1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
|
// GetDP - Copyright (C) 1997-2018 P. Dular and C. Geuzaine, University of Liege
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/getdp/getdp/issues
#include <math.h>
#include "Gauss.h"
#include "Gauss_Triangle.h"
#include "Message.h"
#include "MallocUtils.h"
/* Gauss Integration over a triangle */
void Gauss_Triangle(int Nbr_Points, int Num,
double *u, double *v, double *w, double *wght)
{
switch (Nbr_Points) {
case 1 : *u= xt1 [Num] ; *v= yt1 [Num] ; *w= 0. ; *wght= pt1 [Num] ; break ;
case 3 : *u= xt3 [Num] ; *v= yt3 [Num] ; *w= 0. ; *wght= pt3 [Num] ; break ;
case 4 : *u= xt4 [Num] ; *v= yt4 [Num] ; *w= 0. ; *wght= pt4 [Num] ; break ;
case 6 : *u= xt6 [Num] ; *v= yt6 [Num] ; *w= 0. ; *wght= pt6 [Num] ; break ;
case 7 : *u= xt7 [Num] ; *v= yt7 [Num] ; *w= 0. ; *wght= pt7 [Num] ; break ;
case 12 : *u= xt12[Num] ; *v= yt12[Num] ; *w= 0. ; *wght= pt12[Num] ; break ;
case 13 : *u= xt13[Num] ; *v= yt13[Num] ; *w= 0. ; *wght= pt13[Num] ; break ;
case 16 : *u= xt16[Num] ; *v= yt16[Num] ; *w= 0. ; *wght= pt16[Num] ; break ;
default :
Message::Error("Wrong number of Gauss points for Triangle: "
"valid choices: 1, 3, 4, 6, 7, 12, 13, 16");
break;
}
}
/* Degenerate n1Xn2 Gauss-Legendre scheme to integrate over a tri */
static int glt[MAX_LINE_POINTS] = {-1};
static double *glxt[MAX_LINE_POINTS], *glyt[MAX_LINE_POINTS], *glpt[MAX_LINE_POINTS];
static void quadToTri(double xi,double eta,double *r, double *s, double *J)
{
double r1;
*r = 0.5e0 * (1.0e0 + xi);
r1 = 1.0e0 - (*r);
*s = 0.5e0 * (1.0e0 + eta) * r1;
*J = 0.25e0 * r1;
}
void GaussLegendre_Triangle(int Nbr_Points, int Num,
double *u, double *v, double *w, double *wght)
{
int i,j,index=0,nb;
double pt1,pt2,wt1,wt2,dJ,dum;
nb = (int)sqrt((double)Nbr_Points);
if(nb*nb != Nbr_Points || nb > MAX_LINE_POINTS){
Message::Error("Number of points should be n^2 with n in [1,%d]", MAX_LINE_POINTS) ;
return;
}
if(glt[0] < 0) for(i=0 ; i < MAX_LINE_POINTS ; i++) glt[i] = 0 ;
if(!glt[nb - 1]){
Message::Info("Computing degenerate GaussLegendre %dX%d for Triangle", nb, nb);
glxt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double));
glyt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double));
glpt[nb - 1] = (double*)Malloc(Nbr_Points * sizeof(double));
for(i = 0; i < nb; i++) {
Gauss_Line(nb, i, &pt1, &dum, &dum, &wt1);
for(j = 0; j < nb; j++) {
Gauss_Line(nb, j, &pt2, &dum, &dum, &wt2);
quadToTri(pt1, pt2, &glxt[nb - 1][index], &glyt[nb - 1][index], &dJ);
glpt[nb - 1][index++] = dJ * wt1 * wt2;
}
}
glt[nb - 1] = 1;
}
*u = glxt[nb - 1][Num] ; *v = glyt[nb - 1][Num] ; *w = 0. ; *wght = glpt[nb - 1][Num] ;
}
/* Gauss Integration over a triangle with a 1/R singularity over node (0,0,0) */
void GaussSingularR_Triangle(int Nbr_Points, int Num,
double *u, double *v, double *w, double *wght)
{
switch (Nbr_Points) {
case 1 : *u= xts1 [Num] ; *v= yts1 [Num] ; *w= 0. ; *wght= pts1 [Num] ; break ;
case 3 : *u= xts3 [Num] ; *v= yts3 [Num] ; *w= 0. ; *wght= pts3 [Num] ; break ;
case 4 : *u= xts4 [Num] ; *v= yts4 [Num] ; *w= 0. ; *wght= pts4 [Num] ; break ;
default :
Message::Error("Wrong number of (modified) Gauss points for Triangle: "
"valid choices: 1, 3, 4");
break;
}
}
|
