sfepy.discrete.common.global_interp module

Global interpolation functions.

sfepy.discrete.common.global_interp.get_potential_cells(coors, cmesh, centroids=None, extrapolate=True)

Get cells that potentially contain points with the given physical coordinates.

Parameters:

coorsarray

The physical coordinates.

cmeshCMesh instance

The cmesh defining the cells.

centroidsarray, optional

The centroids of the cells.

extrapolatebool

If True, even the points that are surely outside of the cmesh are considered and assigned potential cells.

Returns:

potential_cellsarray

The indices of the cells that potentially contain the points.

offsetsarray

The offsets into potential_cells for each point: a point ip is potentially in cells potential_cells[offsets[ip]:offsets[ip+1]].

sfepy.discrete.common.global_interp.get_ref_coors(field, coors, strategy='general', close_limit=0.1, get_cells_fun=None, cache=None, verbose=False)

Get reference element coordinates and elements corresponding to given physical coordinates.

Parameters:

fieldField instance

The field defining the approximation.

coorsarray

The physical coordinates.

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.

verbosebool

If False, reduce verbosity.

Returns:

ref_coorsarray

The reference coordinates.

cellsarray

The cell indices corresponding to the reference coordinates.

statusarray

The status: 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.

sfepy.discrete.common.global_interp.get_ref_coors_convex(field, coors, close_limit=0.1, cache=None, verbose=False)

Get reference element coordinates and elements corresponding to given physical coordinates.

Parameters:

fieldField instance

The field defining the approximation.

coorsarray

The physical coordinates.

close_limitfloat, optional

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

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.

verbosebool

If False, reduce verbosity.

Returns:

ref_coorsarray

The reference coordinates.

cellsarray

The cell indices corresponding to the reference coordinates.

statusarray

The status: 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.

Notes

Outline of the algorithm for finding xi such that X(xi) = P:

1. make inverse connectivity - for each vertex have cells it is in.

2. find the closest vertex V.

3. choose initial cell: i0 = first from cells incident to V.

4. while not P in C_i, change C_i towards P, check if P in new C_i.

sfepy.discrete.common.global_interp.get_ref_coors_general(field, coors, close_limit=0.1, get_cells_fun=None, cache=None, verbose=False)

Get reference element coordinates and elements corresponding to given physical coordinates.

Parameters:

fieldField instance

The field defining the approximation.

coorsarray

The physical coordinates.

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. 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.

verbosebool

If False, reduce verbosity.

Returns:

ref_coorsarray

The reference coordinates.

cellsarray

The cell indices corresponding to the reference coordinates.

statusarray

The status: 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 status 5 indicates points outside of the field domain that had no potential cells.