# Building RHS block vector manually
**URL:** https://community.freefem.org/t/building-rhs-block-vector-manually/4131
**Category:** General Discussion
**Created:** [November 11, 2025, 7:22pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131 "2025-11-11T19:22:40Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@gart1542](https://community.freefem.org/u/gart1542)
#### Post date: [November 11, 2025, 7:22pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/1 "2025-11-11T19:22:40Z")
Hello all,
I have the following weak formulations:
> varf Lhs([dc, dmu], [v, psi]) =
>
> ```auto
> int2d(Th)((1/chi^2)\*(tau\*eps\*((dx(dmu))\*(dx(v)) + (dy(dmu))\*(dy(v)))) + dc\*v )
>
> + int2d(Th)( dmu\*psi - (chi^2)\*(3./eps)\*(c\*c)\*dc\*psi - (chi^2)\*eps\*( (dx(dc))\*(dx(psi)) + (dy(dc))\*(dy(psi)) ) );
>
> ```
>
> varf Rhs([dc, dmu], [v, psi]) =
>
> ```auto
> int2d(Th)((1/chi)\*(tau\*eps\*((dx(mu))\*(dx(v)) + (dy(mu))\*(dy(v))) + (c - c0)\*v) )
>
> + int2d(Th)( chi\*(mu\*psi - (1/eps)\*(c\*c\*c - c0)\*psi - eps\*((dx(c))\*(dx(psi)) + (dy(c))\*(dy(psi)))) );
>
> ```
And I wish to build the RHS vector manually.
The LHS seems to work, I have built it as follows:
> varf vK([u1,u2],[v1,v2]) = int2d(Th) ( dx(u1)\*dx(v1) + dy(u1)\*dy(v1) );
>
> varf vM([u1,u2],[v1,v2]) = int2d(Th)( u1\*v1 );
>
> matrix K = vK(Vh,Vh);
>
> matrix M = vM(Vh,Vh);
>
> varf j(u,v) = int2d(Th)( 3.0\*(c\*c) \* u \* v );
>
> matrix J = j(Vh, Vh);
>
> matrix A11 = (1/chi^2)\*(tau\*eps)\*K;
>
> matrix A12 = M;
>
> matrix A21 = M;
>
> matrix A22 = -(chi^2)\*J -(chi^2)\*K;
>
> matrix A = [
>
> ```auto
> \[A11, A12\],
>
> \[A21, A22\]
>
> \];
>
> ```
And I wish to build the RHS the same way. So far I have:
> varf rhsF1([dmu, dc], [v, psi]) = int2d(Th)( (c - c0)\*v );
>
> varf rhsF2([dmu, dc], [v, psi]) = int2d(Th)( (tau\*eps\*( (dx(mu))\*(dx(v)) + (dy(mu))\*(dy(v)) ) ));
>
> varf rhsG1([dmu, dc], [v, psi]) = int2d(Th)(mu\*psi);
>
> varf rhsG2([dmu, dc], [v, psi]) = int2d(Th)(-(1/eps)\*(c\*c\*c - c0)\*psi);
>
> varf rhsG3([dmu, dc], [v, psi]) = int2d(Th)( - eps\*((dx(c))\*(dx(psi)) + (dy(c))\*(dy(psi))));
>
> matrix F1 = rhsF1(ME,ME);
>
> matrix F2 = rhsF2(ME,ME);
>
> matrix G1 = rhsG1(ME,ME);
>
> matrix G2 = rhsG2(ME,ME);
>
> matrix G3 = rhsG3(ME,ME);
>
> matrix F = (1/chi)\*F1 + (1/chi)\*F2;
>
> matrix G = chi\*G1 + chi\*G2 + chi\*G3;
>
> matrix b = [
>
> ```auto
> [F],
>
> [G]
>
> ];
>
> ```
However, when I try to solve sol = A^-1 \* b, I get the following error:
> real[int] sol = A^-1 \* b; error operator \* \<18Matrice\_Creuse\_invIdE\>, \<14Matrice\_CreuseIdE\>
Is there an issue with building b like a block matrix? Is there a way to do this with the F and G components as I have them defined?
Thanks in advance.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [November 11, 2025, 8:05pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/2 "2025-11-11T20:05:45Z")
Use a `real[int]` for the RHS, not a `matrix`. There are many examples either here or in FreeFEM sources.
---
### Author:  [@gart1542](https://community.freefem.org/u/gart1542)
#### Post date: [November 12, 2025, 12:24am UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/3 "2025-11-12T00:24:57Z")
Is it possible to use it with the manually constructed components like F1,F2, etc.? My goal is to explicitly build the vectors from the variational formulations, without using real[int] b = Rhs(0, ME).
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [November 12, 2025, 4:44am UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/4 "2025-11-12T04:44:32Z")
Yes, again, that’s how it’s done in many examples.
---
### Author:  [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [November 12, 2025, 12:16pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/5 "2025-11-12T12:16:15Z")
You have to use the syntax `real[int] F1 = rhsF1(0, ME)` for each of your `varf`s.
Indeed `a(ME,ME)` where `a` is a `varf` means that you take the bilinear part in `a`, giving a matrix,
whereas `a(0,ME)` means that you take the linear part in `a`, giving a vector.
At the end you build `real[int] b=[F,G]` and `real[int] sol=A^-1*b`
---
### Author:  [@gart1542](https://community.freefem.org/u/gart1542)
#### Post date: [November 12, 2025, 5:50pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/6 "2025-11-12T17:50:47Z")
Thank you! That helped a lot, I can now get through the constructions without any errors. However, when I set `real[int] sol=A^-1*b;` and run the code I get the following error:
```auto
ATERROR 1 : VirtualMatrix:: no solver ???
current line = 117
Exec error : MATERROR
– number :1
Exec error : MATERROR
– number :1
err code 8 , mpirank
```
Do I need to manually set the solver? If so, do I set the solver for A,b, or the components F,G ?
I tried `set(A, solver = sparsesolver);`however, I still receive an error setting up the norm calculations. line 129: `real[int] Asol = A*sol;`
```auto
current line = 129
Assertion fail : (B->ChecknbColumn(y.N()))
line :270, in file ./../femlib/RNM.hpp
Assertion fail : (B->ChecknbColumn(y.N()))
line :270, in file ./../femlib/RNM.hpp
err code 6 , mpirank 0
```
Thank you for the help, I really appreciate it.
---
### Author:  [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [November 12, 2025, 6:11pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/7 "2025-11-12T18:11:20Z")
You are right, you need to set `set(A,solver=sparsesolver);`
About your error, try it in two lines:
```auto
real[int] Asol(sol.n);
Asol=A*sol;
```
But maybe it is not that, I can’t say without your full code.
---
### Author:  [@gart1542](https://community.freefem.org/u/gart1542)
#### Post date: [November 12, 2025, 6:39pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/8 "2025-11-12T18:39:09Z")
Unfortunately, that didn’t work. Here is my full code, please take your time, I really do appreciate it.
[https://github.com/gart1542/Cahn-Hilliard-FreeFEM-.git](https://github.com/gart1542/Cahn-Hilliard-FreeFEM-.git)
---
### Author:  [@fb77](https://community.freefem.org/u/fb77)
#### Post date: [November 12, 2025, 8:29pm UTC](https://community.freefem.org/t/building-rhs-block-vector-manually/4131/9 "2025-11-12T20:29:37Z")
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