Table .

Algorithm VI. Implementation of ${\tilde{\mathbf{u}}}_{\mathrm{sph}}={\mathbf{H}}_{\mathrm{sph}}{\mathit{\alpha }}_{\mathrm{sph}}$ (on host).

Input:αsph, ${\tilde{\mathbf{p}}}_0$

Output:${\tilde{\mathbf{u}}}_{\mathrm{sph}}$

1: fornpth = 0 toNpth − 1 do

2:   parm_fwdarg[npth].npth = npth

3:   parm_fwdarg[npth].${\tilde{p}}_0$ = &${\tilde{\mathbf{p}}}_0\left[0\right]$

4:   parm_fwdarg[npth].αpth=&αsph[npthNxNyNz/Npth]

5:   parm_fwdarg[npth].${\tilde{u}}_{\mathrm{pth}}^{\prime }$=$\&{\tilde{\mathbf{u}}}_{\mathrm{sph}}^{\prime }\left[n_{\mathrm{pth}}{N}_r{N}_v{N}_f\right]$ {Pass addresses

of arrays to each pthread}

6:   pthread_create(&pthreads[npth], NULL, fwd_pthread, (void *)

(parm_fwdarg+npth)) {Call function fwd_pthread}

7: endfor

8: fornpth = 0 toNpth − 1 do

9:   forn = 0 toNrNvNfdo

10:      ${\tilde{\mathbf{u}}}_{\mathrm{sph}}\left[n\right]+={\tilde{\mathbf{u}}}_{\mathrm{sph}}^{\prime }[n+n_{\mathrm{pth}}{N}_r{N}_v{N}_f]$

11:   endfor

12: endfor