System

System(grid; kwargs...)

Create structure of type VoronoiFVM.System{Tv,Ti, Tm, TSpecMat<:AbstractMatrix, TSolArray<:AbstractMatrix} holding data for finite volume system solution.

Parameters:

• grid::ExtendableGrid: 1, 2 or 3D computational grid

Keyword arguments:

• species: vector of integer species indices. Added to all grid regions, avoiding the need to call enable_species! for this default case. If it is kept empty, species have be added to the system after creation via enable_species!.
• unknown_storage: string or symbol. Information on species distribution is kept in sparse or dense matrices matrices and, correspondingly, the solution array is of type SparseSolutionArray or matrix, respectively. In the case of sparse unknown storage, the system matrix handles exactly those degrees of freedom which correspond to unknowns. However, handling of the sparse matrix structures for the bookkeeping of the unknowns creates overhead.
  • :dense : solution vector is an nspecies x nnodes dense matrix
  • :sparse : solution vector is an nspecies x nnodes sparse matrix
• matrixindextype: Integer type. Index type for sparse matrices created in the system.
• is_linear: whether the system is linear or not. If it is linear, only one Newton step is used to solve it.
• assembly: either :cellwise (default) or :edgewise. Determine, how the assembly loop is organized. :cellwise means that the outer loop goes over grid cells (triangles, tetrahedra), and contributions to edge fluxes and node reactions are calculated for each cell. As a consequence, e.g. im 2D for all interior edges, flux functions are callled twice, once for each adjacent cell. Especially in 3D, this becomes a significant overhead. With :edgewise, geometry factors of these edges are pre-assembled, and the outer assembly loops go over all grid edges resp. nodes, still with separate calls if neigboring cells belong to different regions.

Physics keyword arguments:

• flux: Function. Flux between neighboring control volumes: flux(f,u,edge) or flux(f,u,edge,data) should return in f[i] the flux of species i along the edge joining circumcenters of neighboring control volumes. For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
• storage: Function. Storage term (term under time derivative): storage(f,u,node) or storage(f,u,node,data) It should return in f[i] the storage term for the i-th equation. u[i] contains the value of the i-th unknown.
• reaction: Function. Reaction term: reaction(f,u,node) or reaction(f,u,node,data) It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown.
• edgereaction: Function. Edge reeaction term: edgereaction(f,u,edge) or edgereaction(f,u,edge,data) It should return in f[i] the reaction term for the i-th equation. For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
• source: Function. Source term: source(f,node) or source(f,node,data). It should return the in f[i] the value of the source term for the i-th equation.
• bflux: Function. Flux between neighboring control volumes on the boundary
• breaction Function. Boundary reaction term: breaction(f,u,node) or breaction(f,u,node,data) Similar to reaction, but restricted to the inner or outer boundaries.
• bcondition Function. Alias for breaction.
• bsource: Function. Boundary source term: bsource(f,node) or bsource(f,node,data). It should return in f[i] the value of the source term for the i-th equation.
• bstorage: Function. Boundary storage term: bstorage(f,u,node) or bstorage(f,u,node,data) Similar to storage, but restricted to the inner or outer boundaries.
• generic_operator: Function. Generic operator generic_operator(f,u,sys). This operator acts on the full solution u of a system. Sparsity is detected automatically unless generic_operator_sparsity is given.
• generic_operator_sparsity: Function defining the sparsity structure of the generic operator. This should return the sparsity pattern of the generic_operator.
• nparams: number of parameters the system is depending on, and with respect to which the derivatives need to be obtained
• data: User data (parameters). This allows to pass various parameters to the callback functions. If data is given, all callback functions should accept a last data argument. Otherwise, no data are passed explicitly, and constitutive callbacks can take parameters from the closure where the function is defined.
• matrixtype: :sparse, :tridiagonal, :banded, :auto. Default: :sparse. :auto leads to automatic choice for dense solution storage depending on space dimension and number of species.

System(X; kwargs...)

Create an 1D grid from vector X and call VoronoiFVM.System(grid::ExtendableGrid; kwargs...).

System(X,Y; kwargs...)

Create a 2D grid from vectors X,Y and call VoronoiFVM.System(grid::ExtendableGrid; kwargs...).

System(X,Y, Z; kwargs...)

Create a 3D grid from vectors X,Y,Z and call VoronoiFVM.System(grid::ExtendableGrid; kwargs...).

update_grid!(system; grid=system.grid)

Update grid (e.g. after rescaling of coordinates). Uses a lock to ensure parallel access.

physics!(system,physics)

Replace System's physics data

physics!(system; kwargs...)

Replace System's physics data.

enable_species!(system,ispec,regions)

Add species ispec to a list of bulk regions. Species numbers for bulk and boundary species have to be distinct. Once a species has been added, it cannot be removed.

enable_species!(system; kwargs...)

Keyword arguments:

• species: Integer or vector of integers. Species to be added to the system.
• regions: Vector of integers. Regions, where these species shall be added.If nothing, they are added to all species.

Once a species has been added, it cannot be removed.

enable_boundary_species!(system,ispec,regions)

Add species ispec to a list of boundary regions. Species numbers for bulk and boundary species have to be distinct. Once a species has been added, it cannot be removed.

is_boundary_species(AbstractSystem, ispec) -> Bool

Check if species number corresponds to a boundary species.

is_bulk_species(AbstractSystem, ispec) -> Bool

Check if species number corresponds to a bulk species.

num_dof(system)

Number of degrees of freedom for system.

num_species(edge::VoronoiFVM.AbstractEdge) -> Any

Return number of species for edge

num_species(system)

Number of species in system

num_species(a)

Number of species (size of first dimension) of solution array.

data(system)

Retrieve user data record.

unknowns(system; inival, inifunc)

Create a solution vector for system. If inival is not specified, the entries of the returned vector are undefined.

unknowns(impedance_system)

Create a vector of unknowns of the impedance system

unknowns(Tu, system; inival, inifunc)

Create a solution vector for system with elements of type Tu. If inival is not specified, the entries of the returned vector are undefined.

map(inifunc, sys)

Create a solution vector for system using the callback inifunc which has the same signature as a source term.

map(inival, sys)

Create a solution vector for system using a constant initial value

map!(inifunc, U, system)

Map inifunc onto solution array U

isunknownsof(u, sys)

Detect if array fits to the system.

reshape(v, system)

Reshape vector to fit as solution to system.

abstract type AbstractSystem{Tv<:Number, Tc<:Number, Ti<:Integer, Tm<:Integer}

Abstract type for finite volume system structure.

mutable struct System{Tv, Tc, Ti, Tm, TSpecMat<:(AbstractMatrix)} <: VoronoiFVM.AbstractSystem{Tv, Tc, Ti, Tm}

Structure holding data for finite volume system.

Subtype of AbstractSystem.

Type parameters:

• TSpecMat: Type of matrix storing species information (Matrix or SparseMatrixCSC)

For the other type parameters, see AbstractSystem.

• grid::ExtendableGrid: Grid

• physics::VoronoiFVM.Physics: Physics data

• boundary_values::Matrix: Array of boundary condition values

• boundary_factors::Matrix: Array of boundary condition factors

• region_species::AbstractMatrix: Matrix containing species numbers for inner regions

• bregion_species::AbstractMatrix: Matrix containing species numbers for boundary regions

• node_dof::AbstractMatrix: Matrix containing degree of freedom numbers for each node

• matrixtype::Symbol: - :multidiagonal (currently disabled)
  • :sparse
  • :banded
  • :tridiagonal

• species_homogeneous::Bool: Flag which says if the number of unknowns per node is constant

• num_quantities::Any: Number of quantities defined on system

• num_parameters::Any: Number of parameter the system depends on.

• assembly_data::Union{Nothing, VoronoiFVM.AbstractAssemblyData{Tc, Ti}} where {Tc, Ti}: Precomputed form factors for bulk assembly

• boundary_assembly_data::VoronoiFVM.AbstractAssemblyData: Precomputed form factors for boundary assembly

• assembly_type::Symbol: :edgewise or :cellwise

• is_linear::Bool: Is the system linear ?

• outflownoderegions::Union{Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}}: Outflow nodes with their region numbers.

• generic_matrix::SparseArrays.SparseMatrixCSC: Sparse matrix for generic operator handling

• generic_matrix_colors::Vector: Sparse matrix colors for generic operator handling

• is_complete::Bool: Has the system been completed (species information compiled)?

boundary_dirichlet!(system, ispec, ibc, v)

Set Dirichlet boundary condition for species ispec at boundary ibc:

$u_{ispec}=v$ on $\Gamma_{ibc}$

  boundary_dirichlet!(system; kwargs...)

Keyword argument version:

• species: species number
• region: region number
• value: value

boundary_neumann!(system, ispec, ibc, v)

Set Neumann boundary condition for species ispec at boundary ibc:

$\mathrm{flux}_{ispec}\cdot \vec n=v$ on $\Gamma_{ibc}$

  boundary_neumann!(system; kwargs...)

Keyword argument version:

• species: species number
• region: region number
• value: value

boundary_robin!(system, ispec, ibc, α, v)

Set Robin boundary condition for species ispec at boundary ibc:

$\mathrm{flux}_{ispec}\cdot \vec n + \alpha u_{ispec}=v$ on $\Gamma_{ibc}$

  boundary_robin!(system; kwargs...)

Keyword argument version:

• species: species number
• region: region number
• factor: factor
• value: value

const DenseSystem

Type alias for system with dense matrix based species management

const SparseSystem

Type alias for system with sparse matrix based species management

viewK(
    edge::VoronoiFVM.AbstractEdge,
    u
) -> VoronoiFVM.VectorUnknowns

Solution view on first edge node

viewL(
    edge::VoronoiFVM.AbstractEdge,
    u
) -> VoronoiFVM.VectorUnknowns

Solution view on second edge node