locallist

The namelist locallist controls the construction of the Beltrami fields in each volume. More...

Collaboration diagram for locallist:

Variables
integer	inputlist::lbeltrami = 4
	Control flag for solution of Beltrami equation. More...
integer	inputlist::linitgues = 1
	controls how initial guess for Beltrami field is constructed More...
integer	inputlist::lposdef = 0
	redundant;
real	inputlist::maxrndgues = 1.0
	the maximum random number of the Beltrami field if Linitgues = 3
integer	inputlist::lmatsolver = 3
	1 for LU factorization, 2 for GMRES, 3 for GMRES matrix-free
integer	inputlist::nitergmres = 200
	number of max iteration for GMRES
real	inputlist::epsgmres = 1e-14
	the precision of GMRES
integer	inputlist::lgmresprec = 1
	type of preconditioner for GMRES, 1 for ILU sparse matrix
real	inputlist::epsilu = 1e-12
	the precision of incomplete LU factorization for preconditioning

Detailed Description

The namelist locallist controls the construction of the Beltrami fields in each volume.

The transformation to straight-fieldline coordinates is singular when the rotational-transform of the interfaces is rational; however, the rotational-transform is still well defined.

Variable Documentation

lbeltrami

integer inputlist::lbeltrami = 4

Control flag for solution of Beltrami equation.

• if LBeltrami = 1,3,5 or 7, (SQP) then the Beltrami field in each volume is constructed by minimizing the magnetic energy with the constraint of fixed helicity; this is achieved by using sequential quadratic programming as provided by E04UFF . This approach has the benefit (in theory) of robustly constructing minimum energy solutions when multiple, i.e. bifurcated, solutions exist.
• if LBeltrami = 2,3,6 or 7, (Newton) then the Beltrami fields are constructed by employing a standard Newton method for locating an extremum of \(F\equiv \int B^2 dv - \mu (\int {\bf A}\cdot{\bf B}dv-{\cal K})\), where \(\mu\) is treated as an independent degree of freedom similar to the parameters describing the vector potential and \({\cal K}\) is the required value of the helicity; this is the standard Lagrange multipler approach for locating the constrained minimum; this method cannot distinguish saddle-type extrema from minima, and which solution that will be obtained depends on the initial guess;
• if LBeltrami = 4,5,6 or 7, (linear) it is assumed that the Beltrami fields are parameterized by \(\mu\); in this case, it is only required to solve \(\nabla \times {\bf B} = \mu {\bf B}\) which reduces to a system of linear equations; \(\mu\) may or may not be adjusted iteratively, depending on Lconstraint, to satisfy either rotational-transform or helicity constraints;
• for flexibility and comparison, each of the above methods can be employed; for example:
  • if LBeltrami = 1, only the SQP method will be employed;
  • if LBeltrami = 2, only the Newton method will be employed;
  • if LBeltrami = 4, only the linear method will be employed;
  • if LBeltrami = 3, the SQP and the Newton method are used;
  • if LBeltrami = 5, the SQP and the linear method are used;
  • if LBeltrami = 6, the Newton and the linear method are used;
  • if LBeltrami = 7, all three methods will be employed;

Referenced by allglobal::broadcast_inputs(), allglobal::check_inputs(), sphdf5::mirror_input_to_outfile(), preset(), and allglobal::wrtend().

linitgues

integer inputlist::linitgues = 1

controls how initial guess for Beltrami field is constructed

• only relevant for routines that require an initial guess for the Beltrami fields, such as the SQP and Newton methods, or the sparse linear solver;
• if Linitgues = 0, the initial guess for the Beltrami field is trivial
• if Linitgues = 1, the initial guess for the Beltrami field is an integrable approximation
• if Linitgues = 2, the initial guess for the Beltrami field is read from file
• if Linitgues = 3, the initial guess for the Beltrami field will be randomized with the maximum maxrndgues

Referenced by allglobal::broadcast_inputs(), allglobal::check_inputs(), sphdf5::mirror_input_to_outfile(), preset(), and allglobal::wrtend().