[int]`. As we’ve previously discussed, this type of declaration isn’t implemented for composite spaces yet. Perhaps composite space functionality isn’t fully mature at this stage? 😕For now, I will go back to use block system.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [July 14, 2025, 4:34am UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/8 "2025-07-14T04:34:30Z")
Use the named parameter `array`.
---
### Author:  [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [July 14, 2025, 9:26am UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/9 "2025-07-14T09:26:41Z")
For composite spaces involving different meshes, how is domain decomposition implemented? Specifically, when physical domains have overlapping regions, do they share the same decomposition?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [July 14, 2025, 4:07pm UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/10 "2025-07-14T16:07:08Z")
The decomposition is done at the algebraic level (the matrix is decomposed into stripes of contiguous rows, like a typical PETSc `Mat`).
---
### Author:  [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [September 17, 2025, 11:46am UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/11 "2025-09-17T11:46:16Z")
Hi, @prj
In a conjugate heat transfer problem, the fluid domain is usually a subset of the heat domain (which includes both fluid and solid). I have the following questions:
1. How can I perform the same decomposition on both meshes?
I have an idea: mark the fluid domain with a specific region, and then use `trunc` to retrieve the decomposed fluid mesh after the heat domain has been decomposed.
2. If DDM is too complicated, can I bypass it using the algebraic method you mentioned?
How can I use such an algebraic method instead of DDM, as done in many examples?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [September 18, 2025, 6:15am UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/12 "2025-09-18T06:15:49Z")
1. There are multiple examples in the FreeFEM repository, e.g., [FreeFem-sources/examples/hpddm/restriction-2d-PETSc.edp at develop · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/restriction-2d-PETSc.edp) or [FreeFem-sources/examples/hpddm/helmholtz-coupled-2d-PETSc-complex.edp at develop · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/helmholtz-coupled-2d-PETSc-complex.edp).
2. `If DDM is too complicated`, it’s not too complicated, and it’s the only way to do assemblies in parallel.
---
### Author:  [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [October 13, 2025, 1:49pm UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/13 "2025-10-13T13:49:38Z")
Hello! I am not sure how to solve a block system with `EPSSolve`.
My left hand side is:
```auto
J= [[AA, AB, 0],
[BA', BB, BC],
[0 , BC', 0] ];
```
and my right hand side is
```auto
Mat Loc = [[M1M ,0 ,0],
[0 ,M2M ,0],
[0 ,0 ,M3M]];
```
the related vector is `T,[u1,u2],p` for the blocks.
Could you please check out my script to solve a conjugate heat transfer eigenvalue problem:
```auto
// run with MPI: ff-mpirun -np 4 script.edp
// NBPROC 4
//load "iovtk"
load "PETSc-complex"
macro dimension()2//
include "macro_ddm.idp"
func PkU = [P2, P2];
func Pkp = P1;
func PkT = P2;
macro grad(u)[dx(u), dy(u)]//
macro div(u)(dx(u#1) + dy(u#2))//
macro UgradV(u, v)[[u#1, u#2]' * [dx(v#1), dy(v#1)],
[u#1, u#2]' * [dx(v#2), dy(v#2)]]//
int inner = 1;
int outer = 2;
border c1(t=0,2*pi){
x=0.5*cos(t);
y=0.5*sin(t);
label=inner;
}
border c2(t=0,2*pi){
x=1*cos(t);
y=1*sin(t);
label=outer;
}
mesh Th1=buildmesh(c1(-100)+c2(100));
mesh Th2=buildmesh(c1(100));
mesh Th3=Th1+Th2;
plot(Th3,wait=1);
fespace VhU(Th1,[P2,P2]);
fespace Vhp(Th1,P1);
fespace VhT(Th3,P2);
VhU [uc1,uc2]=[0,0];
VhT Tc=y+1;
plot(Th3,Tc,wait=1);
real Pr = 1;
real Ra = 1e3;
real tM=getARGV("-tM", 0.5); // thetaM
real kappa,nu;
func real DefCoef()
{
nu = sqrt(Pr/Ra);
kappa = 1./sqrt(Ra*Pr);
}
DefCoef();
varf A11(T,TT) = int2d(Th3)(
kappa * (grad(T)' * grad(TT))
+ [uc1,uc2]'*[dx(T), dy(T)]*TT)
+ on(outer, T=-y);
varf A12([u1,u2],[TT]) = int2d(Th1)(
[u1,u2]'*[dx(Tc), dy(Tc)]*TT)
//+ on(inner,outer, u1 = 0, u2 = 0)
;
varf A21([v1,v2],[T]) = int2d(Th1)(
- (T)*v2)
/* + on(outer, T=-y) */;
varf A22([u1,u2],[v1,v2]) = int2d(Th1)(
(UgradV(uc, u) + UgradV(u, uc))' * [v1, v2]
+ nu * (grad(u1)' * grad(v1) +
grad(u2)' * grad(v2)))
+ on(inner,outer, u1 = 0, u2 = 0);
varf A23([p],[v1,v2]) = int2d(Th1)(
- p * div(v))
;
varf mass1(T,TT) = int2d(Th3)( T*TT );
varf mass2([u1,u2],[v1,v2]) = int2d(Th1)( [u1,u2]'*[v1,v2] );
varf mass3(p,q) = int2d(Th1)( 0*p*q );
matrix A11m=A11(VhT,VhT);
matrix A12m=A12(VhU,VhT);
matrix A21m=A21(VhT,VhU);
matrix A22m=A22(VhU,VhU);
matrix A23m=A23(Vhp,VhU);
//Mat ;
Mat AA=A11m;
Mat AB=A12m;
Mat BA=A21m;
Mat BB=A22m;
Mat BC=A23m;
Mat J= [[AA, AB, 0],
[BA', BB, BC],
[0 , BC', 0] ];
matrix M1m = mass1(VhT, VhT);
matrix M2m = mass2(VhU, VhU);
matrix M3m = mass3(Vhp, Vhp);
Mat M1M = M1m;
Mat M2M = M2m;
Mat M3M = M3m;
Mat Loc = [[M1M ,0 ,0],
[0 ,M2M ,0],
[0 ,0 ,M3M]];
Mat M(J, Loc, clean = true);
//fespace Wh(Th3, [P2, P2, P2, P1]); // complete space [u, v, T, p]
int dofGlobal = VhT.ndof + VhU.ndof + Vhp.ndof;
int nev = 10;
complex[int,int] vec(dofGlobal,nev);
complex[int] val(nev); // array to store eigenvalues
//Wh[int] [vec,vecB,vecC,vecD](nev); // array to store eigenvectors
complex s = getARGV("-shift_real", 1.0e-6) + getARGV("-shift_imag", 0.6) * 1i;
string params = "-eps_tol 1.0e-6 -eps_nev " + nev + " " +
"-eps_type krylovschur -eps_monitor_all " +
"-eps_target " + real(s) + "+" + imag(s) + "i";
int k = EPSSolve(J, M, array = vec, values = val, sparams = params);
```
I am not sure what’s wrong with my code.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [October 13, 2025, 2:03pm UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/14 "2025-10-13T14:03:38Z")
What is the issue with your code?
---
### Author:  [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [October 15, 2025, 11:43am UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/15 "2025-10-15T11:43:43Z")
Hello,
The example [FreeFem-sources/examples/hpddm/helmholtz-coupled-2d-PETSc-complex.edp at develop · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/helmholtz-coupled-2d-PETSc-complex.edp) can not run with parameter `-user_partitioning`.
`ff-mpirun -n 4 helmholtz-coupled-2d-PETSc-complex.edp -wg` gives a normal end,
but `ff-mpirun -n 4 helmholtz-coupled-2d-PETSc-complex.edp -wg -user_partitioning ` prints:
```auto
0 KSP Residual norm 7.501711698142e-03
** On entry to ZGEMV parameter number 6 had an illegal value
--------------------------------------------------------------------------
mpiexec has exited due to process rank 3 with PID 0 on
node whc-MU71-SU0-00 exiting improperly. There are three reasons this could occur:
1. this process did not call "init" before exiting, but others in
the job did. This can cause a job to hang indefinitely while it waits
for all processes to call "init". By rule, if one process calls "init",
then ALL processes must call "init" prior to termination.
2. this process called "init", but exited without calling "finalize".
By rule, all processes that call "init" MUST call "finalize" prior to
exiting or it will be considered an "abnormal termination"
3. this process called "MPI_Abort" or "orte_abort" and the mca parameter
orte_create_session_dirs is set to false. In this case, the run-time cannot
detect that the abort call was an abnormal termination. Hence, the only
error message you will receive is this one.
This may have caused other processes in the application to be
terminated by signals sent by mpiexec (as reported here).
You can avoid this message by specifying -quiet on the mpiexec command line.
```
---
### Author:  [@quentin](https://community.freefem.org/u/quentin)
#### Post date: [October 15, 2025, 1:37pm UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/16 "2025-10-15T13:37:22Z")
Moreover, could you please tell me the function of `partitionerSeq`, `partitionerPar` and `CoherentGlobalMesh`.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [October 15, 2025, 3:33pm UTC](https://community.freefem.org/t/composite-finite-element-spaces-with-slepc/4000/17 "2025-10-15T15:33:08Z")
Thanks for the report, this is fixed in [Properly-sized interpolation matrix · FreeFem/FreeFem-sources@b406672 · GitHub](https://github.com/FreeFem/FreeFem-sources/commit/b406672e636729797ef76582d5f52cf12697f2ff), but it also needs a PR from Htool [Avoid empty-sized gemv by prj- · Pull Request #64 · htool-ddm/htool · GitHub](https://github.com/htool-ddm/htool/pull/64), so it will take a while to get everything integrated. `partitionerSeq` is to call a sequential mesh partitioner, `partitionerPar` is to call a distributed-memory mesh partitioner or broadcast the result from a sequential mesh partitioner, and `CoherentGlobalMesh` is to make sure that the numbering of the mesh is coherent for doing either a FEM or a BEM assembly. These questions are unrelated to your initial inquiries (I believe?), so it would be best to open new posts.