Mapping

abstract type Grid{N, T} end

Defines an abstract type for grid-based structures in N dimensions with floating-point values T.

get_pos_by_coord(grid::Grid{N, T}, x::SVector{N, T}) -> NTuple{N, Int}

Returns the discrete position (grid indices) corresponding to a coordinate x.

• The cell (0,0) is centered between -h/2 and +h/2.
• h is the length of a grid cell in each dimension.

GridFree{N,T} <: Grid{N,T}

Uniform grid on unbounded space, centered at orig and with steps set by the vector h.

GridEllipsoidalRectangular{N,T} <: Grid{N,T}

Uniform grid on rectangular space rect, centered at orig and with steps set by the vector h. Cells are (possibly overlapping) ellipsoids defined at each grid point c as (x-c)'P(x-c) ≤ 1.

DeformedGrid{N, T} <: Grid{N, T}

Represents a deformed version of a GridFree grid, where points are mapped via an invertible transformation f and its inverse fi.

Fields

• grid::GridFree{N, T} : The underlying grid.
• f::Function : The forward transformation (physical -> deformed).
• fi::Function : The inverse transformation (deformed -> physical).
• A::Union{Nothing, SMatrix{N, N, T, N*N}} : Optional linear transformation matrix for volume calculations.

AbstractMapping{N,T}:

• defines a universe of labels (1..getnstate)
• provides coord <-> state conversions

GridMapping{N,T} <: AbstractMapping{N,T}:

• adds grid, and pos <-> state conversions

ListMapping{N,T} <: AbstractMapping{N,T}

Finite list of concrete points (SVector{N,T}) with id=1..K.

ExplicitGridMapping: explicit enumeration of positions -> ids (dict) and ids -> positions (vector)

ImplicitGridMapping:

• universe is a rectangular index box (minpos..maxpos) possibly periodic
• id computed by row-major linearization (no dict)
• pos recovered by inverse mapping

HierarchicalGridMapping:

• multiscale grid mapping with multiple levels of resolution
• each level is a GridMapping (e.g. ImplicitGridMapping)

PeriodicGridMapping{N, T, M, P} <: GridMapping{N, T}

A periodic wrapper over an underlying GridMapping.

Fields (mirrors PeriodicDomainList):

• periodic_dims::SVector{P, Int}
• periods::SVector{P, T}
• start::SVector{P, T}
• underlying_mapping::M
• periodic_index_map::NTuple{N, Union{Nothing, Int}}