test_Quadrature.cpp File Reference

Comprehensive doctest-based unit tests for numerical quadrature accuracy. More...

#include "doctest.h"
#include "Geom/Quadrature.hpp"
#include "Geom/Elements.hpp"
#include "Geom/BaseFunction.hpp"
#include <cmath>
#include <array>
#include <iostream>

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Classes
struct	TestConfig
struct	TestCase

Macros
#define	DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN

Functions
std::vector< std::array< int, 3 > >	GetTaylorBasisMonomials (int dim, int maxOrder)
	Get the list of Taylor basis monomial exponents up to given order.
t_real	EvalMonomial (const tPoint &p, int a, int b=0, int c=0)
	Evaluate a monomial x^a * y^b * z^c at point p.
t_real	ExactMonomialIntegral (ParamSpace ps, int a, int b=0, int c=0)
	Compute exact integral of monomial over parametric reference element.
t_real	QuadratureMonomialIntegral (ParamSpace ps, int int_order, int a, int b=0, int c=0)
	Numerically integrate a monomial using quadrature.
ParamSpace	GetParamSpaceFromElement (ElemType t)
	Get parametric space from element type for testing.
	TEST_CASE ("Quadrature: scheme constants are valid")
	TEST_CASE ("Quadrature: weight sums equal reference element volumes")
	TEST_CASE ("Quadrature: Line integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Quad integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Hex integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Triangle integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Tetrahedron integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Prism integrates polynomials up to expected order")
	TEST_CASE ("Quadrature: Pyramid integrates constant and low-degree polynomials")
	TEST_CASE ("Quadrature: Quadrature class Integration method works")
	TEST_CASE ("Quadrature: GetQuadraturePointInfo returns correct data")
	TEST_CASE ("Quadrature: IntegrationSimple overloads work correctly")
	for (const auto &cfg :configs)
	for (int deg=0;deg<=3;deg++) monomials.push_back(
	for (const auto &tc :tests)
	TEST_CASE ("Quadrature: FPolynomialFill consistency check")

Variables
TestConfig	configs []
std::vector< std::array< int, 3 > >	monomials
TestCase	tests [] = {{1, 1}, {3, 3}, {5, 5}, {6, 5}}

Detailed Description

Comprehensive doctest-based unit tests for numerical quadrature accuracy.

Tests cover:

1. Polynomial integration accuracy (0th to 6th degree)
   • For each parametric space: Line, Tri, Quad, Tet, Hex, Prism, Pyramid
   • Tests exactness up to the theoretical order of each quadrature scheme
2. Complete Taylor basis integration (degree <= 3)
   • Uses BaseFunction utilities for systematic testing
   • All monomials: 1, x, y, z, x², xy, y², xz, yz, z², x³, x²y, xy², y³, ...
3. Weight sum verification (should equal parametric space volume)
4. Integration scheme selection correctness

Theoretical exactness:

• Gauss-Legendre on [-1,1]^d: exact for polynomials up to 2n-1
• Hammer rules on simplex: exactness varies by rule
• Product rules: exactness determined by component rules

Definition in file test_Quadrature.cpp.

Macro Definition Documentation

DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN

#define DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN

Definition at line 21 of file test_Quadrature.cpp.

Function Documentation

EvalMonomial()

t_real EvalMonomial	(	const tPoint &	p,
		int	a,
		int	b = 0,
		int	c = 0
	)

Evaluate a monomial x^a * y^b * z^c at point p.

Definition at line 83 of file test_Quadrature.cpp.

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ExactMonomialIntegral()

t_real ExactMonomialIntegral	(	ParamSpace	ps,
		int	a,
		int	b = 0,
		int	c = 0
	)

Compute exact integral of monomial over parametric reference element.

Reference domains:

• Line: [-1, 1] integral = 2/(a+1) for x^a (if a even)
• Quad: [-1, 1]^2 integral = product of 1D integrals
• Hex: [-1, 1]^3 integral = product of 1D integrals
• Tri: {xi>=0, et>=0, xi+et<=1} integral = a!*b!/(a+b+2)!
• Tet: {xi>=0, et>=0, zt>=0, xi+et+zt<=1}
• Prism: Triangle x [-1,1]
• Pyramid: Special domain

Definition at line 104 of file test_Quadrature.cpp.

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for() [1/3]

for

(

const auto &cfg :configs

)

Definition at line 835 of file test_Quadrature.cpp.

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for

(

const auto &tc :tests

)

Definition at line 957 of file test_Quadrature.cpp.

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for

(

int

deg = 0; deg <= 3; deg++

)

Definition at line 950 of file test_Quadrature.cpp.

GetParamSpaceFromElement()

ParamSpace GetParamSpaceFromElement

(

ElemType

t

)

Get parametric space from element type for testing.

Definition at line 244 of file test_Quadrature.cpp.

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GetTaylorBasisMonomials()

std::vector< std::array< int, 3 > > GetTaylorBasisMonomials	(	int	dim,
		int	maxOrder
	)

Get the list of Taylor basis monomial exponents up to given order.

Uses BaseFunction's diffOperatorOrderList to get exponents (nx, ny, nz) for each polynomial basis function.

Parameters

dim	Dimension (2 or 3)
maxOrder	Maximum polynomial order (0-3)

Returns

Vector of {nx, ny, nz} exponent triplets

Definition at line 49 of file test_Quadrature.cpp.

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QuadratureMonomialIntegral()

t_real QuadratureMonomialIntegral	(	ParamSpace	ps,
		int	int_order,
		int	a,
		int	b = 0,
		int	c = 0
	)

Numerically integrate a monomial using quadrature.

Definition at line 225 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: FPolynomialFill consistency check"

)

Definition at line 1024 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: GetQuadraturePointInfo returns correct data"

)

Definition at line 756 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Hex integrates polynomials up to expected order"

)

Definition at line 483 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: IntegrationSimple overloads work correctly"

)

Definition at line 783 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Line integrates polynomials up to expected order"

)

Definition at line 420 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Prism integrates polynomials up to expected order"

)

Definition at line 611 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Pyramid integrates constant and low-degree polynomials"

)

Definition at line 646 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Quad integrates polynomials up to expected order"

)

Definition at line 449 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Quadrature class Integration method works"

)

Definition at line 720 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: scheme constants are valid"

)

Definition at line 254 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Tetrahedron integrates polynomials up to expected order"

)

Definition at line 570 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: Triangle integrates polynomials up to expected order"

)

Definition at line 515 of file test_Quadrature.cpp.

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TEST_CASE

(

"Quadrature: weight sums equal reference element volumes"

)

Definition at line 296 of file test_Quadrature.cpp.

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Variable Documentation

configs

TestConfig configs

Initial value:

= {
        
        {TriSpace, 2, 3, {{1, 1}, {2, 2}, {4, 4}, {5, 5}, {6, 6}}},
        
        {QuadSpace, 2, 3, {{1, 1}, {3, 3}, {5, 5}, {6, 5}}},  
    }

Definition at line 828 of file test_Quadrature.cpp.

monomials

auto monomials

Initial value:

{
    constexpr t_real tol = 1e-12

Definition at line 949 of file test_Quadrature.cpp.

tests

TestCase tests = {{1, 1}, {3, 3}, {5, 5}, {6, 5}}

Definition at line 955 of file test_Quadrature.cpp.