sfepy.discrete.common.fields module

class sfepy.discrete.common.fields.Field(**kwargs)[source]

Base class for fields.


Clear current reference mappings.


Create a mesh for evaluating the field. The default implementation returns None, because this mesh is for most fields the same as the one created by Field.create_mesh().

evaluate_at(coors, source_vals, 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 source DOF values corresponding to the field in the given coordinates using the field interpolation.

coorsarray, shape (n_coor, dim)

The coordinates the source values should be interpolated into.

source_valsarray, shape (n_nod, n_components)

The source DOF values corresponding to the field.

mode{‘val’, ‘grad’, ‘div’, ‘cauchy_strain’}, optional

The evaluation mode: the field value (default), the field value gradient, divergence, or cauchy strain.

strategy{‘general’, ‘convex’}, optional

The strategy for finding the elements that contain the coordinates. For convex meshes, the ‘convex’ strategy might be faster than the ‘general’ one.

close_limitfloat, optional

The maximum limit distance of a point from the closest element allowed for extrapolation.

get_cells_funcallable, optional

If given, a function with signature get_cells_fun(coors, cmesh, **kwargs) returning cells and offsets that potentially contain points with the coordinates coors. Applicable only when strategy is ‘general’. When not given, get_potential_cells() is used.

cacheStruct, optional

To speed up a sequence of evaluations, the field mesh and other data can be cached. Optionally, the cache can also contain the reference element coordinates as cache.ref_coors, cache.cells and cache.status, if the evaluation occurs in the same coordinates repeatedly. In that case the mesh related data are ignored. See Field.get_evaluate_cache().

ret_ref_coorsbool, optional

If True, return also the found reference element coordinates.

ret_statusbool, optional

If True, return also the enclosing cell status for each point.

ret_cellsbool, optional

If True, return also the cell indices the coordinates are in.


If False, reduce verbosity.


The interpolated values with shape (n_coor, n_components, 1) or gradients with shape (n_coor, n_components, dim) according to the mode. If ret_status is False, the values where the status is greater than one are set to numpy.nan.


The found reference element coordinates, if ret_ref_coors is True.


The cell indices, if ret_ref_coors or ret_cells or ret_status are True.


The status, if ret_ref_coors or ret_status are True, with the following meaning: 0 is success, 1 is extrapolation within close_limit, 2 is extrapolation outside close_limit, 3 is failure, 4 is failure due to non-convergence of the Newton iteration in tensor product cells. If close_limit is 0, then for the ‘general’ strategy the status 5 indicates points outside of the field domain that had no potential cells.

static from_args(name, dtype, shape, region, approx_order=1, space='H1', poly_space_base='lagrange')[source]

Create a Field subclass instance corresponding to a given space.


The field name.


The field data type: float64 or complex128.


The field shape: 1 or (1,) or ‘scalar’, space dimension (2, or (2,) or 3 or (3,)) or ‘vector’, or a tuple. The field shape determines the shape of the FE base functions and is related to the number of components of variables and to the DOF per node count, depending on the field kind.


The region where the field is defined.


The FE approximation order, e.g. 0, 1, 2, ‘1B’ (1 with bubble).


The function space name.


The name of polynomial space base.


Assumes one cell type for the whole region!

static from_conf(conf, regions)[source]

Create a Field subclass instance based on the configuration.

get_mapping(region, integral, integration, get_saved=False, return_key=False)[source]

For given region, integral and integration type, get a reference mapping, i.e. jacobians, element volumes and base function derivatives for Volume-type geometries, and jacobians, normals and base function derivatives for Surface-type geometries corresponding to the field approximation.

The mappings are cached in the field instance in mappings attribute. The mappings can be saved to mappings0 using Field.save_mappings. The saved mapping can be retrieved by passing get_saved=True. If the required (saved) mapping is not in cache, a new one is created.

geoPyCMapping instance

The reference mapping.

mappingFEMapping or IGMapping instance

The mapping.


The key of the mapping in mappings or mappings0.


Save current reference mappings to mappings0 attribute.

set_dofs(fun=0.0, region=None, dpn=None, warn=None)[source]

Set the values of DOFs in a given region using a function of space coordinates or value fun.

If fun is a function, the l2 projection that is global for all region facets is used to set the DOFs.

If dpn > 1, and fun is a function, it has to return the values point-by-point, i.e. all components in the first point, in the second point etc., concatenated to an array that is reshapable to the shape (n_point, dpn).

funfloat or array of length dpn or callable

The DOF values.


The region containing the DOFs.

dpnint, optional

The DOF-per-node count. If not given, the number of field components is used.

warnstr, optional

The warning message printed when the region selects no DOFs.

nodsarray, shape (n_dof,)

The field DOFs (or node indices) given by the region.

valsarray, shape (n_dof, dpn)

The values of the DOFs, node-by-node when raveled in C (row-major) order.


The nodal basis fields (lagrange) reimplement this function to set DOFs directly.

The hierarchical basis field (lobatto) do not support surface mappings, so also reimplement this function.

sfepy.discrete.common.fields.fields_from_conf(conf, regions)[source]

Parse the uniform approximation order value (str or int).

sfepy.discrete.common.fields.parse_shape(shape, dim)[source]

Setup extra data required for non-volume integration.