fokker_planck_calculus

module for functions used in calculating the integrals and doing the numerical differentiation for the implementation of the the Full-F Fokker-Planck Collision Operator moment_kinetics.fokker_planck.

Parallelisation of the collision operator uses a special 'anyv' region type, see Collision operator and anyv region.

a struct to contain the integration weights for the boundary points in the (vpa,vperp) domain

a struct used for calculating the integration weights for the boundary of the velocity space domain in (vpa,vperp) coordinates

a struct of dummy arrays and precalculated coefficients for the weak-form Fokker-Planck collision operator

Function to carry out the integration of the revelant distribution functions to form the required coefficients for the full-F operator. We assume that the weights are precalculated. The function takes as arguments the arrays of coefficients (which we fill), the required distributions, the precomputed weights, the indicies of the `field' velocities, and the sizes of the primed vpa and vperp coordinates arrays.

function to enforce boundary conditions on the collision operator result to be consistent with the boundary conditions imposed on the the pdf

function for getting the indices used to choose the integration quadrature

get_global_compound_index(vpa,vperp,ielement_vpa,ielement_vperp,ivpa_local,ivperp_local)

For local (within the single element specified by ielement_vpa and ielement_vperp) indices ivpa_local and ivperp_local, get the global index in the 'linear-indexed' 2d space of size (vperp.n, vpa.n) (as returned by ic_func).

ic_func(ivpa::mk_int,ivperp::mk_int,nvpa::mk_int)

Get the 'linear index' corresponding to ivpa and ivperp. Defined so that the linear index corresponds to the underlying layout in memory of a 2d array indexed by [ivpa,ivperp], i.e. for a 2d array f2d:

• size(f2d) == (vpa.n, vperp.n)
• For a reference to f2d that is reshaped to a vector (a 1d array) f1d = vec(f2d) than for any ivpa and ivperp it is true that f1d[ic_func(ivpa,ivperp)] == f2d[ivpa,ivperp].

function to find the element in which x sits

function that precomputes the required integration weights only along the velocity space boundaries

function that precomputes the required integration weights

function to interpolate f(vpa,vperp) from one velocity grid to another, assuming that both grids are represented by vpa, vperp in normalised units, but have different normalisation factors defining the meaning of these grids in physical units.

E.g. vpai, vperpi = ci * vpa, ci * vperp vpae, vperpe = ce * vpa, ce * vperp

with ci = sqrt(Ti/mi), ce = sqrt(Te/mi)

scalefac = ci / ce is the ratio of the two reference speeds

ivpa_func(ic::mk_int,nvpa::mk_int)

Get the vpa index ivpa that corresponds to a 'linear index' ic that spans a 2d velocity space.

Defined so that ivpa_func(inc_func(ivpa,ivperp,nvpa), nvpa) == ivpa.

See also ic_func, ivperp_func.

ivperp_func(ic::mk_int,nvpa::mk_int)

Get the vperp index ivperp that corresponds to a 'linear index' ic that spans a 2d velocity space.

Defined so that ivperp_func(inc_func(ivpa,ivperp,nvpa), nvpa) == ivperp.

See also ic_func, ivpa_func.

function for getting the basic quadratures used for the numerical integration of the Lagrange polynomials and the Green's function.