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API Reference

This page lists the main public symbols exported by CartesianOperators.

Capacity & Layout

  • AbstractCapacity{N,T}
  • AssembledCapacity{N,T}
  • assembled_capacity(m::GeometricMoments{N,T}; bc=zero(T))
  • rebuild!(cap::AssembledCapacity{N,T}, m::GeometricMoments{N,T}; bc=zero(T))
  • UnknownLayout
  • layout_mono(ntotal)
  • layout_diph(ntotal)

Differential/Assembly Routines

  • build_differential_operator(op_fn, nnodes::NTuple{N,Int}, dim::Int; periodic=false)
  • build_Winv(cap::AssembledCapacity{N,T})
  • build_GHW(cap::AssembledCapacity{N,T}; periodic=ntuple(_ -> false, N))

build_GHW returns:

(G, H, Winv, nnodes, D_m, D_p, S_m, S_p)

with shapes:

  • size(G) == size(H) == (N*ntotal, ntotal)
  • size(Winv) == (N*ntotal, N*ntotal)

Operator Containers

  • DiffusionOps(cap::AssembledCapacity{N,Float64}; periodic=...)
  • ConvectionOps(cap::AssembledCapacity{N,Float64}, uω, uγ; periodic=...)
  • AdvectionOps{N,T}
  • advection_ops(cap, uω, uγ; periodic=..., scheme=Centered())

Advection schemes:

  • AdvectionScheme
  • Centered <: AdvectionScheme
  • Upwind1 <: AdvectionScheme
  • S_plus(n, periodic=false) shift helper used by centered assembly

Apply APIs

Gradient:

  • gradient(op, xω, xγ; split=false)
  • gradient!(q, op, xω, xγ)
  • gradient!(qω, qγ, op, xω, xγ) (split in-place)

Divergence:

  • divergence(op, qω, qγ; split=false)
  • divergence!(out, op, qω, qγ)
  • divergence!(d_faces, d_int, op, qω, qγ) (split in-place)

Curl:

  • curl(op, qω, qγ; split=false) (2D scalar curl; CCW-positive)
  • curl(op, qω; split=false) (shorthand with zero interface flux)
  • curl!(out, op, qω, qγ) (2D in-place scalar curl)
  • 3D curl currently throws an informative not-implemented error.

Boundary Helpers

  • periodic_flags(bc::BorderConditions, N)
  • side_info(side::Symbol, N)
  • each_boundary_cell(nnodes, side)
  • apply_box_bc_mono!(A, b, cap, ops, D, bc_border; t=..., layout=...)

Miscellaneous

  • eval_coeff(D, x, t, row_lin) coefficient sampling helper

Notes

  • build_differential_operator uses Kronecker lifting and zeroes halo rows.
  • build_Winv builds a diagonal CSC directly from capacity buffers (O(N*ntotal)).
  • gradient, divergence, and 2D curl work on both DiffusionOps and ConvectionOps.