=None, integral=None, integration=None, step=0, time_derivative=None, is_trace=False, dt=None, bf=None)[source]¶ Evaluate various quantities related to the variable according to mode in quadrature points defined by integral.
The evaluated data are cached in the variable instance in evaluate_cache attribute.
Parameters: - mode : one of ‘val’, ‘grad’, ‘div’, ‘cauchy_strain’
The evaluation mode.
- region : Region instance, optional
The region where the evaluation occurs. If None, the underlying field region is used.
- integral : Integral instance, optional
The integral defining quadrature points in which the evaluation occurs. If None, the first order volume integral is created. Must not be None for surface integrations.
- integration : ‘volume’, ‘surface’, ‘surface_extra’, or ‘point’
The term integration type. If None, it is derived from integral.
- step : int, default 0
The time step (0 means current, -1 previous, …).
- time_derivative : None or ‘dt’
If not None, return time derivative of the data, approximated by the backward finite difference.
- is_trace : bool, default False
Indicate evaluation of trace of the variable on a boundary region.
- dt : float, optional
The time step to be used if derivative is ‘dt’. If None, the dt attribute of the variable is used.
- bf : Base function, optional
The base function to be used in ‘val’ mode.
Returns: - out : array
The 4-dimensional array of shape (n_el, n_qp, n_row, n_col) with the requested data, where n_row, n_col depend on mode.
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evaluate_at
(coors, mode=’val’, strategy=’general’, close_limit=0.1, get_cells_fun=None, cache=None, ret_cells=False, ret_status=False, ret_ref_coors=False, verbose=False)[source]¶ Evaluate the variable in the given physical coordinates. Convenience wrapper around
Field.evaluate_at()
, see its docstring for more details.
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get_data_shape
(integral, integration=’volume’, region_name=None)[source]¶ Get element data dimensions for given approximation.
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 : 5 ints
The (n_el, n_qp, dim, n_en, n_comp) for volume shape kind, (n_fa, n_qp, dim, n_fn, n_comp) for surface shape kind and (n_nod, 0, 0, 1, n_comp) 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_comp = number of variable components in a point/node
- n_nod = number of element nodes
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get_dof_conn
(dc_type, is_trace=False)[source]¶ Get active dof connectivity of a variable.
Notes
The primary and dual variables must have the same Region.
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get_full
(r_vec, r_offset=0, force_value=None, vec=None, offset=0)[source]¶ Get the full DOF vector satisfying E(P)BCs from a reduced DOF vector.
Notes
The reduced vector starts in r_vec at r_offset. Passing a force_value overrides the EBC values. Optionally, vec argument can be provided to store the full vector (in place) starting at offset.
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get_interp_coors
(strategy=’interpolation’, interp_term=None)[source]¶ Get the physical coordinates to interpolate into, based on the strategy used.
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get_mapping
(region, integral, integration, get_saved=False, return_key=False)[source]¶ Get the reference element mapping of the underlying field.
See also
sfepy.discrete.fem.fields.Field.get_mapping
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get_reduced
(vec, offset=0, follow_epbc=False)[source]¶ Get the reduced DOF vector, with EBC and PBC DOFs removed.
Notes
The full vector starts in vec at offset. If ‘follow_epbc’ is True, values of EPBC master DOFs are not simply thrown away, but added to the corresponding slave DOFs, just like when assembling. For vectors with state (unknown) variables it should be set to False, for assembled vectors it should be set to True.
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get_state_in_region
(region, reshape=True, step=0)[source]¶ Get DOFs of the variable in the given region.
Parameters: - region : Region
The selected region.
- reshape : bool
If True, reshape the DOF vector to a 2D array with the individual components as columns. Otherwise a 1D DOF array of the form [all DOFs in region node 0, all DOFs in region node 1, …] is returned.
- step : int, default 0
The time step (0 means current, -1 previous, …).
Returns: - out : array
The selected DOFs.
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has_same_mesh
(other)[source]¶ Returns: - flag : int
The flag can be either ‘different’ (different meshes), ‘deformed’ (slightly deformed same mesh), or ‘same’ (same).
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invalidate_evaluate_cache
(step=0)[source]¶ Invalidate variable data in evaluate cache for time step given by step (0 is current, -1 previous, …).
This should be done, for example, prior to every nonlinear solver iteration.
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save_as_mesh
(filename)[source]¶ Save the field mesh and the variable values into a file for visualization. Only the vertex values are stored.
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set_from_function
(fun, step=0)[source]¶ Set the variable data (the vector of DOF values) using a function of space coordinates.
Parameters: - fun : callable
The function of coordinates returning DOF values of shape (n_coor, n_components).
- step : int, optional
The time history step, 0 (default) = current.
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set_from_other
(other, strategy=’projection’, close_limit=0.1)[source]¶ Set the variable using another variable. Undefined values (e.g. outside the other mesh) are set to numpy.nan, or extrapolated.
Parameters: - strategy : ‘projection’ or ‘interpolation’
The strategy to set the values: the L^2 orthogonal projection (not implemented!), or a direct interpolation to the nodes (nodal elements only!)
Notes
If the other variable uses the same field mesh, the coefficients are set directly.
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class
sfepy.discrete.variables.
Variable
(name, kind, order=None, primary_var_name=None, special=None, flags=None, **kwargs)[source]¶ -
advance
(ts)[source]¶ Advance in time the DOF state history. A copy of the DOF vector is made to prevent history modification.
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get_dual
()[source]¶ Get the dual variable.
Returns: - var : Variable instance
The primary variable for non-state variables, or the dual variable for state variables.
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get_primary
()[source]¶ Get the corresponding primary variable.
Returns: - var : Variable instance
The primary variable, or self for state variables or if primary_var_name is None, or None if no other variables are defined.
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set_data
(data=None, indx=None, step=0, preserve_caches=False)[source]¶ Set data (vector of DOF values) of the variable.
Parameters: - data : array
The vector of DOF values.
- indx : int, optional
If given, data[indx] is used.
- step : int, optional
The time history step, 0 (default) = current.
- preserve_caches : bool
If True, do not invalidate evaluate caches of the variable.
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class
sfepy.discrete.variables.
Variables
(variables=None)[source]¶ Container holding instances of Variable.
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apply_ebc
(vec, force_values=None)[source]¶ Apply essential (Dirichlet) and periodic boundary conditions defined for the state variables to vector vec.
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apply_ic
(vec, force_values=None)[source]¶ Apply initial conditions defined for the state variables to vector vec.
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check_vector_size
(vec, stripped=False)[source]¶ Check whether the shape of the DOF vector corresponds to the total number of DOFs of the state variables.
Parameters: - vec : array
The vector of DOF values.
- stripped : bool
If True, the size of the DOF vector should be reduced, i.e. without DOFs fixed by boundary conditions.
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equation_mapping
(ebcs, epbcs, ts, functions, problem=None, active_only=True)[source]¶ Create the mapping of active DOFs from/to all DOFs for all state variables.
Parameters: - ebcs : Conditions instance
The essential (Dirichlet) boundary conditions.
- epbcs : Conditions instance
The periodic boundary conditions.
- ts : TimeStepper instance
The time stepper.
- functions : Functions instance
The user functions for boundary conditions.
- problem : Problem instance, optional
The problem that can be passed to user functions as a context.
- active_only : bool
If True, the active DOF info
self.adi
uses the reduced (active DOFs only) numbering. Otherwise it is the same asself.di
.
Returns: - active_bcs : set
The set of boundary conditions active in the current time.
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static
from_conf
(conf, fields)[source]¶ This method resets the variable counters for automatic order!
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get_dual_names
()[source]¶ Get names of pairs of dual variables.
Returns: - duals : dict
The dual names as virtual name : state name pairs.
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get_state_parts
(vec=None)[source]¶ Return parts of a state vector corresponding to individual state variables.
Parameters: - vec : array, optional
The state vector. If not given, then the data stored in the variables are returned instead.
Returns: - out : dict
The dictionary of the state parts.
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link_duals
()[source]¶ Link state variables with corresponding virtual variables, and assign link to self to each variable instance.
Usually, when solving a PDE in the weak form, each state variable has a corresponding virtual variable.
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make_full_vec
(svec, force_value=None, vec=None)[source]¶ Make a full DOF vector satisfying E(P)BCs from a reduced DOF vector.
Parameters: - svec : array
The reduced DOF vector.
- force_value : float, optional
Passing a force_value overrides the EBC values.
- vec : array, optional
If given, the buffer for storing the result (zeroed).
Returns: - vec : array
The full DOF vector.
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set_adof_conns
(adof_conns)[source]¶ Set all active DOF connectivities to self as well as relevant sub-dicts to the individual variables.
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set_data
(data, step=0, ignore_unknown=False, preserve_caches=False)[source]¶ Set data (vectors of DOF values) of variables.
Parameters: - data : array
The state vector or dictionary of {variable_name : data vector}.
- step : int, optional
The time history step, 0 (default) = current.
- ignore_unknown : bool, optional
Ignore unknown variable names if data is a dict.
- preserve_caches : bool
If True, do not invalidate evaluate caches of variables.
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set_from_state
(var_names, state, var_names_state)[source]¶ Set variables with names in var_names from state variables with names in var_names_state using DOF values in the state vector state.
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setup_dtype
()[source]¶ Setup data types of state variables - all have to be of the same data type, one of nm.float64 or nm.complex128.
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setup_lcbc_operators
(lcbcs, ts=None, functions=None)[source]¶ Prepare linear combination BC operator matrix and right-hand side vector.
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state_to_output
(vec, fill_value=None, var_info=None, extend=True, linearization=None)[source]¶ Convert a state vector to a dictionary of output data usable by Mesh.write().
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strip_state_vector
(vec, follow_epbc=False, svec=None)[source]¶ Get the reduced DOF vector, with EBC and PBC DOFs removed.
Notes
If ‘follow_epbc’ is True, values of EPBC master dofs are not simply thrown away, but added to the corresponding slave dofs, just like when assembling. For vectors with state (unknown) variables it should be set to False, for assembled vectors it should be set to True.
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sfepy.discrete.variables.
create_adof_conn
(eq, conn, dpn, offset)[source]¶ Given a node connectivity, number of DOFs per node and equation mapping, create the active dof connectivity.
Locally (in a connectivity row), the DOFs are stored DOF-by-DOF (u_0 in all local nodes, u_1 in all local nodes, …).
Globally (in a state vector), the DOFs are stored node-by-node (u_0, u_1, …, u_X in node 0, u_0, u_1, …, u_X in node 1, …).
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sfepy.discrete.variables.
create_adof_conns
(conn_info, var_indx=None, active_only=True, verbose=True)[source]¶ Create active DOF connectivities for all variables referenced in conn_info.
If a variable has not the equation mapping, a trivial mapping is assumed and connectivity with all DOFs active is created.
DOF connectivity key is a tuple
(primary variable name, region name, type, is_trace flag)
.Notes
If active_only is False, the DOF connectivities contain all DOFs, with the E(P)BC-constrained ones stored as -1 - <DOF number>, so that the full connectivities can be reconstructed for the matrix graph creation.
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sfepy.discrete.variables.
expand_basis
(basis, dpn)[source]¶ Expand basis for variables with several components (DOFs per node), in a way compatible with
create_adof_conn()
, according to dpn (DOF-per-node count).