fem.basic

In order to avoid multiple inheritence, we define the base objects for Finite Elements as abstract classes that contain a topological member. This member can be used to specify the used data structure for example.

Classes

FemField(space[, coeffs])	Element of a finite element space V.
FemSpace()	Generic Finite Element space V.

Details

In order to avoid multiple inheritence, we define the base objects for Finite Elements as abstract classes that contain a topological member. This member can be used to specify the used data structure for example.

class FemSpace

Bases: object

Generic Finite Element space V.

A unique basis is associated to a FemSpace, i.e. FemSpace = Span( basis )

abstract property ldim

Number of dimensions in logical space, i.e. number of scalar logical coordinates.

abstract property periodic

Tuple of booleans: along each logical dimension, say if domain is periodic.

abstract property mapping

Mapping from logical coordinates ‘eta’ to physical coordinates ‘x’. If None, we assume identity mapping (hence x=eta).

abstract property vector_space

Topologically associated vector space.

abstract property is_product

Boolean flag that describes whether the space is a product space. If True, an element of this space can be decomposed into separate fields.

abstract property symbolic_space

Symbolic space.

abstract eval_field(field, *eta, weights=None)

Evaluate field at location(s) eta.

Parameters:

fieldFemField

Field object (element of FemSpace) to be evaluated.

etalist of float or numpy.ndarray

Evaluation point(s) in logical domain.

weightsStencilVector, optional

Weights of the basis functions, such that weights.space == field.coeffs.space.

Returns:

valuefloat or numpy.ndarray

Field value(s) at location(s) eta.

abstract eval_field_gradient(field, *eta, weights=None)

Evaluate field gradient at location(s) eta.

Parameters:

fieldFemField

Field object (element of FemSpace) to be evaluated.

etalist of float or numpy.ndarray

Evaluation point(s) in logical domain.

weightsStencilVector, optional

Weights of the basis functions, such that weights.space == field.coeffs.space.

Returns:

valuefloat or numpy.ndarray

Value(s) of field gradient at location(s) eta.

class FemField(space, coeffs=None)

Bases: object

Element of a finite element space V.

Parameters:

spacepsydac.fem.basic.FemSpace

Finite element space to which this field belongs.

coeffspsydac.linalg.basic.Vector (optional)

Vector of coefficients in finite element basis (by default assume zero vector).

property space

Finite element space to which this field belongs.

property coeffs

Coefficients that uniquely identify this field as a linear combination of the elements of the basis of a Finite element space.

Coefficients are stored into one element of the vector space in ‘self.space.vector_space’, which is topologically associated to the finite element space.

property fields

gradient(*eta, weights=None)

Evaluate gradient of weighted field at location identified by logical coordinates eta.

divergence(*eta, weights=None)

Evaluate divergence of weighted vector field at location identified by logical coordinates eta.

copy()