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SPEC 3.20
Stepped Pressure Equilibrium Code
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SPEC 3.20
Stepped Pressure Equilibrium Code
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Functions/Subroutines | |
| subroutine | df00ab (pNN, xi, Fxi, DFxi, Ldfjac, iflag) |
| Evaluates volume integrals, and their derivatives w.r.t. interface geometry, using "packed" format. More... | |
| subroutine | ma00aa (lquad, mn, lvol, lrad) |
| Calculates volume integrals of Chebyshev polynomials and metric element products. More... | |
| subroutine | spsint (lquad, mn, lvol, lrad) |
| Calculates volume integrals of Chebyshev-polynomials and metric elements for preconditioner. More... | |
| subroutine df00ab | ( | integer, intent(in) | pNN, |
| real, dimension(0:pnn-1), intent(in) | xi, | ||
| real, dimension(0:pnn-1), intent(out) | Fxi, | ||
| real, dimension(0:ldfjac-1,0:pnn-1), intent(out) | DFxi, | ||
| integer, intent(in) | Ldfjac, | ||
| integer, intent(in), value | iflag | ||
| ) |
Evaluates volume integrals, and their derivatives w.r.t. interface geometry, using "packed" format.
| [in] | pNN | |
| [in] | xi | |
| [out] | Fxi | |
| [out] | DFxi | |
| [in] | Ldfjac | |
| [in] | iflag |
References allglobal::cpus, df00ab(), allglobal::dma, allglobal::dmd, constants::half, inputlist::helicity, allglobal::ivol, allglobal::mbpsi, allglobal::mpi_comm_spec, allglobal::myid, inputlist::nvol, constants::one, fileunits::ounit, numerical::small, constants::two, and constants::zero.
Referenced by df00ab(), and ma02aa().
| subroutine ma00aa | ( | integer, intent(in) | lquad, |
| integer, intent(in) | mn, | ||
| integer, intent(in) | lvol, | ||
| integer, intent(in) | lrad | ||
| ) |
Calculates volume integrals of Chebyshev polynomials and metric element products.
Chebyshev-metric information
The following quantities are calculated:
\begin{eqnarray} \verb+DToocc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \\ \verb+DToocs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \\ \verb+DToosc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \\ \verb+DTooss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \end{eqnarray}
\begin{eqnarray} \verb+TTsscc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{ss} \\ \verb+TTsscs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{ss} \\ \verb+TTsssc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{ss} \\ \verb+TTssss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j} \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{ss} \end{eqnarray}
\begin{eqnarray} \verb+TDstcc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{s\theta} \\ \verb+TDstcs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{s\theta} \\ \verb+TDstsc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{s\theta} \\ \verb+TDstss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{s\theta} \end{eqnarray}
\begin{eqnarray} \verb+TDstcc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{s\zeta} \\ \verb+TDstcs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{s\zeta} \\ \verb+TDstsc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{s\zeta} \\ \verb+TDstss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i} \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{s\zeta} \end{eqnarray}
\begin{eqnarray} \verb+DDstcc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{\theta\theta} \\ \verb+DDstcs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{\theta\theta} \\ \verb+DDstsc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{\theta\theta} \\ \verb+DDstss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{\theta\theta} \end{eqnarray}
\begin{eqnarray} \verb+DDstcc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{\theta\zeta} \\ \verb+DDstcs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{\theta\zeta} \\ \verb+DDstsc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{\theta\zeta} \\ \verb+DDstss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{\theta\zeta} \end{eqnarray}
\begin{eqnarray} \verb+DDstcc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \cos\alpha_j \; \bar g_{\zeta\zeta} \\ \verb+DDstcs(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \cos\alpha_i \sin\alpha_j \; \bar g_{\zeta\zeta} \\ \verb+DDstsc(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \cos\alpha_j \; \bar g_{\zeta\zeta} \\ \verb+DDstss(l,p,i,j)+ & \equiv & \int ds \; {\overline T}_{l,i}^\prime \; {\overline T}_{p,j}^\prime \; \oint\!\!\!\oint \!d\theta d\zeta \,\,\, \sin\alpha_i \sin\alpha_j \; \bar g_{\zeta\zeta} \end{eqnarray}
where \({\overline T}_{l,i}\equiv T_l \, \bar s^{m_i/2}\) if the domain includes the coordinate singularity, and \({\overline T}_{l,i}\equiv T_l\) if not; and \(\bar g_{\mu\nu} \equiv g_{\mu\nu} / \sqrt g\).
The double-angle formulae are used to reduce the above expressions to the Fourier harmonics of \(\bar g_{\mu\nu}\): see kija and kijs, which are defined in preset.f90 .
| [in] | lquad | degree of quadrature |
| [in] | mn | number of Fourier harmonics |
| [in] | lvol | index of nested volume |
| [in] | lrad | order of Chebychev polynomials |
References compute_guvijsave(), allglobal::cpus, allglobal::dbdx, allglobal::ddttcc, allglobal::ddttcs, allglobal::ddttsc, allglobal::ddttss, allglobal::ddtzcc, allglobal::ddtzcs, allglobal::ddtzsc, allglobal::ddtzss, allglobal::ddzzcc, allglobal::ddzzcs, allglobal::ddzzsc, allglobal::ddzzss, allglobal::dtoocc, allglobal::dtoocs, allglobal::dtoosc, allglobal::dtooss, allglobal::gaussianabscissae, allglobal::gaussianweight, get_cheby(), get_zernike(), allglobal::goomne, allglobal::goomno, allglobal::gssmne, allglobal::gssmno, allglobal::gstmne, allglobal::gstmno, allglobal::gszmne, allglobal::gszmno, allglobal::gttmne, allglobal::gttmno, allglobal::gtzmne, allglobal::gtzmno, allglobal::gzzmne, allglobal::gzzmno, constants::half, allglobal::im, allglobal::in, allglobal::ki, allglobal::kija, allglobal::kijs, allglobal::lcoordinatesingularity, allglobal::lsavedguvij, ma00aa(), metrix(), allglobal::mne, allglobal::mpi_comm_spec, inputlist::mpol, allglobal::myid, allglobal::ncpu, allglobal::notstellsym, constants::one, fileunits::ounit, constants::pi, constants::pi2, allglobal::regumm, allglobal::tdstcc, allglobal::tdstcs, allglobal::tdstsc, allglobal::tdstss, allglobal::tdszcc, allglobal::tdszcs, allglobal::tdszsc, allglobal::tdszss, allglobal::ttsscc, allglobal::ttsscs, allglobal::ttsssc, allglobal::ttssss, constants::two, volume(), inputlist::wmacros, allglobal::yesstellsym, and constants::zero.
Referenced by dfp100(), get_lu_beltrami_matrices(), and ma00aa().
| subroutine spsint | ( | integer, intent(in) | lquad, |
| integer, intent(in) | mn, | ||
| integer, intent(in) | lvol, | ||
| integer, intent(in) | lrad | ||
| ) |
Calculates volume integrals of Chebyshev-polynomials and metric elements for preconditioner.
Computes the integrals needed for spsmat.f90. Same as ma00aa.f90, but only compute the relevant terms that are non-zero.
| lquad | |
| mn | |
| lvol | |
| lrad |
References allglobal::cpus, allglobal::ddttcc, allglobal::ddttcs, allglobal::ddttsc, allglobal::ddttss, allglobal::ddtzcc, allglobal::ddtzcs, allglobal::ddtzsc, allglobal::ddtzss, allglobal::ddzzcc, allglobal::ddzzcs, allglobal::ddzzsc, allglobal::ddzzss, allglobal::dtoocc, allglobal::dtoocs, allglobal::dtoosc, allglobal::dtooss, allglobal::gaussianabscissae, allglobal::gaussianweight, get_cheby(), get_zernike(), allglobal::guvijsave, constants::half, allglobal::im, allglobal::in, allglobal::ki, allglobal::kija, allglobal::kijs, allglobal::lcoordinatesingularity, allglobal::mne, allglobal::mpi_comm_spec, inputlist::mpol, allglobal::myid, allglobal::ncpu, allglobal::notstellsym, allglobal::ntz, constants::one, fileunits::ounit, constants::pi, constants::pi2, allglobal::regumm, numerical::small, spsint(), numerical::sqrtmachprec, allglobal::tdstcc, allglobal::tdstcs, allglobal::tdstsc, allglobal::tdstss, allglobal::tdszcc, allglobal::tdszcs, allglobal::tdszsc, allglobal::tdszss, allglobal::ttsscc, allglobal::ttsscs, allglobal::ttsssc, allglobal::ttssss, constants::two, numerical::vsmall, inputlist::wmacros, allglobal::yesstellsym, and constants::zero.
Referenced by dfp100(), and spsint().
1.9.2