SN

SN

Structure used to define the discretization method associated with the transport of a particle.

Mandatory field(s)

• particle::Particle : particle for which the discretization methods is defined
• solver_type::String : type of solver for the transport calculations.
• quadrature_type::String : type of quadrature for the angular domain.
• quadrature_order::Int64 : order of the quadrature for the angular domain.
• legendre_order::Int64 : maximum order of the Legendre expansion for the differential cross-sections.
• scheme_type::Dict{String,String} : type of schemes for the spatial or energy discretization.
• scheme_order::Dict{String,Int64} : order of the expansion for the discretization schemes.

Optional field(s) - with default values

• angular_fokker_planck::String = "finite-difference" : type of discretization for the angular Fokker-Planck operation.
• angular_boltzmann::String = "galerkin-d" : type of discretization for the Boltzmann operation.
• convergence_criterion::Float64 = 1e-7 : convergence criterion of in-group iterations.
• maximum_iteration::Int64 = 300 : maximum number of in-group iterations.
• acceleration::Int64 = "none" : acceleration method for the in-group iterations.

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

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

Input Argument(s)

• this::SN : discretization method.
• particle::Particle : particle.

Output Argument(s)

N/A

Examples

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

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

To set the solver for the particle transport.

Input Argument(s)

• this::SN : discretization method.
• solver_type::String : solver type, which can takes the following values:
  • solver_type = "BTE" : Boltzmann transport equation
  • solver_type = "BFP" : Boltzmann Fokker-Planck equation
  • solver_type = "BCSD" : Boltzmann-CSD equation
  • solver_type = "FP" : Fokker-Planck equation
  • solver_type = "CSD" : Continuous slowing-down only equation
  • solver_type = "BFP-EF" : Boltzmann Fokker-Planck without elastic

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_particle("BFP")

set_quadrature(this::SN,type::String,order::Int64,Qdims::Int64=0)

To set the quadrature properties for the discretization of the angular domain.

Input Argument(s)

• this::SN : discretization method.
• type::String : type of quadrature, which can takes the following values:
  • type = "gauss-legendre" : Gauss-Legendre quadrature (1D Cartesian geometry only).
  • type = "gauss-lobatto" : Gauss-Lobatto quadrature (1D Cartesian geometry only).
  • type = "carlson" : Carlson quadrature (2D or 3D Cartesian geometry only).
  • type = "gauss-legendre-chebychev" : product quadrature between Gauss-Legendre and Chebychev quadratures (2D or 3D Cartesian geometry only).
  • type = "lebedev" : Lebedev quadrature (2D or 3D Cartesian geometry only).
• order::Int64 : order of the quadrature, which is any integer greater than 2.
• Qdims::Int64 : quadrature dimension, which can takes the following values:
  • Qdims = 0 : default value, Qdims = 1 with 1D quadrature, Qdims = 3 with quadrature over the unit sphere in 1D or in 2D geometry or in 3D geometry.
  • Qdims = 1 : 1D quadrature.
  • Qdims = 2 : quadrature over half the unit-sphere.
  • Qdims = 3 : quadrature over the unit sphere.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_quadrature("gauss-legendre",4)

set_legendre_order(this::SN,legendre_order::Int64)

To set the maximum order of the Legendre expansion of the differential cross-sections.

Input Argument(s)

• this::SN : discretization method.
• legendre_order::Int64 : maximum order of the Legendre expansion of the differential cross-sections.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_legendre_order(7)

set_angular_fokker_planck(this::SN,angular_fokker_planck::String)

To set the discretization method for the angular Fokker-Planck term.

Input Argument(s)

• this::SN : discretization method.
• angular_fokker_planck::String : discretization method for the angular Fokker-Planck term, which can takes the following values:
  • angular_fokker_planck = "finite-difference" : finite difference discretization.
  • angular_fokker_planck = "galerkin" : galerkin moment-based discretization.
  • angular_fokker_planck = "differential-quadrature" : finite difference discretization (1D Cartesian geometry only).

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_angular_fokker_planck("differential-quadrature")

set_angular_boltzmann(this::SN,angular_boltzmann::String)

To set the angular discretization method for the Boltzmann operator.

Input Argument(s)

• this::SN : discretization method.
• angular_boltzmann::String : angular discretization method for the Boltzmann operator, which can takes the following values:
  • angular_boltzmann = "standard" : standard discrete ordinates (SN) method.
  • angular_boltzmann = "galerkin-m" : Galerkin method by inversion of the discrete-to-moment M matrix.
  • angular_boltzmann = "galerkin-d" : Galerkin method by inversion of the moment-to-discrete D matrix.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_angular_boltzmann("standard")

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

To set the convergence criterion for the in-group iterations.

Input Argument(s)

• this::SN : discretization method.
• convergence_criterion::Float64 : convergence criterion.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_convergence_criterion(1e-5)

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

To set the maximum number of in-group iterations.

Input Argument(s)

• this::SN : discretization method.
• maximum_iteration::Int64 : maximum number of in-group iterations.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_maximum_iteration(50)

set_scheme(this::SN,axis::String,scheme_type::String,scheme_order::Int64)

To set the type of discretization scheme for derivative along the specified spatial or energy axis.

Input Argument(s)

• this::SN : discretization method.
• axis::String : variable of the derivative for which the scheme is applied, which can takes the following values:
  • axis = "x" : spatial x axis (discretization of the streaming term)
  • axis = "y" : spatial y axis (discretization of the streaming term)
  • axis = "z" : spatial z axis (discretization of the streaming term)
  • axis = "E" : spatial E axis (discretization of the continuous slowing-down term)
• scheme_type::String : type of scheme to be applied, which can takes the following values:
  • scheme_type = "DD" : diamond difference scheme (any order)
  • scheme_type = "DG" : discontinuous Galerkin scheme (any order)
  • scheme_type = "AWD" : adaptive weighted scheme (1st and 2nd order only)
• scheme_order::Int64 : scheme order, which takes values greater than 1.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_scheme("x","DD",1)
julia> m.set_scheme("E","DG",2)

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

To set the acceleration method for the in-group iteration process.

Input Argument(s)

• this::SN : discretization method.
• acceleration::String : acceleration method, which takes the following values
  • acceleration = "none" : source iteration without acceleration
  • 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 for the chosen method. It is the Krylov subspace size before restart for "gmres" (default 30) and the memory depth for "anderson" (default 3); it is ignored by the other methods. A value of 0 keeps the current default.

Output Argument(s)

N/A

Examples

julia> m = SN()
julia> m.set_acceleration("gmres")      # GMRES with the default restart of 30
julia> m.set_acceleration("gmres",50)   # GMRES restarted every 50 Krylov vectors
julia> m.set_acceleration("anderson",5) # Anderson acceleration with memory depth 5

set_is_full_coupling(this::SN,isFC::Bool)

Set, for multidimensional high-order schemes, if the high-order moments are fully coupled or not. For example, with two linear schemes, the moments are either fully coupled [00,10,01,11] or not [00,10,01].

Input Argument(s)

• this::SN : discretization method.
• isFC::Bool : boolean indicating if the high-orde moments are fully coupled or not.

Output Argument(s)

N/A

get_particle(this::SN)

Get the particle associated with the discretization methods.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• particle::Particle : particle.

get_solver_type(this::SN)

Get the type of solver for transport calculations.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

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

get_quadrature_type(this::SN)

Get the quadrature type.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• quadrature_type::String : quadrature type.

get_quadrature_order(this::SN)

Get the quadrature order.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• quadrature_order::Int64 : quadrature order.

get_quadrature_dimension(this::SN)

Get the quadrature dimension.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• quadrature_dimension::Int64 : quadrature dimension.

get_legendre_order(this::SN)

Get the Legendre truncation order.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• legendre_order::Int64 : Legendre truncation order.

get_angular_boltzmann(this::SN)

Get the type of angular discretization for the Boltzmann operator.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• angular_boltzmann::String : type of angular discretization for the Boltzmann operator.

get_angular_fokker_planck(this::SN)

Get the type of angular discretization for the Fokker-Planck operator.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• angular_fokker_planck::String : type of angular discretization for the Fokker-Planck operator.

get_convergence_criterion(this::SN)

Get the convergence criterion for in-group iteration convergence.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• convergence_criterion::Float64 : convergence criterion.

get_maximum_iteration(this::SN)

Get the maximum number of iterations for in-group iteration convergence.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• maximum_iteration::Int64 : maximum number of iterations.

get_acceleration(this::SN)

Get the acceleration method for in-group iteration convergence.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• acceleration::String : acceleration method.

get_gmres_restart(this::SN)

Get the GMRES restart parameter for in-group iteration convergence.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• gmres_restart::Int64 : Krylov subspace size before restart.

get_anderson_depth(this::SN)

Get the Anderson acceleration memory depth for in-group iteration convergence.

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

• anderson_depth::Int64 : Anderson memory depth.

get_is_full_coupling(this::SN)

Get, for multidimensional high-order schemes, if the high-order moments are fully coupled or not. For example, with two linear schemes, the moments are either fully coupled [00,10,01,11] or not [00,10,01].

Input Argument(s)

• this::SN : discretization method.

Output Argument(s)

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

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

Get the space and/or energy schemes informations.

Input Argument(s)

• this::SN : discretization 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.