New step tutorial elastic wave equation with PMLs, complex-valued algebra

[Daniel Garcia]

Hi,

I'm a researcher at the CNRS (Paris). My nickname in GitHub is dangars (I contributed with a couple of pull requests)

I work in optomechanics/phononics. I've been using deal.ii for 6 months and it works great! I developed a model of the elastic wave equation in 2D that uses PMLs.

I'm preparing a contribution of a new step tutorial of the elastic wave equation with PMLs in 3D to GitHub/dealii. This will be useful for the phononics and optomechanics communities.

The separation real/imag works very well with PMLs.

The elastic/PML matrix with real/imag separation is big. If I use complex numbers the matrix will be compact and will fit in one line (much better for a step tutorial)

What is the status of complex valued calculations? Is it ready to solve a differential equations? Is there a performance penalty with complex numbers vs separate real/imag parts?

According to this, it seems to be almost ready:

https://github.com/dealii/dealii/projects/1

Thanks,

Daniel Garcia

[Denis Davydov]

Hi Daniel,

Thanks for willing to contribute the tutorial.

As far as as recall there just a few things left related to complex numbers. 

The biggest one is complex-valued Dirichlet constraints in ConstraintMatrix object

https://github.com/dealii/dealii/issues/1760 

That's not possible yet. Otherwise all the solvers and linear algebra is ready. So you can certainly assemble system and solve it.

Denis.

[Daniel Garcia]

Thanks Denis,

I will try to assemble and solve the system using complex-valued algebra.

Best,

Daniel

[Wolfgang Bangerth]

On 04/28/2018 10:36 PM, Denis Davydov wrote:
>
> As far as as recall there just a few things left related to complex numbers.
> The biggest one is complex-valued Dirichlet constraints in ConstraintMatrix object
> https://github.com/dealii/dealii/issues/1760
> That's not possible yet. Otherwise all the solvers and linear algebra is
> ready. So you can certainly assemble system and solve it.

Denis -- out of curiosity, what solver are you using for complex-valued linear
systems? I don't think the deal.II SolverGMRES class works, and obviously the
other iterative solvers don't either. Nor does UMFPACK.

Best
W.

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

[Denis Davydov]

> On 30 Apr 2018, at 04:54, Wolfgang Bangerth <bang...@colostate.edu> wrote:
>
> On 04/28/2018 10:36 PM, Denis Davydov wrote:
>> As far as as recall there just a few things left related to complex numbers.
>> The biggest one is complex-valued Dirichlet constraints in ConstraintMatrix object
>> https://github.com/dealii/dealii/issues/1760
>> That's not possible yet. Otherwise all the solvers and linear algebra is ready. So you can certainly assemble system and solve it.
>
> Denis -- out of curiosity, what solver are you using for complex-valued linear systems? I don't think the deal.II SolverGMRES class works, and obviously the other iterative solvers don't either. Nor does UMFPACK.

I would not be so sure about it, but I have not tried either.
I am quite certain complex-valued PETSc will work.

ps. I don’t use any of them, some time ago I invested a lot of efforts to push forward
complex-valued algebra in deal.II (which was also followed by others), but strangely enough I never used it.

>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> www: http://www.math.colostate.edu/~bangerth/
>

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[Daniel Garcia]

On Monday, April 30, 2018 at 7:13:26 AM UTC+2, Denis Davydov wrote:

> On 30 Apr 2018, at 04:54, Wolfgang Bangerth <bang...@colostate.edu> wrote:
>
> On 04/28/2018 10:36 PM, Denis Davydov wrote:
>> As far as as recall there just a few things left related to complex numbers.
>> The biggest one is complex-valued Dirichlet constraints in ConstraintMatrix object
>> https://github.com/dealii/dealii/issues/1760
>> That's not possible yet. Otherwise all the solvers and linear algebra is ready. So you can certainly assemble system and solve it.
>
> Denis -- out of curiosity, what solver are you using for complex-valued linear systems? I don't think the deal.II SolverGMRES class works, and obviously the other iterative solvers don't either. Nor does UMFPACK.

I would not be so sure about it, but I have not tried either.
I am quite certain complex-valued PETSc will work.

ps. I don’t use any of them, some time ago I invested a lot of efforts to push forward
complex-valued algebra in deal.II (which was also followed by others), but strangely enough I never used it.

 

I will write the first version of the code with real/imag separation and UMFPACK. This works well with PML matrices.

Then I will modify the code and use complex-valued algebra with PETSc.

This is an extra-step, but it will allow to compare the results. 

Best,

Daniel