### [SOLVED] How to give the Dirichlet boundary values correctly ? (The value needed to calculated before boundary definition )

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Hi, all

I confused by a new question, which can be expressed as follows.

I want to solve a Poisson equation, whose boundary conditions are not a function or a constant.

$\Delta u=f$Δ

The solution $u$

some example code:

grad_phi = project(grad(phi), V)

left = DirichletBC(V,(0,grad_phi[1]),Left)

AND THE ERROR:

File "/usr/lib/python2.7/dist-packages/dolfin/functions/expression.py", line 602, in __new__

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/expressions.py", line 217, in compile_expressions

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/expressions.py", line 145, in compile_expression_code

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/jit.py", line 64, in mpi_jit

return local_jit(*args, **kwargs)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/compilemodule.py", line 458, in compile_extension_module

**instant_kwargs)

File "/usr/lib/python2.7/dist-packages/instant/build.py", line 563, in build_module

recompile(modulename, module_path, new_compilation_checksum, build_system)

File "/usr/lib/python2.7/dist-packages/instant/build.py", line 165, in recompile

instant_error(msg % (cmd, compile_log_filename_dest))

I know the assignment, must be wrong, however, i do not know how to make it to work.

Anyone can help to make it clear?

Best, Hamilton

I confused by a new question, which can be expressed as follows.

I want to solve a Poisson equation, whose boundary conditions are not a function or a constant.

$\Delta u=f$Δ

`u`=`ƒ`; in $\Omega$Ω with boundary conditions $u=g\left(\phi\right);$`u`=`g`(`ϕ`); on $\partial\Omega$∂Ω .The solution $u$

`u`is a vector. So, the boundary condition value can be written in a form $g=(0,\frac{d\phi}{dx})^T$`g`=(0,`d``ϕ``d``x`)^{T}, where, $\phi$`ϕ`is a function or a solution comes from the previous step, and the superscript T is a transposition of a vector.some example code:

grad_phi = project(grad(phi), V)

left = DirichletBC(V,(0,grad_phi[1]),Left)

AND THE ERROR:

File "/usr/lib/python2.7/dist-packages/dolfin/functions/expression.py", line 602, in __new__

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/expressions.py", line 217, in compile_expressions

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/expressions.py", line 145, in compile_expression_code

mpi_comm=mpi_comm)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/jit.py", line 64, in mpi_jit

return local_jit(*args, **kwargs)

File "/usr/lib/python2.7/dist-packages/dolfin/compilemodules/compilemodule.py", line 458, in compile_extension_module

**instant_kwargs)

File "/usr/lib/python2.7/dist-packages/instant/build.py", line 563, in build_module

recompile(modulename, module_path, new_compilation_checksum, build_system)

File "/usr/lib/python2.7/dist-packages/instant/build.py", line 165, in recompile

instant_error(msg % (cmd, compile_log_filename_dest))

I know the assignment, must be wrong, however, i do not know how to make it to work.

Anyone can help to make it clear?

Best, Hamilton

Community: FEniCS Project

### 1 Answer

1

If V is a vector function space you can try something like this

`left = DirichletBC(V, as_vector([0, grad_phi[0]]), Left)`

That is weird. The next example works fine for me in dolfin 2017.1

```
from dolfin import *
mesh = UnitSquareMesh(10,10)
V = VectorFunctionSpace(mesh, "Lagrange", 2)
# Create boundary condition
grad_phi = project(Expression(("x[0]", "x[1]"), degree=2), V)
bc = DirichletBC(V, as_vector([0, grad_phi[1]]), "on_boundary")
# Test
u = Function(V)
bc.apply(u.vector())
plot(u, interactive=True)
```

written
10 months ago by
Hernán Mella

It works for me now.

I made a mistake definition.

THE METHOD WORKS!

Thanks so much

Best, Hamilton

I made a mistake definition.

THE METHOD WORKS!

Thanks so much

Best, Hamilton

written
10 months ago by
Hamilton

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V = VectorFunctionSpace(mesh, "Lagrange", 2); V is a VectorFcuntionSpace

TypeError: 'VectorFunctionSpace' object does not support indexing