api.feec

Classes

DiscreteDeRham(domain_h, *spaces)	A discrete de Rham sequence built over a single-patch geometry.
DiscreteDeRhamMultipatch(*, domain_h, spaces)	Represents the discrete de Rham sequence for multipatch domains.

Details

class DiscreteDeRham(domain_h, *spaces)

Bases: BasicDiscrete

A discrete de Rham sequence built over a single-patch geometry.

Parameters:

domain_hGeometry

The discretized domain, which is a single-patch geometry.

*spaceslist of FemSpace

The discrete spaces of the de Rham sequence.

Notes

• This constructor should not be called directly, but rather from the discretize_derham function in psydac.api.discretization.

property dim

Dimension of the physical and logical domains, which are assumed to be the same.

property domain_h

Discretized domain.

property spaces

Spaces of the proper de Rham sequence (excluding Hvec).

property V0

First space of the de Rham sequence : H1 space

property V1

Second space of the de Rham sequence : - 1d : L2 space - 2d : either Hdiv or Hcurl space - 3d : Hcurl space

property V2

Third space of the de Rham sequence : - 2d : L2 space - 3d : Hdiv space

property V3

Fourth space of the de Rham sequence : L2 space in 3d

property sequence

property H1vec

Vector-valued H1 space built as the Cartesian product of N copies of V0, where N is the dimension of the (logical) domain.

property mapping

The mapping from the logical space to the physical space.

property callable_mapping

The mapping as a callable.

projectors(*, kind='global', nquads=None)

Projectors mapping callable functions of the physical coordinates to a corresponding FemField object in the de Rham sequence.

Parameters:

kindstr

Type of the projection : at the moment, only global is accepted and returns geometric commuting projectors based on interpolation/histopolation for the de Rham sequence (GlobalProjector objects).

nquadslist(int) | tuple(int)

Number of quadrature points along each direction, to be used in Gauss quadrature rule for computing the (approximated) degrees of freedom.

Returns:

P0, …, Pncallables

Projectors that can be called on any callable function that maps from the physical space to R (scalar case) or R^d (vector case) and returns a FemField belonging to the i-th space of the de Rham sequence

derivatives(kind='femlinop')

conforming_projectors(kind='femlinop', mom_pres=False, p_moments=-1, hom_bc=False)

return the conforming projectors of the broken multi-patch space

Parameters:

p_moments<int>

The number of moments preserved by the projector.

hom_bc: <bool>

Apply homogenous boundary conditions if True

kind<str>

The kind of the projector, can be ‘femlinop’ or ‘linop’. - ‘femlinop’ returns a psydac FemLinearOperator (default) - ‘linop’ returns a psydac LinearOperator

Returns:

cP0, cP1, cP2Tuple of <psydac.fem.basic.FemLinearOperator> or <psydac.linalg.basic.LinearOperator>

The conforming projectors of each space and in desired form.

hodge_operator(space=None, dual=False, kind='femlinop', backend_language='python')

Returns the Hodge operator for the given space and specified kind.

Parameters:

spacestr or None

The space for which to return the Hodge operator, can be ‘V0’, ‘V1’, ‘V2’ or None. If None, returns a tuple with all three Hodge operators.

dualbool

If True, returns the dual Hodge operator.

kind<str>

The kind of the projector, can be ‘femlinop’ or ‘linop’. - ‘femlinop’ returns a psydac FemLinearOperator (default) - ‘linop’ returns a psydac LinearOperator

backend_languagestr

The backend used to accelerate the code, default is ‘python’.

Returns:

The Hodge operator of the space of the specified kind.

H<psydac.fem.basic.FemLinearOperator> or <psydac.linalg.basic.LinearOperator>

hodge_operators(dual=False, kind='femlinop', backend_language='python')

Returns the Hodge operators for the specified kind.

Parameters:

dualbool

If True, returns the dual Hodge operator.

kind<str>

The kind of the projector, can be ‘femlinop’ or ‘linop’. - ‘femlinop’ returns a psydac FemLinearOperator (default) - ‘linop’ returns a psydac LinearOperator

backend_languagestr

The backend used to accelerate the code, default is ‘python’.

Returns:

The Hodge operators of all spaces and of the specified kind.

class DiscreteDeRhamMultipatch(*, domain_h, spaces)

Bases: DiscreteDeRham

Represents the discrete de Rham sequence for multipatch domains.

It only works when the number of patches>1.

Parameters:

domain_h: <Geometry>

The discrete domain

spaces: <list,tuple>

The discrete spaces that are contained in the de Rham sequence

property H1vec

Vector-valued H1 space built as the Cartesian product of N copies of V0, where N is the dimension of the (logical) domain.

projectors(*, kind='global', nquads=None)

This method returns the patch-wise commuting projectors on the broken multi-patch space

Parameters:

kind: <str>

The projectors kind, can be global or local

nquads: <list,tuple>

The number of quadrature points.

Returns:

P0: <MultipatchGeometricProjector>

Patch wise H1 projector

P1: <MultipatchGeometricProjector>

Patch wise Hcurl projector

P2: <MultipatchGeometricProjector>

Patch wise L2 projector

Notes

• when applied to smooth functions they return conforming fields

• default ‘global projectors’ correspond to geometric interpolation/histopolation operators on Greville grids

• here ‘global’ is a patch-level notion, as the interpolation-type problems are solved on each patch independently