Glossary

Terms as ClimaCore uses them. For the atmosphere model's state-vector notation (Y, Yₜ, p, ᶜ, ᶠ) see ClimaAtmos's notation and glossary pages; for ecosystem-wide software terms see docs/dev-guides/code-quality/glossary.md.

CG (continuous Galerkin). The spectral-element discretization in which node values on shared element boundaries are single-valued and element-local weak-form operators are completed by DSS. Selected with Grids.CG().

Completion. The step that turns an element-local weak-form tendency into the tendency of the whole discretization: DSS on a CG space, interface numerical fluxes on a DG space. Operators.tendency_completion builds the completion object for a tendency field; Operators.complete_tendency! applies it.

Contravariant components. Components of a vector in the basis eⁱ = ∇ξⁱ normal to the coordinate surfaces; the form a divergence needs. Types Contravariant12Vector, Contravariant3Vector, Contravariant123Vector.

Covariant components. Components in the basis e_i = ∂x/∂ξⁱ tangent to the coordinate lines; the form a gradient returns and the atmosphere's prognostic velocity uses. Types Covariant12Vector, Covariant3Vector, Covariant123Vector.

DG (discontinuous Galerkin). The spectral-element discretization in which each element holds its own copy of boundary-node values and elements are coupled by numerical fluxes across their faces. Selected with Grids.DG().

Domain. The continuous region a grid covers: an interval, a rectangle, or the sphere, with named boundaries.

DSS (direct stiffness summation). Replacing every copy of an element-boundary node value by the volume-weighted average of its copies in the adjacent elements, which makes a field continuous. Spaces.weighted_dss!.

Element. One quadrilateral (horizontal) or interval (vertical) cell of a mesh; the unit on which spectral-element operators act.

Extruded space. The product of a horizontal spectral-element grid and a vertical finite-difference grid; the space of a three-dimensional model. Spaces.ExtrudedFiniteDifferenceSpace.

Face, center. The two staggerings of the vertical grid: faces are the interfaces between cells, centers their midpoints. A column with Nv cells has Nv centers and Nv + 1 faces. Grids.CellFace(), Grids.CellCenter().

Field. Values of one type at every node of a space. Fields.Field.

FieldVector. A named collection of fields, possibly on different spaces, that acts as one vector for a time stepper. Fields.FieldVector.

GLL nodes. Gauss–Lobatto–Legendre quadrature points, the nodes of a spectral element; they include the element endpoints, so neighboring elements share nodes. Quadratures.GLL{Nq}.

Grid. Topology, quadrature, and the local geometry at every node; for spectral-element grids also the discretization. Grids.SpectralElementGrid2D and relatives.

Halo (ghost) exchange. The MPI communication of element-boundary data between neighboring processes, inside DSS or before DG face fluxes.

Hypsography. The terrain-following transformation of the vertical coordinate: Hypsography.LinearAdaption, Hypsography.SLEVEAdaption.

Local geometry. The coordinates, Jacobian, and metric tensors stored at each node. Fields.local_geometry_field(space).

Mesh. The partition of a domain into elements. Meshes.IntervalMesh, Meshes.RectilinearMesh, Meshes.EquiangularCubedSphere.

Node. A quadrature point of an element; the location of one degree of freedom.

Numerical flux. On a DG grid, the single-valued flux through a face computed from the states on its two sides, numflux(normal, argvals⁻, argvals⁺); Operators.RusanovNumericalFlux, Operators.CentralNumericalFlux.

Operator. An object that computes a spatial derivative or interpolation inside a broadcast expression. Spectral-element operators are element-local; finite-difference operators act along a column.

Space. A grid plus a staggering; what a field lives on.

Staggering. See face, center.

Strong and weak form. The two forms of a spectral-element derivative: the strong form differentiates the interpolant; the weak form is its negative adjoint under the quadrature inner product. Divergence() versus Divergence{WeakForm}().

Topology. The connectivity of a mesh's elements, and their distribution over MPI processes. Topologies.Topology2D.

UVW components. Components in the local orthonormal frame: zonal, meridional, radial on the sphere; x, y, z in a box. UVector, UVVector, WVector, UVWVector.

WJ. The product of the quadrature weights and the Jacobian at a node: its discrete volume, the weight of every integral and of DSS.