puncturedfem.Quad

1-dimensional quadrature object.

Attributes:

Name	Type	Description
type	str	Label for quadrature variant. Default is "trap", for trapezoid rule. Other options are "kress" and "martensen".
n	int	Interval sampled at 2*n points, excluding the last endpoint.
N	int	Number of points in the quadrature.
h	float	Step size.
t	np.ndarray	Sample points.
wgt	np.ndarray	Quadrature weights.

__init__(qtype='trap', n=16, p=7)

Initialize a Quad object.

Parameters:

Name	Type	Description	Default
qtype	str, optional	Label for Quadrature variant. Default is "trap".	'trap'
n	int, optional	Interval sampled at 2*n points, excluding the last endpoint. Default is 16.	16
p	int, optional	Kress parameter. Default is 7.	7

__repr__()

Return a string representation of the Quad object.

kress(p)

Kress quadrature.

Used to parameterize an Edge that terminates at corners. For a complete description, see: R. Kress, A Nyström method for boundary integral equations in domains with corners, Numer. Math., 58 (1990), pp. 145-161.

martensen()

Martensen Quadrature.

E. Martensen, Über eine Methode zum räumlichen Neumannschen Problem mit einer An-wendung für torusartige Berandungen, Acta Math., 109 (1963), pp. 75-135.

trap()

Trapezoid rule (default).

Technically, this defines a left-hand sum. But in our context, all functions are periodic, since we are parameterizing closed contours.