Quadrature

Integration rules on canonical reference cells. More...

Collaboration diagram for Quadrature:

Files
file	QuadratureRule.cpp
	Internal construction and structural validation for quadrature rules.
file	QuadratureRule.h
	Value type for reference-space quadrature rules.

Classes
class	svmp::FE::quadrature::QuadratureRule
	Owning value type for quadrature rules on canonical reference cells. More...

Typedefs
using	svmp::FE::quadrature::QuadPoint = math::Vector< double, 3 >
	Three-component coordinate used for every reference quadrature point.

Detailed Description

Integration rules on canonical reference cells.

A QuadratureRule owns ordered reference coordinates and weights for

\[ \int_{\hat K} f(\hat x)\,d\hat x \approx \sum_q w_q f(\hat x_q). \]

Supported families use these canonical reference cells:

Family	Reference cell	Measure
Point	\((0,0,0)\)	\(1\)
Line	\([-1,1]\)	\(2\)
Triangle	\(\{(x,y):x,y\geq0,\ x+y\leq1\}\)	\(1/2\)
Quad	\([-1,1]^2\)	\(4\)
Tetra	\(\{(x,y,z):x,y,z\geq0,\ x+y+z\leq1\}\)	\(1/6\)
Hex	\([-1,1]^3\)	\(8\)
Wedge	unit triangle \(\times[-1,1]\)	\(1\)

The family therefore determines both reference dimension and cell measure. Quadrature points are not required to lie inside the reference cell. Generating code is responsible for verifying weight normalization and declared polynomial exactness through analytic moment tests.

Typedef Documentation

QuadPoint

using svmp::FE::quadrature::QuadPoint = typedef math::Vector<double, 3>

Three-component coordinate used for every reference quadrature point.

Only the first QuadratureRule::dimension() components are active; remaining components must be zero.