Gauss_quadrature.hpp File Reference

This file defines gauss quadrature and related functions. More...

#include <math.h>
#include <vector>
#include <iostream>
#include <fstream>
#include <sstream>
#include <omp.h>
#include "linalg/Linear_algebra.hpp"

Go to the source code of this file.

Functions
void	get_gauss_quadrature_weight_VWU (const int &gaussQuadratureN, Matrix &vwu, Matrix &weight)
	Calculate the VMU (barycentric coordinates) and weight for a Gaussian quadrature point.
void	get_shapefunction (const Matrix &vwu, Matrix &shapefunction)
	Calculate the shape function and its derivatives at a given barycentric coordinate.
void	get_shapefunction_vector (const Matrix &vwuMat, std::vector< Matrix > &sfVec)
	Calculate the shape function and its derivatives at a set of barycentric coordinates.
void	get_subdivision_matrices (Matrix &mat, Matrix &subMat1, Matrix &subMat2, Matrix &subMat3, Matrix &subMat4)
	Calculate the four subdivision matrices for an irregular patch.

Detailed Description

This file defines gauss quadrature and related functions.

Author

Y Ying

Y Fu

Version

0.1

Date

2023-03-10

Copyright

Copyright (c) 2023

Function Documentation

get_gauss_quadrature_weight_VWU()

void get_gauss_quadrature_weight_VWU	(	const int &	gaussQuadratureN,
		Matrix &	vwu,
		Matrix &	weight
	)

Calculate the VMU (barycentric coordinates) and weight for a Gaussian quadrature point.

This function calculates a matrix (N, 3) of VMUs based on the specified number of quadrature points, storing the result in the provided matrix vmu. It also calculates a matrix (N, 1) of weights for each point, storing the result in the provided matrix weight.

Note that the vmu and weight matrices will be overwritten and should be initialized before calling this function.

Parameters

gaussQuadratureN	The number of Gauss quadrature points to use.
vwu	A matrix for storing the calculated barycentric coordinates (N, 3).
weight	A matrix for storing the calculated weights (N, 1).

get_shapefunction()

void get_shapefunction	(	const Matrix &	vwu,
		Matrix &	shapefunction
	)

Calculate the shape function and its derivatives at a given barycentric coordinate.

This function calculates the shape function and its derivatives at a given barycentric coordinate vwu, storing the result in the provided matrix shapefunction. The shape function and its derivatives are stored in rows 0 to 6 of the matrix as follows:

shapefunction(0,:), shape functions; shapefunction(1,:), differential to v; shapefunction(2,:), differential to w; shapefunction(3,:), double differential to v; shapefunction(4,:), double differential to w; shapefunction(5,:), differential to v and w; shapefunction(6,:), differential to w and v;

Parameters

vwu	The barycentric (1, 3) coordinate to evaluate the shape function at.
shapefunction	A (7, 12) matrix for storing the calculated shape function and its derivatives (7, 12).

get_shapefunction_vector()

void get_shapefunction_vector	(	const Matrix &	vwuMat,
		std::vector< Matrix > &	sfVec
	)

Calculate the shape function and its derivatives at a set of barycentric coordinates.

This function calculates the shape function and its derivatives at each barycentric coordinate in the provided matrix vwuMat, storing the result in the provided vector sfVec. Each element of sfVec is a matrix representing the shape function and its derivatives at one barycentric coordinate.

Parameters

vwuMat	A matrix of barycentric coordinates (N,3).
sfVec	A vector for storing the calculated shape functions and their derivatives.

get_subdivision_matrices()

void get_subdivision_matrices	(	Matrix &	mat,
		Matrix &	subMat1,
		Matrix &	subMat2,
		Matrix &	subMat3,
		Matrix &	subMat4
	)

Calculate the four subdivision matrices for an irregular patch.

This function calculates the four subdivision matrices for an irregular patch using the provided matrix mat, storing the result in the provided matrices subMat1, subMat2, subMat3, and subMat4.

Parameters

mat	The input matrix from which to compute the subdivision matrices.
subMat1	A matrix for storing the first subdivision matrix.
subMat2	A matrix for storing the second subdivision matrix.
subMat3	A matrix for storing the third subdivision matrix.
subMat4	A matrix for storing the fourth subdivision matrix.