# Mesh, regions and numbering

**URL:** https://community.freefem.org/t/mesh-regions-and-numbering/3961
**Category:** General Discussion
**Created:** [June 6, 2025, 8:06pm UTC](https://community.freefem.org/t/mesh-regions-and-numbering/3961 "2025-06-06T20:06:44Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![pi.3.141](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@pi.3.141](https://community.freefem.org/u/pi.3.141)
#### Post date: [June 6, 2025, 8:06pm UTC](https://community.freefem.org/t/mesh-regions-and-numbering/3961/1 "2025-06-06T20:06:44Z")

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Hello,  
I have a problem with two meshes, say Th1 and Th2, with Th1 extracted from Th2 (Th1 subset of Th2). I have to integrate in Th1 a product u1\*u2, with u1 in Th1, u2 in Th2, and u1 and u2 say of class P1.

I prefer to make the integration “by hand” (not using int2d(Th1)), and for this I need the values of u2 on the nodes of Th1.

I thought I could call u2 as u2[Th1[nT1][jj]], with nT1 triangle in Th1, but it seems that this call refers to different values of u2.

So, it seems that the numbering of triangles and nodes/triangle of Th2 and Th1 is not the same in the intersection. I have attached a simple code which demonstrate this.

My question is how one can call the right values of u2 in Th1, knowing the triangle index nT1 and jj in Th1 .  
Thank you!

* * *

load “Curvature”  
int lb11=11,lb12=12,lb21=21;  
// borders  
border b11(t=0,2) {  
if (t\<=1) {x=1; y=t;}  
else {x=2-t; y=1.;}  
label=lb11;}

border b12(t=0,2) {  
if (t\<=1) {x=0; y=1.-t;}  
else {x=t-1.; y=0;}  
label=lb12;}

border b21(t=4,10) {  
if (t\<=5) {x=t-3; y=0;}  
else if (t\<=7) {x=2.; y=t-5.;}  
else if (t\<=9) {x=9-t; y=2.;}  
else {x=0;y=11-t;}  
label=lb21;}

//plot(b11(2)+b12(2),wait=1,dim=2);  
//meshes  
//plot(b21(6),dim=2,wait=1);  
mesh Th2 = buildmesh(b11(2)+b12(2)+b21(6));  
//plot(Th2,wait=1);

real[int,int] XYb11(3,1);  
real lengthb11=extractborder(Th2,lb11,XYb11);  
border newb11(t=0,XYb11.m-1){ P.x=XYb11(0,t); P.y=XYb11(1,t);  
label=lb11;}  
Th2=buildmesh(newb11((XYb11.m-1))+b12(2)+b21(6),fixeborder=1);  
plot(Th2,wait=1,cmm=“Th2”);

int reg1=Th2(0.1,0.1).region,  
reg2=Th2(1.9,1.9).region;

mesh Th1=trunc(Th2,region==reg1);  
//plot(Th1,wait=1,cmm=“Th1/reg1”);

mesh th1=Th1;  
plot(Th1,Th2,wait=1,cmm=“Th1, Th2”);  
plot(th1,Th2,wait=1,cmm=“th1, Th2”);

fespace V2(Th2,P1); V2 u2=x+4_y;  
fespace V1(Th1,P1); V1 u1=x+4_y;

for (int i=0; i \< Th2.nt; i++) {  
cout \<\< "i2/Th2 = " \<\< i \<\< "; "  
\<\< Th2[i][0] \<\< " " \<\< Th2[i][1] \<\< " " \<\< Th2[i][2] \<\< endl;  
if (i\<Th1.nt) {  
cout \<\< "i1/Th1 = " \<\< i \<\< "; "  
\<\< Th1[i][0] \<\< " " \<\< Th1[i][1] \<\< " " \<\< Th1[i][2] \<\< endl;  
cout \<\< "i1/th1 = " \<\< i \<\< "; "  
\<\< th1[i][0] \<\< " " \<\< th1[i][1] \<\< " " \<\< th1[i][2] \<\< endl;  
for (int j=0; j\<3; j++) {  
if (Th2[i][j]!=Th1[i][j])  
cout \<\< "nodes are different in triangle i = " \<\< i \<\< endl;  
if (u2[Th2[i][j]] != u1[Th1[i][j]])  
cout \<\< "u2!=u1 in triangle i = " \<\< i \<\< endl;  
} } }

---

<div class="post-metadata">

### Author: ![pi.3.141](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@pi.3.141](https://community.freefem.org/u/pi.3.141)
#### Post date: [June 8, 2025, 2:52am UTC](https://community.freefem.org/t/mesh-regions-and-numbering/3961/2 "2025-06-08T02:52:30Z")

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Update:  
If the mesh Th2 is constructed as: Th2=Th1+(mesh of Th2/Th1) then numbering of nodes/triangle of Th1 is the same as of Th2\cap Th1.