How to create 1d mesh

General Discussion
1

i want to solve a 1d heat equation. how to create 1d mesh?

2

This does not seem to be highlighted but there is some support.
Search the docs for “Sline” and see “msh3”
I wrote a special gaphics app, “mjmdatascope” that I first tested on Freefem
because I could not find good 1D graphics though.
The attached is an old example from someone on the forum earlier
that contains the use of “Sline” with mjmdatascope but there are
a few examples around .

MWGFEM_1.edp (3.3 KB)

https://github.com/mmarchywka/mjmdatascope

3

can this work?
int m=500;
Th=square(1,m);
plot(Th,wait=1);

fespace Vh(Th,P2,periodic=[[2,y],[4,y]]);

4

I guess you can setup the problem and get the matrix and rhs with
FF “varf” and see what you think. As long as there are no derivatives in
the perpendicular direction it might work but probably have extra
elements.

Do you actually want periodicity along the 1D mesh?

.

5

Actually I am solving for temporal hydrodynamic stability of a 2d parallel base flow. for this i have to solve an eigen value problem in 1d mesh.
i was thinking of using periodicity as a way to convert a 2d mesh into 1d mesh.
is this approach right?

6

Yes it works.

The following examples may help you: 2d periodic + SLEPc solver or consider this one for true 1d + arpack solver

7

Is that plot only supported on more recent FF? Mine dies although IIRC
there have been other causes for errors like that. Thanks.


FreeFem++ LapEigen1DBeltrami.edp 
-- FreeFem++ v4.12 (Sat 20 May 2023 07:29:03 PM EDT - git no git)
   file : LapEigen1DBeltrami.edp
 Load: lg_fem lg_mesh lg_mesh3 eigenvalue 
    1 : // test to validate the addition of surfacic finite elements in FreeFEM
    2 : 
    3 : load "msh3"
    4 : load "medit"
    5 : 
    6 : 
    7 : /////variational form
    8 : 
    9 : /////////////////////////////////
   10 : // laplacian 2D
   11 : real R = 3, r=1; 
   12 : real h = 0.1; // 
   13 : int nx = R*2*pi/h;
   14 : func torex= (R+r*cos(y*pi*2))*cos(x*pi*2);
   15 : func torey= (R+r*cos(y*pi*2))*sin(x*pi*2);
   16 : func torez= r*sin(y*pi*2);
   17 : 
   18 : 
   19 : meshL Th=segment(nx,[torex,torey,torez],removeduplicate=true) ;
   20 : fespace Vh(Th,P1);
   21 : macro Grad3(uSVar) [dx(uSVar),dy(uSVar),dz(uSVar)]   )  // EOM
   22 : 
   23 : //with variational form
   24 : real sigma = 1; 
   25 : varf a(u,v) = int1d(Th)(Grad3(u)    [dx(u),dy(u),dz(u)]  '*Grad3(v)    [dx(v),dy(v),dz(v)]  - sigma* u*v);
   26 : varf m(u,v) = int1d(Th)( u*v);
   27 : 
   28 : matrix A =a(Vh,Vh);
   29 : matrix B =m(Vh,Vh,solver=CG);
   30 : int nev=100;  // number of computed eigen valeu close to sigma
   31 : 
   32 : real[int] ev(nev); // to store nev eigein value
   33 : Vh[int] eV(nev);   // to store nev eigen vector
   34 : 
   35 : int k=EigenValue(A,B,sym=true,sigma=sigma,value=ev,vector=eV,tol=1e-10,maxit=0,ncv=0,which="LM"); // which="LM" default 
   36 : 
   37 : for (int i=0;i<k;i++) 
   38 : 	plot(eV[i],cmm=" (new plot in test) Eigen  Vector "+i+" valeur =" + ev[i]  ,wait=1,value=1,dim=3,fill=1,CutPlane=0,ShowAxes=1, nbiso=40);  
   39 : 
   40 :  sizestack + 1024 =1896  ( 872 )

  -- FESpace: Nb of Nodes 188 Nb of DoF 188
Real symmetric eigenvalue problem: A*x - B*x*lambda
  Plot::  Sorry no ps version for this type of plot 14
  Plot::  Sorry no ps version for this type of plot 14
  Plot::  Sorry no ps version for this type of plot 14
  Plot::  Sorry no ps version for this type of plot 14
  Plot::  Sorry no ps version for this type of plot 14
terminate called after throwing an instance of 'std::bad_alloc'
  what():  std::bad_alloc
Aborted (core dumped)