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Christophe Geuzaine authoredChristophe Geuzaine authored
BF_Node.cpp 14.70 KiB
// GetDP - Copyright (C) 1997-2018 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>.
//
// Contributor(s):
// Christophe Trophime
//
#include "ProData.h"
#include "Message.h"
#define SQU(a) ((a)*(a))
/* ------------------------------------------------------------------------ */
/* B F _ N o d e */
/* ------------------------------------------------------------------------ */
#define WrongNumNode Message::Error("Wrong Node number in 'BF_Node'")
void BF_Node(struct Element * Element, int NumNode,
double u, double v, double w, double *s )
{
double r;
switch (Element->Type) {
case POINT :
switch(NumNode) {
case 1 : *s = 1. ; break ;
default : WrongNumNode ;
}
break ;
case LINE :
switch(NumNode) {
case 1 : *s = 0.5 * (1.-u) ; break ;
case 2 : *s = 0.5 * (1.+u) ; break ;
default : WrongNumNode ;
}
break ;
case TRIANGLE :
switch(NumNode) {
case 1 : *s = 1.-u-v ; break ;
case 2 : *s = u ; break ;
case 3 : *s = v ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE :
switch(NumNode) {
case 1 : *s = 0.25 * (1.-u) * (1.-v) ; break ;
case 2 : *s = 0.25 * (1.+u) * (1.-v) ; break ;
case 3 : *s = 0.25 * (1.+u) * (1.+v) ; break ;
case 4 : *s = 0.25 * (1.-u) * (1.+v) ; break ;
default : WrongNumNode ;
}
break ;
case TETRAHEDRON :
switch(NumNode) {
case 1 : *s = 1.-u-v-w ; break ;
case 2 : *s = u ; break ;
case 3 : *s = v ; break ;
case 4 : *s = w ; break ;
default : WrongNumNode ;
}
break ;
case HEXAHEDRON :
switch(NumNode) {
case 1 : *s = (1.-u) * (1.-v) * (1.-w) * 0.125 ; break ;
case 2 : *s = (1.+u) * (1.-v) * (1.-w) * 0.125 ; break ;
case 3 : *s = (1.+u) * (1.+v) * (1.-w) * 0.125 ; break ;
case 4 : *s = (1.-u) * (1.+v) * (1.-w) * 0.125 ; break ;
case 5 : *s = (1.-u) * (1.-v) * (1.+w) * 0.125 ; break ;
case 6 : *s = (1.+u) * (1.-v) * (1.+w) * 0.125 ; break ;
case 7 : *s = (1.+u) * (1.+v) * (1.+w) * 0.125 ; break ;
case 8 : *s = (1.-u) * (1.+v) * (1.+w) * 0.125 ; break ;
default : WrongNumNode ;
}
break ;
case PRISM :
switch(NumNode) {
case 1 : *s = (1.-u-v) * (1.-w) * 0.5 ; break ;
case 2 : *s = u * (1.-w) * 0.5 ; break ;
case 3 : *s = v * (1.-w) * 0.5 ; break ;
case 4 : *s = (1.-u-v) * (1.+w) * 0.5 ; break ;
case 5 : *s = u * (1.+w) * 0.5 ; break ;
case 6 : *s = v * (1.+w) * 0.5 ; break ;
default : WrongNumNode ;
}
break ;
case PYRAMID :
if(w != 1. && NumNode != 5) r = u*v*w / (1.-w) ;
else r = 0. ;
switch(NumNode) {
case 1 : *s = 0.25 * ((1.-u) * (1.-v) - w + r); break ;
case 2 : *s = 0.25 * ((1.+u) * (1.-v) - w - r); break ;
case 3 : *s = 0.25 * ((1.+u) * (1.+v) - w + r); break ;
case 4 : *s = 0.25 * ((1.-u) * (1.+v) - w - r); break ;
case 5 : *s = w ; break ;
default : WrongNumNode ;
}
break ;
case LINE_2 :
switch(NumNode) {
case 1 : *s = 0.5*u*(u-1.) ; break ;
case 2 : *s = 0.5*u*(1.+u) ; break ;
case 3 : *s = 1.-u*u ; break ;
default : WrongNumNode ;
}
break ;
case TRIANGLE_2 :
r = 1.-u-v ;
switch(NumNode) {
case 1 : *s = r*(2.*r-1.) ; break ;
case 2 : *s = u*(2.*u-1.) ; break ;
case 3 : *s = v*(2.*v-1.) ; break ;
case 4 : *s = 4.*r*u ; break ;
case 5 : *s = 4.*u*v ; break ;
case 6 : *s = 4.*v*r ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE_2 :
switch(NumNode) {
case 1 : *s = 0.25 * (1.-u) * (1.-v) * u * v ; break ;
case 2 : *s = -0.25 * (1.+u) * (1.-v) * u * v ; break ;
case 3 : *s = 0.25 * (1.+u) * (1.+v) * u * v ; break ;
case 4 : *s = -0.25 * (1.-u) * (1.+v) * u * v ; break ;
case 5 : *s = -0.5 * (1.-u*u)* (1.-v) * v ; break ;
case 6 : *s = 0.5 * (1.+u) * (1.-v*v)* u ; break ;
case 7 : *s = 0.5 * (1.-u*u)* (1.+v) * v ; break ; case 8 : *s = -0.5 * (1.-u) * (1.-v*v)* u ; break ;
case 9 : *s = (1.-u*u)* (1.-v*v) ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE_2_8N :
switch(NumNode) {
case 1 : *s = -0.25 * (1.-u) * (1.-v) * (1.+u+v) ; break ;
case 2 : *s = -0.25 * (1.+u) * (1.-v) * (1.-u+v) ; break ;
case 3 : *s = -0.25 * (1.+u) * (1.+v) * (1.-u-v) ; break ;
case 4 : *s = -0.25 * (1.-u) * (1.+v) * (1.+u-v) ; break ;
case 5 : *s = 0.5 * (1.-u*u)* (1.-v) ; break ;
case 6 : *s = 0.5 * (1.+u) * (1.-v*v) ; break ;
case 7 : *s = 0.5 * (1.-u*u)* (1.+v) ; break ;
case 8 : *s = 0.5 * (1.-u) * (1.-v*v) ; break ;
default : WrongNumNode ;
}
break ;
case TETRAHEDRON_2 :
r = 1.-u-v-w ;
switch(NumNode) {
case 1 : *s = r*(2.*r-1.) ; break ;
case 2 : *s = u*(2.*u-1.) ; break ;
case 3 : *s = v*(2.*v-1.) ; break ;
case 4 : *s = w*(2.*w-1.) ; break ;
case 5 : *s = 4.*r*u ; break ;
case 6 : *s = 4.*u*v ; break ;
case 7 : *s = 4.*r*v ; break ;
case 8 : *s = 4.*r*w ; break ;
case 9 : *s = 4.*v*w ; break ;
case 10 : *s = 4.*u*w ; break ;
default : WrongNumNode ;
}
break ;
default :
Message::Error("Unknown type of Element in BF_Node");
break;
}
}
#undef WrongNumNode
/* ------------------------------------------------------------------------ */
/* B F _ G r a d N o d e */
/* ------------------------------------------------------------------------ */
#define WrongNumNode Message::Error("Wrong Node number in 'BF_GradNode'")
void BF_GradNode(struct Element * Element, int NumNode,
double u, double v, double w, double s[])
{
double r;
switch (Element->Type) {
case POINT :
switch(NumNode) {
case 1 : s[0] = 0. ; s[1] = 0. ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case LINE :
switch(NumNode) {
case 1 : s[0] = -0.5 ; s[1] = 0. ; s[2] = 0. ; break ;
case 2 : s[0] = 0.5 ; s[1] = 0. ; s[2] = 0. ; break ;
default : WrongNumNode ; }
break ;
case TRIANGLE :
switch(NumNode) {
case 1 : s[0] = -1. ; s[1] = -1. ; s[2] = 0. ; break ;
case 2 : s[0] = 1. ; s[1] = 0. ; s[2] = 0. ; break ;
case 3 : s[0] = 0. ; s[1] = 1. ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE :
switch(NumNode) {
case 1 : s[0] = -0.25 * (1.-v) ; s[1] = -0.25 * (1.-u) ; s[2] = 0. ; break ;
case 2 : s[0] = 0.25 * (1.-v) ; s[1] = -0.25 * (1.+u) ; s[2] = 0. ; break ;
case 3 : s[0] = 0.25 * (1.+v) ; s[1] = 0.25 * (1.+u) ; s[2] = 0. ; break ;
case 4 : s[0] = -0.25 * (1.+v) ; s[1] = 0.25 * (1.-u) ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case TETRAHEDRON :
switch(NumNode) {
case 1 : s[0] = -1. ; s[1] = -1. ; s[2] = -1. ; break ;
case 2 : s[0] = 1. ; s[1] = 0. ; s[2] = 0. ; break ;
case 3 : s[0] = 0. ; s[1] = 1. ; s[2] = 0. ; break ;
case 4 : s[0] = 0. ; s[1] = 0. ; s[2] = 1. ; break ;
default : WrongNumNode ;
}
break ;
case HEXAHEDRON :
switch(NumNode) {
case 1 : s[0] = -0.125 * (1.-v) * (1.-w) ;
s[1] = -0.125 * (1.-u) * (1.-w) ;
s[2] = -0.125 * (1.-u) * (1.-v) ; break ;
case 2 : s[0] = 0.125 * (1.-v) * (1.-w) ;
s[1] = -0.125 * (1.+u) * (1.-w) ;
s[2] = -0.125 * (1.+u) * (1.-v) ; break ;
case 3 : s[0] = 0.125 * (1.+v) * (1.-w) ;
s[1] = 0.125 * (1.+u) * (1.-w) ;
s[2] = -0.125 * (1.+u) * (1.+v) ; break ;
case 4 : s[0] = -0.125 * (1.+v) * (1.-w) ;
s[1] = 0.125 * (1.-u) * (1.-w) ;
s[2] = -0.125 * (1.-u) * (1.+v) ; break ;
case 5 : s[0] = -0.125 * (1.-v) * (1.+w) ;
s[1] = -0.125 * (1.-u) * (1.+w) ;
s[2] = 0.125 * (1.-u) * (1.-v) ; break ;
case 6 : s[0] = 0.125 * (1.-v) * (1.+w) ;
s[1] = -0.125 * (1.+u) * (1.+w) ;
s[2] = 0.125 * (1.+u) * (1.-v) ; break ;
case 7 : s[0] = 0.125 * (1.+v) * (1.+w) ;
s[1] = 0.125 * (1.+u) * (1.+w) ;
s[2] = 0.125 * (1.+u) * (1.+v) ; break ;
case 8 : s[0] = -0.125 * (1.+v) * (1.+w) ;
s[1] = 0.125 * (1.-u) * (1.+w) ;
s[2] = 0.125 * (1.-u) * (1.+v) ; break ;
default : WrongNumNode ;
}
break ;
case PRISM :
switch(NumNode) {
case 1 : s[0] = -0.5 * (1.-w) ;
s[1] = -0.5 * (1.-w) ;
s[2] = -0.5 * (1.-u-v) ; break ;
case 2 : s[0] = 0.5 * (1.-w) ;
s[1] = 0. ;
s[2] = -0.5 * u ; break ; case 3 : s[0] = 0. ;
s[1] = 0.5 * (1.-w) ;
s[2] = -0.5 * v ; break ;
case 4 : s[0] = -0.5 * (1.+w) ;
s[1] = -0.5 * (1.+w) ;
s[2] = 0.5 * (1.-u-v) ; break ;
case 5 : s[0] = 0.5 * (1.+w) ;
s[1] = 0. ;
s[2] = 0.5 * u ; break ;
case 6 : s[0] = 0. ;
s[1] = 0.5 * (1.+w) ;
s[2] = 0.5 * v ; break ;
default : WrongNumNode ;
}
break ;
case PYRAMID :
if(w == 1. && NumNode != 5) {
//When w = 1 => u=v=0
switch(NumNode) {
case 1 : s[0] = -0.25 ;
s[1] = -0.25 ;
s[2] = -0.25 ; break ;
case 2 : s[0] = 0.25 ;
s[1] = -0.25 ;
s[2] = -0.25 ; break ;
case 3 : s[0] = 0.25 ;
s[1] = 0.25 ;
s[2] = -0.25 ; break ;
case 4 : s[0] = -0.25 ;
s[1] = 0.25 ;
s[2] = -0.25 ; break ;
case 5 : s[0] = 0. ;
s[1] = 0. ;
s[2] = 1. ; break ;
default : WrongNumNode ;
}
}
else{
switch(NumNode) {
case 1 : s[0] = 0.25 * ( v/(1 - w) - 1) ;
s[1] = 0.25 * ( u/(1 - w) - 1) ;
s[2] = 0.25 * ( u*v/SQU(1 - w) - 1) ; break ;
case 2 : s[0] = 0.25 * (-v/(1 - w) + 1) ;
s[1] = 0.25 * (-u/(1 - w) - 1) ;
s[2] = 0.25 * (-u*v/SQU(1 - w) - 1) ; break ;
case 3 : s[0] = 0.25 * ( v/(1 - w) + 1) ;
s[1] = 0.25 * ( u/(1 - w) + 1) ;
s[2] = 0.25 * ( u*v/SQU(1 - w) - 1) ; break ;
case 4 : s[0] = 0.25 * (-v/(1 - w) - 1) ;
s[1] = 0.25 * (-u/(1 - w) + 1) ;
s[2] = 0.25 * (-u*v/SQU(1 - w) - 1) ; break ;
case 5 : s[0] = 0. ;
s[1] = 0. ;
s[2] = 1. ; break ;
default : WrongNumNode ;
}
}
break ;
case LINE_2 :
switch(NumNode) {
case 1 : s[0] = -0.5+u ; s[1] = 0. ; s[2] = 0. ; break ;
case 2 : s[0] = 0.5+u ; s[1] = 0. ; s[2] = 0. ; break ;
case 3 : s[0] = -2.*u ; s[1] = 0. ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case TRIANGLE_2 : r = 1.-u-v ;
switch(NumNode) {
case 1 : s[0] = 1.-4.*r ; s[1] = 1.-4.*r ; s[2] = 0. ; break ;
case 2 : s[0] =-1.+4.*u ; s[1] = 0. ; s[2] = 0. ; break ;
case 3 : s[0] = 0. ; s[1] =-1.+4.*v ; s[2] = 0. ; break ;
case 4 : s[0] = 4.*(r-u); s[1] = -4.*u ; s[2] = 0. ; break ;
case 5 : s[0] = 4.*v ; s[1] = 4.*u ; s[2] = 0. ; break ;
case 6 : s[0] =-4.*v ; s[1] = 4.*(r-v); s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE_2 :
switch(NumNode) {
case 1 : s[0] = 0.25 * (1.-2.*u) * (1.-v) * v ; s[1] = 0.25 * (1.-u) * (1.-2.*v) * u ; s[2] = 0. ; break ;
case 2 : s[0] = -0.25 * (1.+2.*u) * (1.-v) * v ; s[1] = -0.25 * (1.+u) * (1.-2.*v) * u ; s[2] = 0. ; break ;
case 3 : s[0] = 0.25 * (1.+2.*u) * (1.+v) * v ; s[1] = 0.25 * (1.+u) * (1.+2.*v) * u ; s[2] = 0. ; break ;
case 4 : s[0] = -0.25 * (1.-2.*u) * (1.+v) * v ; s[1] = -0.25 * (1.-u) * (1.+2.*v) * u ; s[2] = 0. ; break ;
case 5 : s[0] = (1.-v) * u * v ; s[1] = -0.5 * (1.-u*u) * (1.-2.*v) ; s[2] = 0. ; break ;
case 6 : s[0] = 0.5 * (1.+2.*u) * (1.-v*v) ; s[1] = -(1.+u) * u * v ; s[2] = 0. ; break ;
case 7 : s[0] = -(1.+v) * u * v ; s[1] = 0.5 * (1.-u*u) * (1.+2.*v) ; s[2] = 0. ; break ;
case 8 : s[0] = -0.5 * (1.-2.*u) * (1.-v*v) ; s[1] = (1.-u) * u * v ; s[2] = 0. ; break ;
case 9 : s[0] = -2. * (1.-v*v) * u ; s[1] = -2. * (1.-u*u) * v ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case QUADRANGLE_2_8N :
switch(NumNode) {
case 1 : s[0] = 0.25 * (1.-v) * (2.*u+v) ; s[1] = 0.25 * (1.-u) * (u+2.*v) ; s[2] = 0. ; break ;
case 2 : s[0] = 0.25 * (1.-v) * (2.*u-v) ; s[1] = -0.25 * (1.+u) * (u-2.*v) ; s[2] = 0. ; break ;
case 3 : s[0] = 0.25 * (1.+v) * (2.*u+v) ; s[1] = 0.25 * (1.+u) * (u+2.*v) ; s[2] = 0. ; break ;
case 4 : s[0] = 0.25 * (1.+v) * (2.*u-v) ; s[1] = -0.25 * (1.-u) * (u-2.*v) ; s[2] = 0. ; break ;
case 5 : s[0] = -(1.-v) * u ; s[1] = -0.5 * (1.-u*u) ; s[2] = 0. ; break ;
case 6 : s[0] = 0.5 * (1.-v*v) ; s[1] = -(1.+u) * v ; s[2] = 0. ; break ;
case 7 : s[0] = -(1.+v) * u ; s[1] = 0.5 * (1.-u*u) ; s[2] = 0. ; break ;
case 8 : s[0] = -0.5 * (1.-v*v) ; s[1] = -(1.-u) * v ; s[2] = 0. ; break ;
default : WrongNumNode ;
}
break ;
case TETRAHEDRON_2 :
r = 1.-u-v-w ;
switch(NumNode) {
case 1 : s[0] = -(4.*r-1) ; s[1] = -(4.*r-1) ; s[2] = -(4.*r-1) ; break ;
case 2 : s[0] = (4.*u-1) ; s[1] = 0 ; s[2] = 0 ; break ;
case 3 : s[0] = 0 ; s[1] = (4.*v-1) ; s[2] = 0 ; break ;
case 4 : s[0] = 0 ; s[1] = 0 ; s[2] = (4.*w-1) ; break ;
case 5 : s[0] = 4.*(r-u) ; s[1] = -4.*u ; s[2] = -4.*u ; break ;
case 6 : s[0] = 4.*v ; s[1] = 4.*u ; s[2] = 0 ; break ;
case 7 : s[0] = -4.*v ; s[1] = 4.*(r-v) ; s[2] = -4.*v ; break ;
case 8 : s[0] = -4.*w ; s[1] = -4.*w ; s[2] = 4.*(r-w) ; break ;
case 9 : s[0] = 0 ; s[1] = 4.*w ; s[2] = 4.*v ; break ;
case 10 : s[0] = 4.*w ; s[1] = 0 ; s[2] = 4.*u ; break ;
default : WrongNumNode ;
}
break ;
default :
Message::Error("Unknown type of Element in BF_GradNode");
break;
}
}
#undef WrongNumNode