Element

The element module defines reference elements such as the QuadElement and TriangularElement, but also more exotic objects like the TrimmedElement. A set of (interconnected) elements together form a nutils.topology. Elements have edges and children (for refinement), which are in turn elements and map onto self by an affine transformation. They also have a well defined reference coordinate system, and provide pointsets for purposes of integration and sampling.

class nutils.element.TrimmedIScheme(levelset, ischeme, maxrefine, finestscheme='uniform1', degree=3, retain=None)

integration scheme for truncated elements

generate_ischeme(elem, maxrefine)

generate integration scheme

class nutils.element.Transformation(fromdim, todim)

transform points

eval(points)

evaluate

class nutils.element.SliceTransformation(fromdim, start=None, stop=None, step=None)

take slice

class nutils.element.AffineTransformation(offset, transform)

affine transformation

invtrans

inverse transformation

det

determinant

nest(other)

merge transformations

get_transform()

get transformation copy

invapply(coords)

apply inverse transformation

class nutils.element.Element(ndims, vertices, index=None, parent=None, context=None, interface=None)

Element base class.

Represents the topological shape.

neighbor(other)

level of neighborhood; 0=self

eval(where)

get points

zoom(elemset, points)

zoom points

intersected(levelset, lscheme, evalrefine=0)

check levelset intersection:

+1 for levelset > 0 everywhere -1 for levelset < 0 everywhere =0 for intersected element

trim(levelset, maxrefine, lscheme, finestscheme, evalrefine)

trim element along levelset

get_simplices(maxrefine)

divide in simple elements

class nutils.element.ProductElement(elem1, elem2)

element product

orientation

Neighborhood of elem1 and elem2 and transformations to get mutual overlap in right location. Returns 3-element tuple: * neighborhood, as given by Element.neighbor(), * transf1, required rotation of elem1 map: {0:0, 1:pi/2, 2:pi, 3:3*pi/2}, * transf2, required rotation of elem2 map (is indep of transf1 in UnstructuredTopology.

eval(where)

get integration scheme

class nutils.element.TrimmedElement(elem, levelset, maxrefine, lscheme, finestscheme, evalrefine, parent, vertices)

trimmed element

children

all 1x refined elements

edge(iedge)

get_simplices(maxrefine)

divide in simple elements

class nutils.element.QuadElement(ndims, vertices, index=None, parent=None, context=None, interface=None)

quadrilateral element

children_by(N)

divide element by n

children

all 1x refined elements

ribbons

ribbons

edge(iedge)

refine(n)

refine n times

select_contained(points, eps=0)

select points contained in element

class nutils.element.TriangularElement(vertices, index=None, parent=None, context=None)

Triangular element. Conventions: * reference elem: unit simplex {(x,y) | x>0, y>0, x+y<1} * vertex numbering: {(1,0):0, (0,1):1, (0,0):2} * edge numbering: {bottom:0, slanted:1, left:2} * edge local coords run counter-clockwise.

children

all 1x refined elements

edge(iedge)

refined(n)

refine

select_contained(points, eps=0)

select points contained in element

class nutils.element.TetrahedronElement(vertices, index=None, parent=None, context=None)

tetrahedron element

children

all 1x refined elements

edge(iedge)

refined(n)

refine

select_contained(points, eps=0)

select points contained in element

class nutils.element.StdElem

stdelem base class

extract(extraction)

apply extraction matrix

class nutils.element.PolyProduct

multiply standard elements

class nutils.element.PolyLine(poly)

polynomial on a line

classmethod bernstein_poly(degree)

bernstein polynomial coefficients

classmethod spline_poly(p, n)

spline polynomial coefficients

classmethod spline(degree, nelems, periodic=False, neumann=0, curvature=False)

spline elements, any amount

extract(extraction)

apply extraction

class nutils.element.PolyTriangle

poly triangle (linear for now) conventions: dof numbering as vertices, see TriangularElement docstring.

class nutils.element.BubbleTriangle

linear triangle + bubble function conventions: dof numbering as vertices (see TriangularElement docstring), then barycenter.

class nutils.element.ExtractionWrapper(stdelem, extraction)

extraction wrapper