pg_utils.numerics.matrices.InnerProdQuad

class pg_utils.numerics.matrices.InnerProdQuad(inner_prod: InnerProduct1D, quad_method: str, *args, **kwargs)

Bases: object

Quadrature of inner product class generator for all inner product quadratures in 1D

Compared to the direct quadratures of the integral form, calculating quadratures in the notation of inner products “allows” one to drastically save of time of basis evaluation. When calculating the integral in the form of:

Integral(w(x)*Phi1(l, x)*Phi2(n, x), (x, -1, 1))

directly calculating the integral using K-point quadrature for 0 <= l,n <= N would need KN^2 evaluations of both Phi1 and Phi2; however, Phi1 and Phi2 in fact only need to be evaluated KN times. This reduces the complexity of evaluation from O(KN^2) to O(KN).

__init__()

Methods

__init__()