global.f90 File Reference

Defines input namelists and global variables, and opens some output files. More...

Data Types
type	typedefns::subgrid
	used for quantities which have different resolutions in different volumes, e.g. the vector potential More...
type	typedefns::matrixlu
type	typedefns::derivative
	\({\rm d}\mathbf{B}/{\rm d}\mathbf{X}\) (?) More...

Modules
module	constants
	some constants used throughout the code
module	numerical
	platform-dependant numerical resolution
module	fileunits
	central definition of file units to avoid conflicts
module	cputiming
	timing variables
module	typedefns
	type definitions for custom datatypes
module	allglobal
	global variable storage used as "workspace" throughout the code
module	fftw_interface
	Interface to FFTW library.

Functions/Subroutines
subroutine	fileunits::mute (action)
subroutine	allglobal::build_vector_potential (lvol, iocons, aderiv)
subroutine	allglobal::set_mpi_comm (comm)
pure character(len=1000) function	allglobal::get_hidden (ext)
subroutine	allglobal::read_inputlists_from_file ()
subroutine	allglobal::write_spec_namelist ()
subroutine	allglobal::check_inputs ()
subroutine	allglobal::broadcast_inputs
subroutine	allglobal::wrtend
	Write the restart file ext.sp.end.
subroutine	allglobal::ismyvolume (vvol)
	Check if volume vvol is associated to the corresponding MPI node. More...
subroutine	allglobal::whichcpuid (vvol, cpu_id)
	Returns which MPI node is associated to a given volume.

Variables
real, parameter	constants::zero = 0.0
	0
real, parameter	constants::one = 1.0
	1
real, parameter	constants::two = 2.0
	2
real, parameter	constants::three = 3.0
	3
real, parameter	constants::four = 4.0
	4
real, parameter	constants::five = 5.0
	5
real, parameter	constants::six = 6.0
	6
real, parameter	constants::seven = 7.0
	7
real, parameter	constants::eight = 8.0
	8
real, parameter	constants::nine = 9.0
	9
real, parameter	constants::ten = 10.0
	10
real, parameter	constants::eleven = 11.0
	11
real, parameter	constants::twelve = 12.0
	12
real, parameter	constants::hundred = 100.0
	100
real, parameter	constants::thousand = 1000.0
	1000
real, parameter	constants::half = one / two
	1/2
real, parameter	constants::third = one / three
	1/3
real, parameter	constants::quart = one / four
	1/4
real, parameter	constants::fifth = one / five
	1/5
real, parameter	constants::sixth = one / six
	1/6
real, parameter	constants::pi2 = 6.28318530717958623
	\(2\pi\)
real, parameter	constants::pi = pi2 / two
	\(\pi\)
real, parameter	constants::mu0 = 2.0E-07 * pi2
	\(4\pi\cdot10^{-7}\)
real, parameter	constants::goldenmean = 1.618033988749895
	golden mean = \(( 1 + \sqrt 5 ) / 2\) ;
real, parameter	constants::version = 3.23
	version of SPEC
real, parameter	numerical::machprec = 1.11e-16
	machine precision: 0.5*epsilon(one) for 64 bit double precision
real, parameter	numerical::vsmall = 100*machprec
	very small number
real, parameter	numerical::small = 10000*machprec
	small number
real, parameter	numerical::sqrtmachprec = sqrt(machprec)
	square root of machine precision
real, parameter	numerical::logtolerance = 1.0e-32
	this is used to avoid taking alog10(zero); see e.g. dforce;
integer	fileunits::iunit = 10
	input; used in global/readin:ext.sp, global/wrtend:ext.sp.end
integer	fileunits::ounit = 6
	screen output;
integer	fileunits::gunit = 13
	wall geometry; used in wa00aa
integer	fileunits::aunit = 11
	vector potential; used in ra00aa:.ext.AtAzmn;
integer	fileunits::dunit = 12
	derivative matrix; used in newton:.ext.GF;
integer	fileunits::hunit = 14
	eigenvalues of Hessian; under re-construction;
integer	fileunits::munit = 14
	matrix elements of Hessian;
integer	fileunits::lunit = 20
	local unit; used in lunit+myid: pp00aa:.ext.poincare,.ext.transform;
integer	fileunits::vunit = 15
	for examination of adaptive quadrature; used in casing:.ext.vcint;
real	cputiming::tmanual = 0.0
real	cputiming::manualt = 0.0
real	cputiming::trzaxis = 0.0
real	cputiming::rzaxist = 0.0
real	cputiming::tpackxi = 0.0
real	cputiming::packxit = 0.0
real	cputiming::tvolume = 0.0
real	cputiming::volumet = 0.0
real	cputiming::tcoords = 0.0
real	cputiming::coordst = 0.0
real	cputiming::tbasefn = 0.0
real	cputiming::basefnt = 0.0
real	cputiming::tmemory = 0.0
real	cputiming::memoryt = 0.0
real	cputiming::tmetrix = 0.0
real	cputiming::metrixt = 0.0
real	cputiming::tma00aa = 0.0
real	cputiming::ma00aat = 0.0
real	cputiming::tmatrix = 0.0
real	cputiming::matrixt = 0.0
real	cputiming::tspsmat = 0.0
real	cputiming::spsmatt = 0.0
real	cputiming::tspsint = 0.0
real	cputiming::spsintt = 0.0
real	cputiming::tmp00ac = 0.0
real	cputiming::mp00act = 0.0
real	cputiming::tma02aa = 0.0
real	cputiming::ma02aat = 0.0
real	cputiming::tpackab = 0.0
real	cputiming::packabt = 0.0
real	cputiming::ttr00ab = 0.0
real	cputiming::tr00abt = 0.0
real	cputiming::tcurent = 0.0
real	cputiming::curentt = 0.0
real	cputiming::tdf00ab = 0.0
real	cputiming::df00abt = 0.0
real	cputiming::tlforce = 0.0
real	cputiming::lforcet = 0.0
real	cputiming::tintghs = 0.0
real	cputiming::intghst = 0.0
real	cputiming::tmtrxhs = 0.0
real	cputiming::mtrxhst = 0.0
real	cputiming::tlbpol = 0.0
real	cputiming::lbpolt = 0.0
real	cputiming::tbrcast = 0.0
real	cputiming::brcastt = 0.0
real	cputiming::tdfp100 = 0.0
real	cputiming::dfp100t = 0.0
real	cputiming::tdfp200 = 0.0
real	cputiming::dfp200t = 0.0
real	cputiming::tdforce = 0.0
real	cputiming::dforcet = 0.0
real	cputiming::tnewton = 0.0
real	cputiming::newtont = 0.0
real	cputiming::tcasing = 0.0
real	cputiming::casingt = 0.0
real	cputiming::tbnorml = 0.0
real	cputiming::bnormlt = 0.0
real	cputiming::tjo00aa = 0.0
real	cputiming::jo00aat = 0.0
real	cputiming::tpp00aa = 0.0
real	cputiming::pp00aat = 0.0
real	cputiming::tpp00ab = 0.0
real	cputiming::pp00abt = 0.0
real	cputiming::tbfield = 0.0
real	cputiming::bfieldt = 0.0
real	cputiming::tstzxyz = 0.0
real	cputiming::stzxyzt = 0.0
real	cputiming::thesian = 0.0
real	cputiming::hesiant = 0.0
real	cputiming::tra00aa = 0.0
real	cputiming::ra00aat = 0.0
real	cputiming::tnumrec = 0.0
real	cputiming::numrect = 0.0
real	cputiming::tdcuhre = 0.0
real	cputiming::dcuhret = 0.0
real	cputiming::tminpack = 0.0
real	cputiming::minpackt = 0.0
real	cputiming::tiqpack = 0.0
real	cputiming::iqpackt = 0.0
real	cputiming::trksuite = 0.0
real	cputiming::rksuitet = 0.0
real	cputiming::ti1mach = 0.0
real	cputiming::i1macht = 0.0
real	cputiming::td1mach = 0.0
real	cputiming::d1macht = 0.0
real	cputiming::tilut = 0.0
real	cputiming::ilutt = 0.0
real	cputiming::titers = 0.0
real	cputiming::iterst = 0.0
real	cputiming::tsphdf5 = 0.0
real	cputiming::sphdf5t = 0.0
real	cputiming::tpreset = 0.0
real	cputiming::presett = 0.0
real	cputiming::tglobal = 0.0
real	cputiming::globalt = 0.0
real	cputiming::txspech = 0.0
real	cputiming::xspecht = 0.0
real	cputiming::tinputlist = 0.0
real	cputiming::inputlistt = 0.0
real	cputiming::treadin = 0.0
real	cputiming::twrtend = 0.0
integer	allglobal::myid
	MPI rank of current CPU.
integer	allglobal::ncpu
	number of MPI tasks
integer	allglobal::ismyvolumevalue
	flag to indicate if a CPU is operating on its assigned volume
real	allglobal::cpus
	initial time
integer	allglobal::mpi_comm_spec
	SPEC MPI communicator.
logical	allglobal::skip_write = .false.
real	allglobal::pi2nfp
	pi2/nfp ; assigned in readin;
real	allglobal::pi2pi2nfp
	pi2*pi2/nfp
real	allglobal::pi2pi2nfphalf
	2*pi*pi/nfp
real	allglobal::pi2pi2nfpquart
	pi*pi/nfp
character(len=1000)	allglobal::ext
real	allglobal::forceerr
	total force-imbalance
real	allglobal::energy
	MHD energy.
real	allglobal::bnserr
	(in freeboundary) error in self-consistency of field on plasma boundary (Picard iteration)
real	allglobal::betatotal = 0.0
	Beta, averaged over entire domain.
real, dimension(:), allocatable	allglobal::ipdt
real, dimension(:,:), allocatable	allglobal::ipdtdpf
	Toroidal pressure-driven current.
integer	allglobal::mvol
	total number of volumes (including the vacuum region in the case of free-boundary calculations)
real	allglobal::total_pflux
logical	allglobal::yesstellsym
	internal shorthand copies of Istellsym, which is an integer input;
logical	allglobal::notstellsym
	internal shorthand copies of Istellsym, which is an integer input;
logical	allglobal::yesmatrixfree
logical	allglobal::notmatrixfree
	to use matrix-free method or not
real, dimension(:,:), allocatable	allglobal::cheby
	local workspace for evaluation of Chebychev polynomials
real, dimension(:,:,:), allocatable	allglobal::zernike
	local workspace for evaluation of Zernike polynomials
real, dimension(:,:,:), allocatable	allglobal::tt
	derivatives of Chebyshev polynomials at the inner and outer interfaces;
real, dimension(:,:,:,:), allocatable	allglobal::rtt
	derivatives of Zernike polynomials at the inner and outer interfaces;
real, dimension(:,:), allocatable	allglobal::rtm
	\(r^m\) term of Zernike polynomials at the origin
real, dimension(:), allocatable	allglobal::zernikedof
	Zernike degree of freedom for each \(m\).
integer	allglobal::mne
	enhanced resolution for metric elements
integer, dimension(:), allocatable	allglobal::ime
	enhanced poloidal mode numbers for metric elements
integer, dimension(:), allocatable	allglobal::ine
	enhanced toroidal mode numbers for metric elements
integer	allglobal::mns
	enhanced resolution for straight field line transformation
integer, dimension(:), allocatable	allglobal::ims
	enhanced poloidal mode numbers for straight field line transformation
integer, dimension(:), allocatable	allglobal::ins
	enhanced toroidal mode numbers for straight field line transformation
integer	allglobal::lmpol
	what is this?
integer	allglobal::lntor
	what is this?
integer	allglobal::smpol
	what is this?
integer	allglobal::sntor
	what is this?
real	allglobal::xoffset = 1.0
	used to normalize NAG routines (which ones exacly where?)
logical, dimension(:), allocatable	allglobal::imagneticok
	used to indicate if Beltrami fields have been correctly constructed;
logical	allglobal::iconstraintok
	Used to break iteration loops of slaves in the global constraint minimization.
real, dimension(:,:), allocatable	allglobal::beltramierror
	to store the integral of |curlB-mu*B| computed by jo00aa;
integer	allglobal::mn
	total number of Fourier harmonics for coordinates/fields; calculated from Mpol, Ntor in readin()
integer, dimension(:), allocatable	allglobal::im
	poloidal mode numbers for Fourier representation
integer, dimension(:), allocatable	allglobal::in
	toroidal mode numbers for Fourier representation
real, dimension(:), allocatable	allglobal::halfmm
	I saw this already somewhere...
real, dimension(:), allocatable	allglobal::regumm
	I saw this already somewhere...
real	allglobal::rscale
	no idea
real, dimension(:,:), allocatable	allglobal::psifactor
	no idea
real, dimension(:,:), allocatable	allglobal::inifactor
	no idea
real, dimension(:), allocatable	allglobal::bbweight
	weight on force-imbalance harmonics; used in dforce()
real, dimension(:), allocatable	allglobal::mmpp
	spectral condensation factors
real, dimension(:,:), allocatable	allglobal::irbc
	cosine R harmonics of interface surface geometry; stellarator symmetric
real, dimension(:,:), allocatable	allglobal::izbs
	sine Z harmonics of interface surface geometry; stellarator symmetric
real, dimension(:,:), allocatable	allglobal::irbs
	sine R harmonics of interface surface geometry; non-stellarator symmetric
real, dimension(:,:), allocatable	allglobal::izbc
	cosine Z harmonics of interface surface geometry; non-stellarator symmetric
real, dimension(:,:), allocatable	allglobal::drbc
	cosine R harmonics of interface surface geometry; stellarator symmetric; linear deformation
real, dimension(:,:), allocatable	allglobal::dzbs
	sine Z harmonics of interface surface geometry; stellarator symmetric; linear deformation
real, dimension(:,:), allocatable	allglobal::drbs
	sine R harmonics of interface surface geometry; non-stellarator symmetric; linear deformation
real, dimension(:,:), allocatable	allglobal::dzbc
	cosine Z harmonics of interface surface geometry; non-stellarator symmetric; linear deformation
real, dimension(:,:), allocatable	allglobal::irij
	interface surface geometry; real space
real, dimension(:,:), allocatable	allglobal::izij
	interface surface geometry; real space
real, dimension(:,:), allocatable	allglobal::drij
	interface surface geometry; real space
real, dimension(:,:), allocatable	allglobal::dzij
	interface surface geometry; real space
real, dimension(:,:), allocatable	allglobal::trij
	interface surface geometry; real space
real, dimension(:,:), allocatable	allglobal::tzij
	interface surface geometry; real space
real, dimension(:), allocatable	allglobal::ivns
	sine harmonics of vacuum normal magnetic field on interfaces; stellarator symmetric
real, dimension(:), allocatable	allglobal::ibns
	sine harmonics of plasma normal magnetic field on interfaces; stellarator symmetric
real, dimension(:), allocatable	allglobal::ivnc
	cosine harmonics of vacuum normal magnetic field on interfaces; non-stellarator symmetric
real, dimension(:), allocatable	allglobal::ibnc
	cosine harmonics of plasma normal magnetic field on interfaces; non-stellarator symmetric
real, dimension(:), allocatable	allglobal::lrbc
	local workspace
real, dimension(:), allocatable	allglobal::lzbs
	local workspace
real, dimension(:), allocatable	allglobal::lrbs
	local workspace
real, dimension(:), allocatable	allglobal::lzbc
	local workspace
integer	allglobal::num_modes
integer, dimension(:), allocatable	allglobal::mmrzrz
integer, dimension(:), allocatable	allglobal::nnrzrz
real, dimension(:,:,:), allocatable	allglobal::allrzrz
integer	allglobal::nt
	discrete resolution along \(\theta\) of grid in real space
integer	allglobal::nz
	discrete resolution along \(\zeta\) of grid in real space
integer	allglobal::ntz
	discrete resolution; Ntz=Nt*Nz shorthand
integer	allglobal::hnt
	discrete resolution; Ntz=Nt*Nz shorthand
integer	allglobal::hnz
	discrete resolution; Ntz=Nt*Nz shorthand
real	allglobal::sontz
	one / sqrt (one*Ntz); shorthand
real, dimension(:,:,:), allocatable	allglobal::rij
	real-space grid; R
real, dimension(:,:,:), allocatable	allglobal::zij
	real-space grid; Z
real, dimension(:,:,:), allocatable	allglobal::xij
	what is this?
real, dimension(:,:,:), allocatable	allglobal::yij
	what is this?
real, dimension(:,:), allocatable	allglobal::sg
	real-space grid; jacobian and its derivatives
real, dimension(:,:,:,:), allocatable	allglobal::guvij
	real-space grid; metric elements
real, dimension(:,:,:), allocatable	allglobal::gvuij
	real-space grid; metric elements (?); 10 Dec 15;
real, dimension(:,:,:,:), allocatable	allglobal::guvijsave
	what is this?
integer, dimension(:,:), allocatable	allglobal::ki
	identification of Fourier modes
integer, dimension(:,:,:), allocatable	allglobal::kijs
	identification of Fourier modes
integer, dimension(:,:,:), allocatable	allglobal::kija
	identification of Fourier modes
integer, dimension(:), allocatable	allglobal::iotakkii
	identification of Fourier modes
integer, dimension(:,:), allocatable	allglobal::iotaksub
	identification of Fourier modes
integer, dimension(:,:), allocatable	allglobal::iotakadd
	identification of Fourier modes
integer, dimension(:,:), allocatable	allglobal::iotaksgn
	identification of Fourier modes
real, dimension(:), allocatable	allglobal::efmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::ofmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::cfmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::sfmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::evmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::odmn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::comn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::simn
	Fourier harmonics; dummy workspace.
real, dimension(:), allocatable	allglobal::ijreal
	what is this ?
real, dimension(:), allocatable	allglobal::ijimag
	what is this ?
real, dimension(:), allocatable	allglobal::jireal
	what is this ?
real, dimension(:), allocatable	allglobal::jiimag
	what is this ?
real, dimension(:), allocatable	allglobal::jkreal
	what is this ?
real, dimension(:), allocatable	allglobal::jkimag
	what is this ?
real, dimension(:), allocatable	allglobal::kjreal
	what is this ?
real, dimension(:), allocatable	allglobal::kjimag
	what is this ?
real, dimension(:,:,:), allocatable	allglobal::bsupumn
	tangential field on interfaces; \(\theta\)-component; required for virtual casing construction of field; 11 Oct 12
real, dimension(:,:,:), allocatable	allglobal::bsupvmn
	tangential field on interfaces; \(\zeta\) -component; required for virtual casing construction of field; 11 Oct 12
real, dimension(:,:), allocatable	allglobal::goomne
	described in preset()
real, dimension(:,:), allocatable	allglobal::goomno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gssmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gssmno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gstmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gstmno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gszmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gszmno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gttmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gttmno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gtzmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gtzmno
	described in preset()
real, dimension(:,:), allocatable	allglobal::gzzmne
	described in preset()
real, dimension(:,:), allocatable	allglobal::gzzmno
	described in preset()
real, dimension(:,:,:,:), allocatable	allglobal::dtoocc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::dtoocs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::dtoosc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::dtooss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ttsscc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ttsscs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ttsssc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ttssss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdstcc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdstcs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdstsc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdstss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdszcc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdszcs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdszsc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::tdszss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddttcc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddttcs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddttsc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddttss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddtzcc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddtzcs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddtzsc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddtzss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddzzcc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddzzcs
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddzzsc
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:,:,:), allocatable	allglobal::ddzzss
	volume-integrated Chebychev-metrics; see matrix()
real, dimension(:,:), allocatable	allglobal::tsc
	what is this?
real, dimension(:,:), allocatable	allglobal::tss
	what is this?
real, dimension(:,:), allocatable	allglobal::dtc
	what is this?
real, dimension(:,:), allocatable	allglobal::dts
	what is this?
real, dimension(:,:), allocatable	allglobal::dzc
	what is this?
real, dimension(:,:), allocatable	allglobal::dzs
	what is this?
real, dimension(:,:), allocatable	allglobal::ttc
	what is this?
real, dimension(:,:), allocatable	allglobal::tzc
	what is this?
real, dimension(:,:), allocatable	allglobal::tts
	what is this?
real, dimension(:,:), allocatable	allglobal::tzs
	what is this?
real, dimension(:), allocatable	allglobal::dtflux
	\(\delta \psi_{toroidal}\) in each annulus
real, dimension(:), allocatable	allglobal::dpflux
	\(\delta \psi_{poloidal}\) in each annulus
real, dimension(:), allocatable	allglobal::sweight
	minimum poloidal length constraint weight
integer, dimension(:), allocatable	allglobal::nadof
	degrees of freedom in Beltrami fields in each annulus
integer, dimension(:), allocatable	allglobal::nfielddof
	degrees of freedom in Beltrami fields in each annulus, field only, no Lagrange multipliers
type(subgrid), dimension(:,:,:), allocatable	allglobal::ate
	magnetic vector potential cosine Fourier harmonics; stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::aze
	magnetic vector potential cosine Fourier harmonics; stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::ato
	magnetic vector potential sine Fourier harmonics; non-stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::azo
	magnetic vector potential sine Fourier harmonics; non-stellarator-symmetric
integer, dimension(:,:), allocatable	allglobal::lma
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmb
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmc
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmd
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lme
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmf
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmg
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmh
	Lagrange multipliers (?)
real, dimension(:,:), allocatable	allglobal::lmavalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmbvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmcvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmdvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmevalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmfvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmgvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmhvalue
	what is this?
integer, dimension(:,:), allocatable	allglobal::fso
	what is this?
integer, dimension(:,:), allocatable	allglobal::fse
	what is this?
logical	allglobal::lcoordinatesingularity
	set by LREGION macro; true if inside the innermost volume
logical	allglobal::lplasmaregion
	set by LREGION macro; true if inside the plasma region
logical	allglobal::lvacuumregion
	set by LREGION macro; true if inside the vacuum region
logical	allglobal::lsavedguvij
	flag used in matrix free
logical	allglobal::localconstraint
	what is this?
real, dimension(:,:), allocatable	allglobal::dma
	energy and helicity matrices; quadratic forms
real, dimension(:,:), allocatable	allglobal::dmb
	energy and helicity matrices; quadratic forms
real, dimension(:,:), allocatable	allglobal::dmd
	energy and helicity matrices; quadratic forms
real, dimension(:), allocatable	allglobal::dmas
	sparse version of dMA, data
real, dimension(:), allocatable	allglobal::dmds
	sparse version of dMD, data
integer, dimension(:), allocatable	allglobal::idmas
	sparse version of dMA and dMD, indices
integer, dimension(:), allocatable	allglobal::jdmas
	sparse version of dMA and dMD, indices
integer, dimension(:), allocatable	allglobal::ndmasmax
	number of elements for sparse matrices
integer, dimension(:), allocatable	allglobal::ndmas
	number of elements for sparse matrices
real, dimension(:), allocatable	allglobal::dmg
	what is this?
real, dimension(:), allocatable	allglobal::adotx
	the matrix-vector product
real, dimension(:), allocatable	allglobal::ddotx
	the matrix-vector product
real, dimension(:,:), allocatable	allglobal::solution
	this is allocated in dforce; used in mp00ac and ma02aa; and is passed to packab
real, dimension(:,:,:), allocatable	allglobal::gmreslastsolution
	used to store the last solution for restarting GMRES
real, dimension(:), allocatable	allglobal::mbpsi
	matrix vector products
logical	allglobal::liluprecond
	whether to use ILU preconditioner for GMRES
real, dimension(:,:), allocatable	allglobal::beltramiinverse
	Beltrami inverse matrix.
real, dimension(:,:,:), allocatable	allglobal::diotadxup
	measured rotational transform on inner/outer interfaces for each volume; d(transform)/dx; (see dforce)
real, dimension(:,:,:), allocatable	allglobal::ditgpdxtp
	measured toroidal and poloidal current on inner/outer interfaces for each volume; d(Itor,Gpol)/dx; (see dforce)
real, dimension(:,:,:,:), allocatable	allglobal::glambda
	save initial guesses for iterative calculation of rotational-transform
integer	allglobal::lmns
	number of independent degrees of freedom in angle transformation;
real, dimension(:,:,:), allocatable	allglobal::dlambdaout
real, dimension(:,:,:), allocatable	allglobal::bemn
	force vector; stellarator-symmetric (?)
real, dimension(:,:), allocatable	allglobal::iomn
	force vector; stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::somn
	force vector; non-stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::pomn
	force vector; non-stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::bomn
	force vector; stellarator-symmetric (?)
real, dimension(:,:), allocatable	allglobal::iemn
	force vector; stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::semn
	force vector; non-stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::pemn
	force vector; non-stellarator-symmetric (?)
real, dimension(:), allocatable	allglobal::bbe
	force vector (?); stellarator-symmetric (?)
real, dimension(:), allocatable	allglobal::iio
	force vector (?); stellarator-symmetric (?)
real, dimension(:), allocatable	allglobal::bbo
	force vector (?); non-stellarator-symmetric (?)
real, dimension(:), allocatable	allglobal::iie
	force vector (?); non-stellarator-symmetric (?)
real, dimension(:,:,:), allocatable	allglobal::btemn
	covariant \(\theta\) cosine component of the tangential field on interfaces; stellarator-symmetric
real, dimension(:,:,:), allocatable	allglobal::bzemn
	covariant \(\zeta\) cosine component of the tangential field on interfaces; stellarator-symmetric
real, dimension(:,:,:), allocatable	allglobal::btomn
	covariant \(\theta\) sine component of the tangential field on interfaces; non-stellarator-symmetric
real, dimension(:,:,:), allocatable	allglobal::bzomn
	covariant \(\zeta\) sine component of the tangential field on interfaces; non-stellarator-symmetric
real, dimension(:,:), allocatable	allglobal::bloweremn
	covariant field for Hessian computation
real, dimension(:,:), allocatable	allglobal::bloweromn
	covariant field for Hessian computation
integer	allglobal::lgdof
	geometrical degrees of freedom associated with each interface
integer	allglobal::ngdof
	total geometrical degrees of freedom
real, dimension(:,:,:), allocatable	allglobal::dbbdrz
	derivative of magnetic field w.r.t. geometry (?)
real, dimension(:,:), allocatable	allglobal::diidrz
	derivative of spectral constraints w.r.t. geometry (?)
real, dimension(:,:,:,:,:), allocatable	allglobal::dffdrz
	derivatives of B^2 at the interfaces wrt geometry
real, dimension(:,:,:,:), allocatable	allglobal::dbbdmp
	derivatives of B^2 at the interfaces wrt mu and dpflux
real, dimension(:,:,:,:,:), allocatable	allglobal::hdffdrz
	derivatives of B^2 at the interfaces wrt geometry 2D Hessian;
real, dimension(:,:,:,:,:), allocatable	allglobal::denergydrr
	derivatives of energy at the interfaces wrt geometry 3D Hessian;
real, dimension(:,:,:,:,:), allocatable	allglobal::denergydrz
	derivatives of energy at the interfaces wrt geometry 3D Hessian;
real, dimension(:,:,:,:,:), allocatable	allglobal::denergydzr
	derivatives of energy at the interfaces wrt geometry 3D Hessian;
real, dimension(:,:,:,:,:), allocatable	allglobal::denergydzz
	derivatives of energy at the interfaces wrt geometry 3D Hessian;
real, dimension(:,:,:,:,:), allocatable	allglobal::dmupfdx
	derivatives of mu and dpflux wrt geometry at constant interface transform
logical	allglobal::lhessianallocated
	flag to indicate that force gradient matrix is allocated (?)
real, dimension(:,:), allocatable	allglobal::hessian
	force gradient matrix (?)
real, dimension(:,:), allocatable	allglobal::dessian
	derivative of force gradient matrix (?)
logical	allglobal::lhessian2dallocated
	flag to indicate that 2D Hessian matrix is allocated (?)
real, dimension(:,:), allocatable	allglobal::hessian2d
	Hessian 2D.
real, dimension(:,:), allocatable	allglobal::dessian2d
	derivative Hessian 2D
logical	allglobal::lhessian3dallocated
	flag to indicate that 2D Hessian matrix is allocated (?)
real, dimension(:,:), allocatable	allglobal::hessian3d
	Hessian 3D.
real, dimension(:,:), allocatable	allglobal::dessian3d
	derivative Hessian 3D
real, dimension(:), allocatable	allglobal::force_final
	Final force on the interfaces [inface*mode].
real, dimension(:,:), allocatable	allglobal::cosi
	some precomputed cosines
real, dimension(:,:), allocatable	allglobal::sini
	some precomputed sines
real, dimension(:), allocatable	allglobal::gteta
	something related to \(\sqrt g\) and \(\theta\) ?
real, dimension(:), allocatable	allglobal::gzeta
	something related to \(\sqrt g\) and \(\zeta\) ?
real, dimension(:), allocatable	allglobal::ajk
	definition of coordinate axis
real, dimension(:,:,:,:), allocatable	allglobal::dradr
	derivatives of coordinate axis
real, dimension(:,:,:,:), allocatable	allglobal::dradz
	derivatives of coordinate axis
real, dimension(:,:,:,:), allocatable	allglobal::dzadr
	derivatives of coordinate axis
real, dimension(:,:,:,:), allocatable	allglobal::dzadz
	derivatives of coordinate axis
real, dimension(:,:,:), allocatable	allglobal::drodr
	derivatives of coordinate axis
real, dimension(:,:,:), allocatable	allglobal::drodz
	derivatives of coordinate axis
real, dimension(:,:,:), allocatable	allglobal::dzodr
	derivatives of coordinate axis
real, dimension(:,:,:), allocatable	allglobal::dzodz
	derivatives of coordinate axis
integer, dimension(:,:), allocatable	allglobal::djkp
	for calculating cylindrical volume
integer, dimension(:,:), allocatable	allglobal::djkm
	for calculating cylindrical volume
real, dimension(:), allocatable	allglobal::lbbintegral
	B.B integral.
real, dimension(:), allocatable	allglobal::labintegral
	A.B integral.
real, dimension(:), allocatable	allglobal::vvolume
	volume integral of \(\sqrt g\); computed in volume
real	allglobal::dvolume
	derivative of volume w.r.t. interface geometry
integer	allglobal::ivol
	labels volume; some subroutines (called by NAG) are fixed argument list but require the volume label
real	allglobal::gbzeta
	toroidal (contravariant) field; calculated in bfield; required to convert \(\dot \theta\) to \(B^\theta\), \(\dot s\) to \(B^s\)
integer, dimension(:), allocatable	allglobal::iquad
	internal copy of Nquad
real, dimension(:,:), allocatable	allglobal::gaussianweight
	weights for Gaussian quadrature
real, dimension(:,:), allocatable	allglobal::gaussianabscissae
	abscissae for Gaussian quadrature
logical	allglobal::lblinear
	controls selection of Beltrami field solver; depends on LBeltrami
logical	allglobal::lbnewton
	controls selection of Beltrami field solver; depends on LBeltrami
logical	allglobal::lbsequad
	controls selection of Beltrami field solver; depends on LBeltrami
real, dimension(1:3)	allglobal::orzp
	used in mg00aa() to determine \((s,\theta,\zeta)\) given \((R,Z,\varphi)\)
type(derivative)	allglobal::dbdx
	\({\rm d}\mathbf{B}/{\rm d}\mathbf{X}\) (?)
integer	allglobal::globaljk
	labels position
real, dimension(:,:), allocatable	allglobal::dxyz
	computational boundary; position
real, dimension(:,:), allocatable	allglobal::nxyz
	computational boundary; normal
real, dimension(:,:), allocatable	allglobal::jxyz
	plasma boundary; surface current
real, dimension(:,:), allocatable	allglobal::pbxyz
	plasma boundary; position
integer	allglobal::prevcstride
	previous virtual casing stride for casinggrid (only relevant when Lvcgrid=1)
real	allglobal::virtualcasingfactor = -one / (four*pi)
	this agrees with diagno
integer	allglobal::iberror
	for computing error in magnetic field
integer	allglobal::nfreeboundaryiterations
	number of free-boundary iterations already performed
integer, parameter	allglobal::node = 2
	best to make this global for consistency between calling and called routines
logical	allglobal::first_free_bound = .false.
	flag to indicate that this is the first free-boundary iteration
type(c_ptr)	fftw_interface::planf
	FFTW-related (?)
type(c_ptr)	fftw_interface::planb
	FFTW-related (?)
complex(c_double_complex), dimension(:,:,:), allocatable	fftw_interface::cplxin
	FFTW-related (?)
complex(c_double_complex), dimension(:,:,:), allocatable	fftw_interface::cplxout
	FFTW-related (?)

Detailed Description

Defines input namelists and global variables, and opens some output files.

Note that all variables in namelist need to be broadcasted in readin.

Input geometry

• The geometry of the \(l\)-th interface, for \(l=0,N\) where \(N\equiv\) Nvol, is described by a set of Fourier harmonics, using an arbitrary poloidal angle,

  \begin{eqnarray} R_l(\theta,\zeta)&=&\sum_{j}R_{j,l}\cos(m_j\theta-n_j\zeta), \\ Z_l(\theta,\zeta)&=&\sum_{j}Z_{j,l}\sin(m_j\theta-n_j\zeta). \end{eqnarray}

• These harmonics are read from the ext.sp file and come directly after the namelists described above. The required format is as follows:

  \begin{eqnarray} \begin{array}{ccccccccc} m_1 & n_1 & R_{1,0} & Z_{1,0} & R_{1,1} & Z_{1,1} & ... & R_{1,N} & Z_{1,N} \\ m_2 & n_2 & R_{2,0} & Z_{2,0} & R_{2,1} & Z_{2,1} & ... & R_{2,N} & Z_{2,N} \\ ... \\ m_j & n_j & R_{j,0} & Z_{j,0} & R_{j,1} & Z_{j,1} & ... & R_{j,N} & Z_{j,N} \\ ... \end{array} \end{eqnarray}

• The coordinate axis corresponds to \(j=0\) and the outermost boundary corresponds to \(j=\) Nvol.
• An arbitrary selection of harmonics may be inluded in any order, but only those within the range specified by Mpol and Ntor will be used.
• The geometry of all the interfaces, i.e. \(l=0,N\), including the degenerate "coordinate-axis" interface, must be given.

---

Data Type Documentation

typedefns::subgrid

type typedefns::subgrid

used for quantities which have different resolutions in different volumes, e.g. the vector potential

Class Members
real, dimension(:), allocatable	s	coefficients
integer, dimension(:), allocatable	i	indices

typedefns::matrixlu

type typedefns::matrixlu

Class Members
real, dimension(:,:), allocatable	mat
integer, dimension(:), allocatable	ipivot

typedefns::derivative

type typedefns::derivative

\({\rm d}\mathbf{B}/{\rm d}\mathbf{X}\) (?)

Class Members
logical	l	what is this?
integer	vol	Used in coords(); required for global constraint force gradient evaluation.
integer	innout	what is this?
integer	ii	what is this?
integer	irz	what is this?
integer	issym	what is this?