sfepy.discrete.dg.fields module

Fields for Discontinous Galerkin method

class sfepy.discrete.dg.fields.DGField(name, dtype, shape, region, space='H1', poly_space_basis='legendre', approx_order=1, integral=None)

Discontinuous Galerkin method approximation with Legendre basis.

Class for usage with DG terms, provides functionality for Discontinous Galerkin method like neighbour look up, projection to discontinuous basis and correct DOF treatment.

clear_facet_neighbour_idx_cache(region=None)

If region is None clear all!

Parameters:

regionsfepy.discrete.common.region.Region

If None clear all.

clear_facet_qp_basis()

Clears facet_qp_basis cache

clear_facet_vols_cache(region=None)

Clears facet volume cache for given region or all regions.

Parameters:

regionsfepy.discrete.common.region.Region

region to clear cache or None to clear all

clear_normals_cache(region=None)

Clears normals cache for given region or all regions.

Parameters:

regionsfepy.discrete.common.region.Region

region to clear cache or None to clear all

create_mapping(region, integral, integration, return_mapping=True)

Creates and returns mapping

Parameters:

regionsfepy.discrete.common.region.Region

integralIntegral

integrationstr

‘volume’ is only accepted option

return_mappingdefault True

(Default value = True)

Returns:

mappingFEMapping

create_output(dofs, var_name, dof_names=None, key=None, extend=True, fill_value=None, linearization=None)

Converts the DOFs corresponding to the field to a dictionary of output data usable by Mesh.write().

For 1D puts DOFs into vairables u_modal{0} … u_modal{n}, where n = approx_order and marks them for writing as cell data.

For 2+D puts dofs into name_cell_nodes and creates sturct with: mode = “cell_nodes”, data and iterpolation scheme.

Also get node values and adds them to dictionary as cell_nodes

Parameters:

dofsndarray, shape (n_nod, n_component)

The array of DOFs reshaped so that each column corresponds to one component.

var_namestr

The variable name corresponding to dofs.

dof_namestuple of str

The names of DOF components. (Default value = None)

keystr, optional

The key to be used in the output dictionary instead of the variable name. (Default value = None)

extendbool, not used

Extend the DOF values to cover the whole domain. (Default value = True)

fill_valuefloat or complex, not used

The value used to fill the missing DOF values if extend is True. (Default value = None)

linearizationStruct or None, not used

The linearization configuration for higher order approximations. (Default value = None)

Returns:

outdict

family_name = 'volume_DG_legendre_discontinuous'

get_bc_facet_idx(region)

Caches results in self.boundary_facet_local_idx

Parameters:

regionsfepy.discrete.common.region.Region

surface region defining BCs

Returns:

bc2bfindarray

index of cells on boundary along with corresponding facets

get_bc_facet_values(fun, region, ret_coors=False, diff=0)

Returns values of fun in facet QPs of the region

Parameters:

diff: derivative 0 or 1 supported

fun: Function value or values to set qps values to

regionsfepy.discrete.common.region.Region

boundary region

ret_coors: default False,

Return physical coors of qps in shape (n_cell, n_qp, dim).

Returns:

valsndarray

In shape (n_cell,) + (self.dim,) * diff + (n_qp,)

get_both_facet_basis_vals(state, region, derivative=None)

Returns values of the basis function in quadrature points on facets broadcasted to all cells inner to the element as well as outer ones along with weights for the qps broadcasted and transformed to elements.

Contains quick fix to flip facet QPs for right integration order.

Parameters:

stateused to get EPBC info

regionsfepy.discrete.common.region.Region for connectivity

derivativeif u need derivative

(Default value = None)

Returns:

outer_facet_basis_vals:

inner_facet_basis_vals:

shape (n_cell, n_el_nod, n_el_facet, n_qp) or

(n_cell, n_el_nod, n_el_facet, dim, n_qp)

when derivative is True or 1

whs: shape (n_cell, n_el_facet, n_qp)

get_both_facet_state_vals(state, region, derivative=None, reduce_nod=True)

Computes values of the variable represented by dofs in quadrature points located at facets, returns both values - inner and outer, along with weights.

Parameters:

statestate variable containing BC info

regionsfepy.discrete.common.region.Region

derivativecompute derivative if truthy,

compute n-th derivative if a number (Default value = None)

reduce_nodif False DOES NOT sum nodes into values at QPs

(Default value = True)

Returns:

inner_facet_values (n_cell, n_el_facets, n_qp),

outer facet values (n_cell, n_el_facets, n_qp), weights, if derivative is True:

inner_facet_values (n_cell, n_el_facets, dim, n_qp), outer_facet values (n_cell, n_el_facets, dim, n_qp)

get_cell_normals_per_facet(region)

Caches results, use clear_normals_cache to clear the cache.

Parameters:

region: sfepy.discrete.common.region.Region

Main region, must contain cells.

Returns:

normals: ndarray

normals of facets in array of shape (n_cell, n_el_facets, dim)

get_coor(nods=None)

Returns coors for matching nodes # TODO revise DG_EPBC and EPBC matching?

Parameters:

nods

if None use all nodes (Default value = None)

Returns:

coorsndarray

coors on surface

get_data_shape(integral, integration='cell', region_name=None)

Returns data shape (n_nod, n_qp, self.gel.dim, self.n_el_nod)

Parameters:

integralintegral used

integration

‘volume’ is only supported value (Default value = ‘volume’)

region_namenot used

(Default value = None)

Returns:

data_shapetuple

get_dofs_in_region(region, merge=True)

Return indices of DOFs that belong to the given region.

Not Used in BC treatment

Parameters:

regionsfepy.discrete.common.region.Region

mergebool

merge dof tuple into one numpy array, default True

Returns:

dofsndarray

get_econn(conn_type, region, trace_region=None)

Getter for econn

Parameters:

conn_typetuple or string

(‘cell’, dim) or ‘cell’ is only supported

regionsfepy.discrete.common.region.Region

trace_regionignored

(Default value = None)

Returns:

econnndarray

connectivity information

get_facet_basis(derivative=False, basis_only=False)

Returns values of basis in facets quadrature points, data shape is a bit crazy right now:

(number of qps, 1, n_el_facets, 1, n_el_nod)

end for derivatine:

(1, number of qps, (dim,) * derivative, n_el_facets, 1, n_el_nod)

Parameters:

derivative: truthy or integer

basis_only: do not return weights

Returns:

facet_bfndarray

values of basis functions in facet qps

weightsndarray, optionally

weights of qps

get_facet_neighbor_idx(region=None, eq_map=None)

Returns index of cell neighbours sharing facet, along with local index of the facet within neighbour, also treats periodic boundary conditions i.e. plugs correct neighbours for cell on periodic boundary. Where there are no neighbours specified puts -1 instead of neighbour and facet id

Cashes neighbour index in self.facet_neighbours

Parameters:

regionsfepy.discrete.common.region.Region

Main region, must contain cells.

eq_map

eq_map from state variable containing information on EPBC and DG EPBC. (Default value = None)

Returns:

facet_neighboursndarray

Shape is

(n_cell, n_el_facet, 2),

first value is index of the neighbouring cell, the second is index of the facet in said nb. cell.

get_facet_qp()

Returns quadrature points on all facets of the reference element in array of shape (n_qp, 1 , n_el_facets, dim)

Returns:

qpsndarray

quadrature points

weightsndarray

Still needs to be transformed to actual facets!

get_facet_vols(region)

Caches results, use clear_facet_vols_cache to clear the cache

Parameters:

regionsfepy.discrete.common.region.Region

Returns:

vols_out: ndarray

volumes of the facets by cells shape (n_cell, n_el_facets, 1)

get_nodal_values(dofs, region, ref_nodes=None)

Computes nodal representation of the DOFs

Parameters

dofsarray_like

dofs to transform to nodes

region : ignored

ref_nodes:

reference node to use instead of default qps

Parameters:

dofsarray_like

regionRegion

ref_nodesarray_like

(Default value = None)

Returns:

nodesndarray

nodal_valsndarray

static get_region_info(region)

Extracts information about region needed in various methods of DGField

Parameters:

regionsfepy.discrete.common.region.Region

Returns:

dim, n_cell, n_el_facets

is_surface = False

set_cell_dofs(fun=0.0, region=None, dpn=None, warn=None)

Compute projection of fun onto the basis, in main region, alternatively set DOFs directly to provided value or values

Parameters:

funcallable, scallar or array corresponding to dofs

(Default value = 0.0)

regionsfepy.discrete.common.region.Region

region to set DOFs on (Default value = None)

dpnnumber of dofs per element

(Default value = None)

warnnot used

(Default value = None)

Returns:

nodsndarray

valsndarray

set_dofs(fun=0.0, region=None, dpn=None, warn=None)

Compute projection of fun into the basis, alternatively set DOFs directly to provided value or values either in main volume region or in boundary region.

Parameters:

funcallable, scalar or array corresponding to dofs

(Default value = 0.0)

regionsfepy.discrete.common.region.Region

region to set DOFs on (Default value = None)

dpnnumber of dofs per element

(Default value = None)

warn

(Default value = None)

Returns:

nodsndarray

valsndarray

set_facet_dofs(fun, region, dpn, warn)

Compute projection of fun onto the basis on facets, alternatively set DOFs directly to provided value or values

Parameters:

funcallable, scalar or array corresponding to dofs

regionsfepy.discrete.common.region.Region

region to set DOFs on

dpnint

number of dofs per element

warn

not used

Returns:

nodsndarray

valsndarray

setup_extra_data(info)

This is called in create_adof_conns(conn_info, var_indx=None,

active_only=True, verbose=True)

for each variable but has no effect.

Parameters:

info

set to self.info

sfepy.discrete.dg.fields.get_gel(region)

Parameters:

regionsfepy.discrete.common.region.Region

Returns:

gel

base geometry element of the region

sfepy.discrete.dg.fields.get_raveler(n_el_nod, n_cell)

Returns function for raveling i.e. packing dof data from two dimensional array of shape (n_cell, n_el_nod, 1) to (n_el_nod*n_cell, 1)

The raveler returns view into the input array.

Parameters:

n_el_nod

param n_el_nod, n_cell: expected dimensions of dofs array

n_cellint

Returns:

ravelcallable

sfepy.discrete.dg.fields.get_unraveler(n_el_nod, n_cell)

Returns function for unraveling i.e. unpacking dof data from serialized array from shape (n_el_nod*n_cell, 1) to (n_cell, n_el_nod, 1).

The unraveler returns non-writeable view into the input array.

Parameters:

n_el_nodint

expected dimensions of dofs array

n_cellint

Returns:

unravelcallable