Improve OpenMP in Biot-Savart code

[pazathoth]

Multi-threaded FFTW starts to be useful when arrays have a few thousand entries, which is currently not the case in the Biot-Savart computations. Thus it would be more useful to use single-threaded FFTW instead and parallelize the surrounding loop, i.e. instead of

p_fft_output = fftw_alloc_complex(int(nfft, c_size_t))
call c_f_pointer(p_fft_output, fft_output, [nfft])
p_AR = fftw_alloc_real(int(nphi, c_size_t))
call c_f_pointer(p_AR, AR, [nphi])
! ... further input arrays
do kZ = 1, nZ
  do kR = 1, nR
    !$omp parallel do shared(AR) ...
    do kphi = 1, nphi
      ! ... fill input arrays
    end do
    !$omp end parallel do
    call fftw_execute_dft_r2c(plan_nphi, AR, fft_output)
    AnR(0:nmax, kR, kZ, kc) = fft_output(1:nmax+1) / dble(nphi)
    ! ... further transforms
  end do
end do

do

!$omp parallel private(AR, fft_output), shared(AnR)
p_fft_output = fftw_alloc_complex(int(nfft, c_size_t))
call c_f_pointer(p_fft_output, fft_output, [nfft])
p_AR = fftw_alloc_real(int(nphi, c_size_t))
call c_f_pointer(p_AR, AR, [nphi])
! ... further input arrays
!$omp do collapse(3) ...
do kZ = 1, nZ
  do kR = 1, nR
    do kphi = 1, nphi
      ! ... fill input arrays
    end do
    call fftw_execute_dft_r2c(plan_nphi, AR, fft_output)
    AnR(0:nmax, kR, kZ, kc) = fft_output(1:nmax+1) / dble(nphi)
    ! ... further transforms
  end do
end do
!$omp end do
!$omp end parallel

Finally, the question is whether to link fftw3 or fftw3_omp.