Question about complex value finite element

[yuesu jin]

Dear all,

  I am adding an absorbing boundary condition like step-24 did in the frequency domain, in which the time derivative gives a complex term.  I also found the complex acoustic wave problem step-29 which splits the complex wave function into two real parts. 

  What I want to know is what if I directly set up the matrix and rhs vector as complex<double> ? Why does step-29 says "it is often more convenient to split complex valued functions into their real and imaginary parts and use separate scalar finite element fields for discretizing each one of them" ? 

Best wishes,

--

Yuesu Jin,

Ph.D student,

University of Houston,

College of Natural Sciences and Mathematics,

Department of Earth and Atmospheric Sciences,
Houston, Texas 77204-5008


346-404-2062

[Wolfgang Bangerth]

Yuesu,

>   I am adding an absorbing boundary condition like step-24 did in the
> frequency domain, in which the time derivative gives a complex term.  I also
> found the complex acoustic wave problem step-29 which splits the complex wave
> function into two real parts.
>   What I want to know is what if I directly set up the matrix and rhs vector

> as complex<double> ? Why does step-29 says "/it is often more convenient to

> split complex valued functions into their real and imaginary parts and use

> separate scalar finite element fields for discretizing each one of them/" ?

The problem is that we don't have iterative solvers for problems in which the
matrix and vectors store complex values. We can, however, use PETSc's
complex-valued solvers as well as the SparseDirectUMFPACK solver. I think you
probably want to look at step-62 and step-58 for other options.

Best
W.


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

[yuesu jin]

Dear Dr. Bangerth,

   Thank you very much! I found step-62 yesterday and I have compared the difference between them.  I want to write two versions and compare their CPU time to get an exact result.

Best regards,

Yuesu 

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[Wolfgang Bangerth]

On 8/16/20 6:38 PM, yuesu jin wrote:
>    Thank you very much! I found step-62 yesterday and I have compared the
> difference between them.  I want to write two versions and compare their CPU
> time to get an exact result.

That would be interesting to hear about -- please let us know what you find!

[yuesu jin]

Sure, I will add my progress following this email. 

Best regards,

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