Support for complex numbers

[HelgeGehring]

Thanks for the great library!

Would it be possible to add support for complex numbers?

[pablorubial]

I have been working on this, and it appears that adding the following simple line of code to the build.jl file of GridapPETSc automatically provides support. With this modification, I was able to successfully solve the Helmholtz equation using complex numbers.

if scalar_type[] == PETSC_DOUBLE &&  scalar_size[] == 8
  PetscScalar = Float64
elseif scalar_type[] == PETSC_DOUBLE &&  scalar_size[] == 4
  PetscScalar = Float32
elseif scalar_type[] == PETSC_COMPLEX &&  scalar_size[] == 16
  PetscScalar = ComplexF64
else
  @error scalar_msg
end

A the same time, you have to compile PETSc locally using the flag --with-scalar-type=complex. For the local compilation something like this work for me:

# Configure PETSc
python3 ./configure \ 
--PETSC_ARCH=linux-gnu-complex-64 \
--with-cc=mpicc \
--with-cxx=mpicxx \
--with-fc=mpif90 \
--with-scalar-type=complex \
--with-pic=1 \
--with-shared-libraries=1 \
--with-debugging=no \
--download-fblaslapack=1 \
--download-metis=1 \
--download-parmetis=1 \
--download-superlu_dist=1 \
--download-mumps=1 \
--download-scalapack=1 \
--download-hypre=1 \
--download-elemental=1 \
--download-cmake
# Compile PETSc
make PETSC_DIR=/home/pablo/software/petsc PETSC_ARCH=linux-gnu-complex-64 all
# Check PETSc build
make PETSC_DIR=/home/pablo/software/petsc PETSC_ARCH=linux-gnu-complex-64 check

Could you check this @JordiManyer @fverdugo ?

[JordiManyer]

Hi @pablorubial thanks for the work! That seems right to me. Would you be able to open a PR with the changes?

[pablorubial]

Done in pull request #106. Thanks to you @JordiManyer!