CP

CP

Structure used to define the collision-probability method (CP) for the transport of a particle. The volumetric and surface fluxes are expanded in spherical harmonics of arbitrary order; in one-dimensional Cartesian geometry the azimuthal symmetry reduces the expansion to Legendre polynomials of degree up to legendre_order (see the TR-02 technical report). The method assembles the collision, leakage and transmission probability matrices and solves the resulting linear system directly, as an alternative to the SN and GN solvers.

Mandatory field(s)

• particle::Particle : particle for which the discretization method is defined.
• solver_type::String : type of solver for the transport calculations ("BTE").

Optional field(s) - with default values

• legendre_order::Int64 = 0 : Legendre order of the volumetric flux expansion.
• surface_order::Int64 = 0 : order of the surface (half-range) flux expansion.
• convergence_criterion::Float64 = 1e-7 : convergence criterion of the group iterations.
• maximum_iteration::Int64 = 300 : maximum number of group iterations.

set_particle(this::CP,particle::Particle)

To set the particle for which the transport discretization method is for.

Input Argument(s)

• this::CP : collision-probability method.
• particle::Particle : particle.

Output Argument(s)

N/A

Examples

julia> m = CP()
julia> m.set_particle(electron)

set_solver_type(this::CP,solver_type::String)

To set the solver for the particle transport.

Input Argument(s)

• this::CP : collision-probability method.
• solver_type::String : solver type, which can take the following value:
  • solver_type = "BTE" : Boltzmann transport equation.

Output Argument(s)

N/A

Examples

julia> m = CP()
julia> m.set_solver_type("BTE")

set_legendre_order(this::CP,legendre_order::Int64)
set_legendre_order(this::CP,volume_order::Int64,surface_order::Int64)

To set the Legendre order of the volumetric and surface flux expansions. The single-argument form sets both the volumetric and the surface order to the same value; the two-argument form sets them independently.

Input Argument(s)

• this::CP : collision-probability method.
• legendre_order::Int64 : Legendre order of both the volumetric and surface flux expansions.
• volume_order::Int64 : Legendre order of the volumetric flux expansion.
• surface_order::Int64 : Legendre order of the surface (half-range) flux expansion.

Output Argument(s)

N/A

Examples

julia> m = CP()
julia> m.set_legendre_order(2)      # volume = surface = 2
julia> m.set_legendre_order(2,4)    # volume = 2, surface = 4

set_surface_order(this::CP,surface_order::Int64)

To set the order of the surface (half-range) flux expansion used by the boundary-coupling probabilities.

Input Argument(s)

• this::CP : collision-probability method.
• surface_order::Int64 : order of the surface flux expansion.

Output Argument(s)

N/A

set_mode(this::CP,mode::String)

To set the solution mode of the collision-probability method.

Input Argument(s)

• this::CP : collision-probability method.
• mode::String : solution mode, which can take the following values:
  • mode = "global" : finite-domain method. The collision-probability matrices couple all regions and surfaces directly and the resulting linear system is solved by a direct factorization. This is the default.
  • mode = "sweeping" : sweeping method. The unit cell is a single voxel and the surface (interface) fluxes are propagated cell by cell, in direct analogy with the discrete- ordinates sweep; the within-group scattering is resolved by source iteration.

Output Argument(s)

N/A

Examples

julia> m = CP()
julia> m.set_mode("sweeping")

set_acceleration(this::CP,acceleration::String,parameter::Int64=0)

To set the acceleration method for the in-group source iteration of the sweeping mode (unused by the direct "global" solve).

Input Argument(s)

• this::CP : collision-probability method.
• acceleration::String : acceleration method, which takes the following values:
  • acceleration = "none" : plain source iteration.
  • acceleration = "livolant" : Livolant two-point extrapolation.
  • acceleration = "anderson" : depth-m Anderson acceleration.
  • acceleration = "gmres" : matrix-free restarted GMRES.
  • acceleration = "bicgstab" : matrix-free BiCGStab.
• parameter::Int64 : optional tuning parameter (GMRES restart or Anderson depth; 0 keeps the current default).

Output Argument(s)

N/A

set_convergence_criterion(this::CP,convergence_criterion::Float64)

To set the convergence criterion for the group iterations.

Input Argument(s)

• this::CP : collision-probability method.
• convergence_criterion::Float64 : convergence criterion.

Output Argument(s)

N/A

set_maximum_iteration(this::CP,maximum_iteration::Int64)

To set the maximum number of group iterations.

Input Argument(s)

• this::CP : collision-probability method.
• maximum_iteration::Int64 : maximum number of group iterations.

Output Argument(s)

N/A

get_particle(this::CP)

Get the particle associated with the discretization method.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• particle::Particle : particle.

get_solver_type(this::CP)

Get the type of solver for transport calculations.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• solver::Int64 : type of solver for transport calculations.
• isCSD::Bool : indicate if the continuous slowing-down term is used or not.

get_legendre_order(this::CP)

Get the Legendre order of the volumetric flux expansion.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• legendre_order::Int64 : Legendre order.

get_surface_order(this::CP)

Get the order of the surface (half-range) flux expansion.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• surface_order::Int64 : surface order.

get_mode(this::CP)

Get the solution mode of the collision-probability method.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• mode::String : solution mode ("global" or "sweeping").

get_schemes(this::CP,geometry::Geometry,isFC::Bool)

Get the space and/or energy schemes informations. The CP assumes a flat (region-averaged) flux, so a single spatial/energy moment is carried per region.

Input Argument(s)

• this::CP : collision-probability method.
• geometry::Geometry : geometry.
• isFC::Bool : boolean indicating if the high-order moments are fully coupled.

Output Argument(s)

• schemes::Vector{String} : scheme types.
• 𝒪::Vector{Int64} : order of the schemes.
• Nm::Vector{Int64} : numbers of moments.

get_is_full_coupling(this::CP)

Get whether the high-order moments are fully coupled or not.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• isFC::Bool : boolean indicating if the high-order moments are fully coupled or not.

get_acceleration(this::CP)

Get the acceleration method (used only by the sweeping mode's in-group source iteration).

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• acceleration::String : acceleration method.

get_gmres_restart(this::CP)

Get the GMRES restart parameter (sweeping mode).

get_anderson_depth(this::CP)

Get the Anderson acceleration memory depth (sweeping mode).

get_convergence_criterion(this::CP)

Get the convergence criterion for the group iterations.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• convergence_criterion::Float64 : convergence criterion.

get_maximum_iteration(this::CP)

Get the maximum number of group iterations.

Input Argument(s)

• this::CP : collision-probability method.

Output Argument(s)

• maximum_iteration::Int64 : maximum number of group iterations.