[bddcml-users] Complex number support

[Sebastian Grimberg]

Hi Jakub,

Thanks for getting back to me, it's nice to meet you!

The applications I'm interested in involve high-frequency time-harmonic
electromagnetics, so typically dealing with complex symmetric indefinite
operators. I know there is quite a bit of H(curl) specific BDDC literature
out there involving better selection of coarse constraints using change of
basis for Nedelec elements, but I figure if I end up needing this I could
use the general user-defined constraints in BDDCML (maybe you have some
thoughts on this?).

I'd be happy to work on implementing complex number support in the library
and see where it goes. I have a few thoughts:

1. At a high level, I could see two ways to manage the different scalar
types.

- First, something like what MUMPS does, is to just maintain two versions
of every type-specific file so the user would include the correct module
for double/complex support. This could be simple for just double/complex,
but if later you also want to add an option for single precision or 64-bit
integers it becomes rather involved.
- Alternatively, we could use conditional compilation in a more "C"
approach to define at compile time the scalar type to be real(kind=8) or
complex(kind=8) and use this throughout the code, wrapping type specific
commands in #if defined/#else pragmas. I'm not even sure if this is
possible in Fortran but would be the way to do it in C/C++ I think. Do you
know anything about this?


2. The blopex object files for double versus complex share the same names
(see the files in blopex_serial_double or blopex_serial_complex which would
be needed). I presume this would cause some build issues, which further
motivates building only a single library for real OR complex numbers and
then just linking to the correct blopex version. But again, I don't know
how this is possible in Fortran.

3. In the case of complex matrices, the partition of unity weights for
interface degrees of freedom could be complex (when using diagonal
stiffness scaling, for example). Is this allowed? Do we require them to be
Hermitian at least? I see that for indefinite problems they are constrained
to be positive. This is a bit beyond my expertise but I am not sure of the
implications for requiring them to always be real and positive or allowing
them to be complex and how to handle that in the dot products required for
Krylov methods. I'm not sure what PETSc's PCBDDC does about this.

Sorry for the long email, I hope this makes sense to you and I'm curious to
know your input before getting started. Thanks again!

Sebastian

On Fri, Jan 22, 2021 at 7:28 AM Jakub Sistek <sistek at math.cas.cz> wrote:

> Hi Sebastian,
>
> first of all, thank you for your interest in BDDCML!
>
> So far, there has been no need for supporting complex numbers in BDDCML,
> so you are the first one asking for this :-) What applications do you have
> in mind?
>
> Implementation-wise, this may not be too bad, as you suggest, although the
> "double" type is hard-coded in a lot of subroutines where it would require
> changing. Even blopex has a version for complex numbers, although one
> should start without the adaptivity. And yes, it would be applicable only
> to Hermitian matrices. MUMPS supports all the types one needs, so this
> should be straightforward.
>
> More flexible variable types would be helpful in other scenarios I am
> interested in, such as
> * using long integers for certain indices for very large problems
> * using single precision instead of double
>
> Also algorithmically, I am not aware of any principal issues. I know other
> DD codes support complex numbers, such as HPDDM or the PCBDDC
> preconditioner in PETSc. I know the developers, so I would be able to ask
> for advice.
>
> This would actually be a nice extension of the functionality of BDDCML! If
> you were interested in helping with this, I would be happy to give you
> access to the project on Github and we could try to devise such version in
> a new branch together.
>
> Let me know what you think.
>
> Best wishes,
>
> Jakub
>
>
>
> On 22/01/2021 05:29, Sebastian Grimberg wrote:
>
> Hello everyone,
>
> I’m a new user and am wondering if there is any interest or thoughts on
> supporting complex numbers in BDDCML? I’m unsure about the blopex
> dependency for adaptivity, and further it may not even be applicable unless
> the input materials is Hermitian, but it seems like it could be doable by
> calling the correct MUMPS library and adjusting the interface a bit. Would
> this be worth spending time to develop, and are there any other foreseeable
> issues?
>
> Cheers,
>
> Sebastian Grimberg
>
> _______________________________________________
> bddcml-users mailing listbddcml-users at math.cas.czhttps://list.math.cas.cz/listinfo/bddcml-users
>
>
>
> --
> Jakub Sistek, Ph.D.
>
> Researcher
> Institute of Mathematics
> Czech Academy of Sciences
> sistek at math.cas.czhttp://www.math.cas.cz/~sistek
> +420 222 090 710
>
>
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