Nonhomogeneous Dirichlet Boundary conditions using a Dirichlet lift

[Giulia Deolmi]

Dear deal.ii users,

is there someone who implemented Nonhomogeneous Dirichlet Boundary conditions using a Dirichlet lift? 

Thanks a lot in advance,

Kind regards,

Giulia

[Praveen C]

Hello Giulia

The usual way of applying Dirichlet bc in deal.II essentially does a lifting approach. If 

u = g on boundary

then the lifting is

u_{g,h}(x) = sum_(i on boundary) g(x_i) \phi_i(x)

Did you want to use a different lifting ?

Best

praveen

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[Giulia Deolmi]

Hi Praveen,

as far as I have understood (but I might be wrong), the functions

VectorTools::interpolate_boundary_values

MatrixTools::apply_boundary_values

find the nodes where Dirichlet BC's are applied and then there impose the corrensponding boundary value, after having built the system matrix and right-hand side.

Another possibility would be to use a Dirichlet lift, change the weak formulation and solve for homogeneous Dirichlet boundary conditions. I am wondering if someone already did this or if it somewhere implemented in deal.ii

I am currently dealing with parameter dependent Dirichlet boundary conditions and I would like to be able to see explicitly how these parameters enter the system matrix and the right-hand side, writing the dependency in an affine way, i.e. p1 A1 + p2 A2 +...= p1 f1 + p2 f2 +.... 

I am currently not able to do it using the function 

MatrixTools::apply_boundary_values .

Thanks for your reply!

Kind regards,

Giulia

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[Wolfgang Bangerth]

> as far as I have understood (but I might be wrong), the functions
> VectorTools::interpolate_boundary_values

> <https://www.dealii.org/8.4.0/doxygen/deal.II/namespaceVectorTools.html#af6f700f193e9d5b52e9efe55e9b872d5>
> MatrixTools::apply_boundary_values
> <https://www.dealii.org/8.4.0/doxygen/deal.II/namespaceMatrixTools.html#a41a069894610445f84840d712d4f891e>

> find the nodes where Dirichlet BC's are applied and then there impose the
> corrensponding boundary value, after having built the system matrix and
> right-hand side.
>
> Another possibility would be to use a Dirichlet lift, change the weak
> formulation and solve for homogeneous Dirichlet boundary conditions. I am
> wondering if someone already did this or if it somewhere implemented in deal.ii

It may not look like it, but that's really what the functions do that you cite
above.

The algorithm is a bit complicated, but take a look at lectures 21.6 and 21.65
here:
http://www.math.colostate.edu/~bangerth/videos.html

Best
Wolfgang

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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Giulia Deolmi]

Thanks a lot!

I will have a look at it,

kind regards,

Giulia