File: Gauss_Quadrangle.h

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// GetDP - Copyright (C) 1997-2016 P. Dular and C. Geuzaine, University of Liege
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <getdp@onelab.info>.

/* 1 integration point */

static double xq1[1] = {0.};
static double yq1[1] = {0.};
static double pq1[1] = {4.};

/* 3 integration points */

static double xq3[3] = {0.816496580928,-0.408248290464,-0.408248290464};
static double yq3[3] = {0.0,0.840896415255,-0.840896415255};
static double pq3[3] = {1.33333333333,1.33333333333,1.33333333333};

/* 4 integration points */

static double xq4[4] = {0.577350269189,-0.577350269189,0.577350269189,-0.577350269189};
static double yq4[4] = {0.577350269189,0.577350269189,-0.577350269189,-0.577350269189};
static double pq4[4] = {1.,1.,1.,1.};

/* 7 integration points */

// WARNING: It seems that there is a problem with the values with 7 integration points ! Geuzaine (16/06/2016)

static double xq7[7] = {0.0,-0.683130051064,0.683130051064,0.890654421782,
			-0.890654421782,0.374256642286,-0.374256642286};
static double yq7[7] = {0.0,-0.683130051064,0.683130051064,-0.374256642286,0.374256642286,
			-0.890654421782,0.890654421782};
static double pq7[7] = {1.142857142857,0.595238095238,0.595238095238,
			0.416666666666,0.416666666666,0.416666666666,0.416666666666};

/*
   GAUSS QUADRANGLE WITH 1/R SINGULARITY OVER NODE (-1,-1,0)

   ref.: H. L. G. Pina, J. L. M. Fernandes, C. A. Brebbia,
         Some numerical integration formulae over triangles and
	 squares with a 1/R singularity,
	 Appl. Math. Modelling, Vol 5, June 1981, pp 209--211
*/

/* 1 integration point */

static double xqs1[1] = {-0.26501817};
static double yqs1[1] = {-0.26501817};
static double pqs1[1] = {3.52549435};

/* 3 integration points */

static double xqs3[3] = {-0.58105530,1.0,-0.21877566};
static double yqs3[3] = {-0.58105530,-0.21877566,1.0};
static double pqs3[3] = {2.37881900,0.57333767,0.57333767};

/* 4 integration points */

static double xqs4[4] = {-0.37512304,0.69629093,-0.92928746,-0.15602536};
static double yqs4[4] = {-0.92928746,-0.15602536,-0.37512304,0.69629093};
static double pqs4[4] = {1.02276580,0.73998134,1.02276580,0.73998134};