API

PlusHalf(i)

Represents i + 1/2, but stored as internally as an integer value. Used for indexing into staggered finite difference meshes: the convention "half" values are indexed at cell faces, whereas centers are indexed at cell centers.

Supports +, - and inequalities.

See also half.

const half = PlusHalf(0)

UnrolledFunctions

A collection of generated functions that get unrolled during compilation, which make it possible to iterate over nonuniform collections without sacrificing type-stability.

The functions exported by this module are

• unrolled_map(f, values, [values2]): alternative to map
• unrolled_any(f, values): alternative to any
• unrolled_all(f, values): alternative to all
• unrolled_filter(f, values): alternative to filter
• unrolled_foreach(f, values): alternative to foreach
• unrolled_in(value, values): alternative to in
• unrolled_unique(values): alternative to unique
• unrolled_flatten(values): alternative to Iterators.flatten
• unrolled_flatmap(f, values): alternative to Iterators.flatmap
• unrolled_product(values1, values2): alternative to Iterators.product
• unrolled_findonly(f, values): checks that only one value satisfies f, and then returns that value
• unrolled_split(f, values): returns a tuple that contains the result of calling unrolled_filter with f and the result of calling it with !f
• unrolled_take(values, ::Val{N}): alternative to Iterators.take, but with an Int wrapped in a Val as the second argument instead of a regular Int; this usually compiles more quickly than values[1:N]
• unrolled_drop(values, ::Val{N}): alternative to Iterators.drop, but with an Int wrapped in a Val as the second argument instead of a regular Int; this usually compiles more quickly than values[(end - N + 1):end]

Utilities.Cache

ClimaCore maintains an internal cache of topology and grid objects: this ensures that if the constructor with the same arguments is invoked again (e.g. by reading from a file), the cached object will be returned (also known as memoization). This has two main advantages:

1. topology and metric information can be reused, reducing memory usage.

2. it is easy to check if two fields live on the same grid: we can just check if the underlying grid objects are the same (===), rather than checking all the fields are equal (via ==).

However this means that objects in the cache will not be removed from the garbage collector, so we provide an interface to remove these.

Utilities.Cache.cached_objects()

List all currently cached objects.

Utilities.Cache.clean_cache!(object)

Remove object from the cache of created objects.

In most cases, this function should not need to be called, unless you are constructing many grid objects, for example when doing a sweep over grid paramaters.

Utilities.Cache.clean_cache!()

Remove all objects from the cache of created objects.

In most cases, this function should not need to be called, unless you are constructing many grid objects, for example when doing a sweep over grid paramaters.

ClimaCore.DataLayouts

Defines the following DataLayouts (see individual docs for more info):

TODO: Add links to these datalayouts

• IJKFVH
• IJFH
• IJHF
• IFH
• IHF
• DataF
• IJF
• IF
• VF
• VIJFH
• VIJHF
• VIFH
• VIHF
• IH1JH2
• IV1JH2

Notation:

• i,j are horizontal node indices within an element
• k is the vertical node index within an element
• f is the field index (1 if field is scalar, >1 if it is a vector field)
• v is the vertical element index in a stack
• h is the element stack index

Data layout is specified by the order in which they appear, e.g. IJKFVH indexes the underlying array as [i,j,k,f,v,h]

Datalayouts that end with the field index

One of the fundamental features of datalayouts is to be able to store multiple variables in the same array, and then access those variables by name. As such, we occasionally must index into multiple variables when performing operations with a datalayout.

We can efficiently support linear indexing with datalayouts whose field index (f) is first or last. This is for the same reason as https://docs.julialang.org/en/v1/devdocs/subarrays/#Linear-indexing:

Linear indexing can be implemented efficiently when the entire array
has a single stride that separates successive elements, starting from
some offset.

Therefore, we provide special handling for these datalayouts where possible to leverage efficient linear indexing.

Here are some references containing relevant discussions and efforts to leverage efficient linear indexing:

• https://github.com/CliMA/ClimaCore.jl/issues/1889
• https://github.com/JuliaLang/julia/issues/28126
• https://github.com/JuliaLang/julia/issues/32051
• https://github.com/maleadt/StaticCartesian.jl
• https://github.com/JuliaGPU/GPUArrays.jl/pull/454#issuecomment-1431575721
• https://github.com/JuliaGPU/GPUArrays.jl/pull/520
• https://github.com/JuliaGPU/GPUArrays.jl/pull/464

DataF{S, A} <: Data0D{S}

Backing DataLayout for 0D point data.

DataF{S}(ArrayType[, ones | zeros | rand])

The ArrayType constructor returns a DataF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand).

IF{S, Ni, A} <: DataSlab1D{S, Ni}

Backing DataLayout for 1D spectral element slab data.

Nodal element data (I) are contiguous for each S datatype struct field (F) for a single element slab.

A DataSlab1D view can be returned from other Data1D objects by calling slab(data, idx...).

IF{S}(ArrayType[, ones | zeros | rand]; Ni)

The keyword constructor returns a IF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Ni quadrature degrees of freedom in the horizontal direction

IJF{S, Nij, A} <: DataSlab2D{S, Nij}

Backing DataLayout for 2D spectral element slab data.

Nodal element data (I,J) are contiguous for each S datatype struct field (F) for a single element slab.

A DataSlab2D view can be returned from other Data2D objects by calling slab(data, idx...).

IJF{S}(ArrayType[, ones | zeros | rand]; Nij)

The keyword constructor returns a IJF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nij quadrature degrees of freedom per horizontal direction

VF{S, A} <: DataColumn{S, Nv}

Backing DataLayout for 1D FV column data.

Column level data (V) are contiguous for each S datatype struct field (F).

A DataColumn view can be returned from other Data1DX, Data2DX objects by calling column(data, idx...).

VF{S}(ArrayType[, ones | zeros | rand]; Nv)

The keyword constructor returns a VF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nv number of vertical degrees of freedom

IFH{S,Ni,Nh,A} <: Data1D{S, Ni}
IFH{S,Ni,Nh}(ArrayType)

Backing DataLayout for 1D spectral element slabs.

Element nodal point (I) data is contiguous for each datatype S struct field (F), for each 1D mesh element (H).

The ArrayType-constructor makes a IFH 1D Spectral DataLayout given the backing ArrayType, quadrature degrees of freedom Ni, and the number of mesh elements Nh.

IFH{S}(ArrayType[, ones | zeros | rand]; Ni, Nh)

The keyword constructor returns a IFH given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Ni quadrature degrees of freedom in the horizontal direction
• Nh number of mesh elements

IJFH{S, Nij, A} <: Data2D{S, Nij}
IJFH{S,Nij}(ArrayType, nelements)

Backing DataLayout for 2D spectral element slabs.

Element nodal point (I,J) data is contiguous for each datatype S struct field (F), for each 2D mesh element slab (H).

The ArrayType-constructor constructs a IJFH 2D Spectral DataLayout given the backing ArrayType, quadrature degrees of freedom Nij × Nij, and the number of mesh elements nelements.

IJFH{S}(ArrayType[, Base.ones | zeros | rand]; Nij, Nh)

The keyword constructor returns a IJFH given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nij quadrature degrees of freedom per horizontal direction
• Nh number of mesh elements

VIFH{S, Nv, Ni, A} <: Data1DX{S, Nv, Ni}

Backing DataLayout for 1D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I) for each datatype S struct field (F), for each 1D mesh element slab (H).

VIFH{S}(ArrayType[, ones | zeros | rand]; Nv, Ni, Nh)

The keyword constructor returns a VIFH given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nv number of vertical degrees of freedom
• Ni quadrature degrees of freedom in the horizontal direction
• Nh number of horizontal elements

VIJFH{S, Nij, A} <: Data2DX{S, Nij}

Backing DataLayout for 2D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I, J) for each S datatype struct field (F), for each 2D mesh element slab (H).

VIJFH{S}(ArrayType[, ones | zeros | rand]; Nv, Nij, Nh)

The keyword constructor returns a VIJFH given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nv number of vertical degrees of freedom
• Nij quadrature degrees of freedom per horizontal direction
• Nh number of horizontal elements

IHF{S,Ni,Nh,A} <: Data1D{S, Ni}
IHF{S,Ni,Nh}(ArrayType)

Backing DataLayout for 1D spectral element slabs.

Element nodal point (I) data is contiguous for each datatype S struct field (F), for each 1D mesh element (H).

The ArrayType-constructor makes a IHF 1D Spectral DataLayout given the backing ArrayType, quadrature degrees of freedom Ni, and the number of mesh elements Nh.

IHF{S}(ArrayType[, ones | zeros | rand]; Ni, Nh)

The keyword constructor returns a IHF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Ni quadrature degrees of freedom in the horizontal direction
• Nh number of mesh elements

IJHF{S, Nij, A} <: Data2D{S, Nij}
IJHF{S,Nij}(ArrayType, nelements)

Backing DataLayout for 2D spectral element slabs.

Element nodal point (I,J) data is contiguous for each datatype S struct field (F), for each 2D mesh element slab (H).

The ArrayType-constructor constructs a IJHF 2D Spectral DataLayout given the backing ArrayType, quadrature degrees of freedom Nij × Nij, and the number of mesh elements nelements.

IJHF{S}(ArrayType[, Base.ones | zeros | rand]; Nij, Nh)

The keyword constructor returns a IJHF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nij quadrature degrees of freedom per horizontal direction
• Nh number of mesh elements

VIHF{S, Nv, Ni, A} <: Data1DX{S, Nv, Ni}

Backing DataLayout for 1D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I) for each datatype S struct field (F), for each 1D mesh element slab (H).

VIHF{S}(ArrayType[, ones | zeros | rand]; Nv, Ni, Nh)

The keyword constructor returns a VIHF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nv number of vertical degrees of freedom
• Ni quadrature degrees of freedom in the horizontal direction
• Nh number of horizontal elements

VIJHF{S, Nij, A} <: Data2DX{S, Nij}

Backing DataLayout for 2D spectral element slab + extruded 1D FV column data.

Column levels (V) are contiguous for every element nodal point (I, J) for each S datatype struct field (F), for each 2D mesh element slab (H).

VIJHF{S}(ArrayType[, ones | zeros | rand]; Nv, Nij, Nh)

The keyword constructor returns a VIJHF given the ArrayType and (optionally) an initialization method (one of Base.ones, Base.zeros, Random.rand) and the keywords:

• Nv number of vertical degrees of freedom
• Nij quadrature degrees of freedom per horizontal direction
• Nh number of horizontal elements

AbstractGlobalGeometry

Determines the conversion from local coordinates and vector bases to a Cartesian basis.

CartesianGlobalGeometry()

Specifies that the local coordinates align with the Cartesian coordinates, e.g. XYZPoint aligns with Cartesian123Point, and UVWVector aligns with Cartesian123Vector.

AbstractPoint

Represents a point in space.

The following types are supported:

• XPoint(x)
• YPoint(y)
• ZPoint(z)
• XYPoint(x, y)
• XZPoint(x, z)
• XYZPoint(x, y, z)
• LatPoint(lat)
• LongPoint(long)
• LatLongPoint(lat, long)
• LatLongZPoint(lat, long, z)
• Cartesian1Point(x1)
• Cartesian2Point(x2)
• Cartesian3Point(x3)
• Cartesian12Point(x1, x2)
• Cartesian13Point(x1, x3)
• Cartesian123Point(x1, x2, x3)

float_type(T)

Return the floating point type backing T: T can either be an object or a type.

AbstractDomain

A domain represents a region of space.

IntervalDomain(coord⁻, coord⁺; periodic=true)
IntervalDomain(coord⁻, coord⁺; boundary_names::Tuple{Symbol,Symbol})

Construct a IntervalDomain, the closed interval is given by coord⁻, coord⁺ coordinate arguments.

Either a periodic or boundary_names keyword argument is required.

RectangleDomain(x1::ClosedInterval, x2::ClosedInterval;
    x1boundary::Tuple{Symbol,Symbol},
    x2boundary::Tuple{Symbol,Symbol},
    x1periodic = false,
    x2periodic = false,
)

Construct a RectangularDomain in the horizontal. If a given x1 or x2 boundary is not periodic, then x1boundary or x2boundary boundary name keyword arguments must be supplied.

SphereDomain(radius)

A domain representing the surface of a sphere with radius radius.

boundary_names(obj::Union{AbstractDomain, AbstractMesh, AbstractTopology})

A tuple or vector of unique boundary names of a spatial domain.

AbstractMesh{dim}

A Mesh is an object which represents how we discretize a domain into elements.

It should be lightweight (i.e. exists on all MPI ranks), e.g for meshes stored in a file, it would contain the filename.

Face and vertex numbering

In 1D, faces and vertices are the same, and both are numbered [1,2].

In 2D, a face is a line segment between to vertices, and both are numbered [1,2,3,4], in a counter-clockwise direction.

 v4        f3        v3
   o-----------------o
   |                 |	    face    vertices
   |                 |	      f1 =>  v1 v2
f4 |                 | f2     f2 =>  v2 v3
   |                 |	      f3 =>  v3 v4
   |                 |        f4 =>  v4 v1
   |                 |
   o-----------------o
  v1       f1        v2

Interface

A subtype of AbstractMesh should define the following methods:

• domain(mesh)
• elements(mesh)
• is_boundary_face(mesh, elem, face)
• boundary_face_name(mesh, elem, face)
• opposing_face(mesh, elem, face)
• coordinates(mesh, elem, vert)
• containing_element (optional)

The following types/methods are provided by AbstractMesh:

• SharedVertices(mesh, elem, vert)
• face_connectivity_matrix(mesh[,elemorder])
• vertex_connectivity_matrix(mesh[,elemorder])

IntervalMesh <: AbstractMesh

A 1D mesh on an IntervalDomain.

Constuctors

IntervalMesh(domain::IntervalDomain, faces::AbstractVector)

Construct a 1D mesh with face locations at faces.

IntervalMesh(domain::IntervalDomain[, stretching=Uniform()]; nelems=)

Constuct a 1D mesh on domain with nelems elements, using stretching. Possible values of stretching are:

• Uniform()
• ExponentialStretching(H)
• GeneralizedExponentialStretching(dz_bottom, dz_top)
• HyperbolicTangentStretching(dz_bottom)

RectilinearMesh <: AbstractMesh2D

Constructors

RectilinearMesh(domain::RectangleDomain, n1, n2)

Construct a RectilinearMesh of equally-spaced n1 by n2 elements on domain.

RectilinearMesh(intervalmesh1::IntervalMesh1, intervalmesh2::IntervalMesh2)

Construct the product mesh of intervalmesh1 and intervalmesh2.

AbstractCubedSphere <: AbstractMesh2D

This is an abstract type of cubed-sphere meshes on SphereDomains. A cubed-sphere mesh has 6 panels, laid out as follows:

                                          :   Panel 1   :
                            +-------------+-------------+
                            |     +x1     |     +x1     |
                            |             |             |
                            |    Panel    |    Panel    |
                            |+x3   5   -x3|-x2   6   +x2|
                            |     -x2     |     -x3     |
                            |             |             |
                            |     -x1     |     -x1     |
              +-------------+-------------+-------------+
              |     -x2     |     -x2     |
              |             |             |
              |    Panel    |    Panel    |
              |+x1   3   -x1|+x3   4   -x3|
              |     +x3     |     -x1     |
              |             |             |
              |     +x2     |     +x2     |
+-------------+-------------+-------------+
|     +x3     |     +x3     |
|             |             |
|    Panel    |    Panel    |
|-x2   1   +x2|+x1   2   -x1|
|     +x1     |     +x2     |
|             |             |
|     -x3     |     -x3     |
+-------------+-------------+
:   Panel 6   :

This is the same panel ordering used by the S2 Geometry library (though we use 1-based instead of 0-based numering).

Elements are indexed by a CartesianIndex{3} object, where the components are:

• horizontal element index (left to right) within each panel.
• vertical element index (bottom to top) within each panel.
• panel number

Subtypes should have the following fields:

• domain: a SphereDomain
• ne: number of elements across each panel

External links

• S2Geometry library
• MIT GCM exch2

EquiangularCubedSphere <: AbstractCubedSphere

An equiangular gnomonic mesh proposed by [7]. Uses the element indexing convention of AbstractCubedSphere.

Constructors

EquiangularCubedSphere(
    domain::Domains.SphereDomain,
    ne::Integer,
    localelementmap=NormalizedBilinearMap()
    )

Constuct an EquiangularCubedSphere on domain with ne elements across each panel.

EquidistantCubedSphere <: AbstractCubedSphere

An equidistant gnomonic mesh outlined in [8] and [9]. Uses the element indexing convention of AbstractCubedSphere.

Constructors

EquidistantCubedSphere(domain::Domains.SphereDomain, ne::Integer)

Constuct an EquidistantCubedSphere on domain with ne elements across each panel.

ConformalCubedSphere <: AbstractCubedSphere

A conformal mesh outlined in [8]. Uses the element indexing convention of AbstractCubedSphere.

Constructors

ConformalCubedSphere(domain::Domains.SphereDomain, ne::Integer)

Constuct a ConformalCubedSphere on domain with ne elements across each panel.

LocalElementMap

An abstract type of mappings from the reference element to a physical domain.

IntrinsicMap()

This LocalElementMap uses the intrinsic mapping of the cubed sphere to map the reference element to the physical domain.

NormalizedBilinearMap()

The LocalElementMap for meshes on spherical domains of [10]. It uses bilinear interpolation between the Cartesian coordinates of the element vertices, then normalizes the result to lie on the sphere.

Uniform()

Use uniformly-sized elements.

ExponentialStretching(H::FT)

Apply exponential stretching to the domain when constructing elements. H is the scale height (a typical atmospheric scale height H ≈ 7.5km).

For an interval $[z_0,z_1]$, this makes the elements uniformally spaced in $\zeta$, where

\[\zeta = \frac{1 - e^{-\eta/h}}{1-e^{-1/h}},\]

where $\eta = \frac{z - z_0}{z_1-z_0}$, and $h = \frac{H}{z_1-z_0}$ is the non-dimensional scale height. If reverse_mode is true, the smallest element is at the top, and the largest at the bottom (this is typical for land model configurations).

Then, the user can define a stretched mesh via

ClimaCore.Meshes.IntervalMesh(interval_domain, ExponentialStretching(H); nelems::Int, reverse_mode = false)

faces contain reference z without any warping.

GeneralizedExponentialStretching(dz_bottom::FT, dz_top::FT)

Apply a generalized form of exponential stretching to the domain when constructing elements. dz_bottom and dz_top are target element grid spacings at the bottom and at the top of the vertical column domain (m). In typical atmosphere configurations, dz_bottom is the smallest grid spacing and dz_top the largest one. On the other hand, for typical land configurations, dz_bottom is the largest grid spacing and dz_top the smallest one.

For land configurations, use reverse_mode = true (default value false).

Then, the user can define a generalized stretched mesh via

ClimaCore.Meshes.IntervalMesh(interval_domain, GeneralizedExponentialStretching(dz_bottom, dz_top); nelems::Int, reverse_mode = false)

faces contain reference z without any warping.

HyperbolicTangentStretching(dz_surface::FT)

Apply a hyperbolic tangent stretching to the domain when constructing elements. dz_surface is the target element grid spacing at the surface. In typical atmosphere configuration, it is the grid spacing at the bottom of the vertical column domain (m). On the other hand, for typical land configurations, it is the grid spacing at the top of the vertical column domain.

For an interval $[z_0,z_1]$, this makes the elements uniformally spaced in $\zeta$, where

\[\eta = 1 - \frac{tanh[\gamma(1-\zeta)]}{tanh(\gamma)},\]

where $\eta = \frac{z - z_0}{z_1-z_0}$. The stretching parameter $\gamma$ is chosen to achieve a given resolution dz_surface at the surface.

Then, the user can define a stretched mesh via

ClimaCore.Meshes.IntervalMesh(interval_domain, HyperbolicTangentStretching(dz_surface); nelems::Int, reverse_mode)

reverse_mode is default to false for atmosphere configurations. For land configurations, use reverse_mode = true.

faces contain reference z without any warping.

truncate_mesh(
    parent_mesh::AbstractMesh,
    trunc_domain::IntervalDomain{CT},
)

Constructs an IntervalMesh, truncating the given parent_mesh defined on a truncated trunc_domain. The truncation preserves the number of degrees of freedom covering the space from the trunc_domain's z_bottom to z_top, adjusting the stretching.

Meshes.domain(mesh::AbstractMesh)

The domain (a subtype of Domains.AbstractDomain) on which the mesh is defined.

Meshes.elements(mesh::AbstractMesh)

An iterator over the elements of a mesh. Elements of a mesh can be of any type.

nelements(mesh::AbstractMesh)

The number of elements in the mesh.

Meshes.is_boundary_face(mesh::AbstractMesh, elem, face::Int)::Bool

Determine whether face face of element elem is on the boundary of mesh.

elem should be an element of elements(mesh).

Meshes.boundary_face_name(mesh::AbstractMesh, elem, face::Int)::Union{Symbol,Nothing}

The name of the boundary facing face of element elem, or nothing if it is not on the boundary.

opelem, opface, reversed = Meshes.opposing_face(mesh::AbstractMesh, elem, face::Int)

The element and face (opelem, opface) that oppose face face of element elem.

Meshes.coordinates(mesh, elem, vert::Int)
Meshes.coordinates(mesh, elem, ξ::SVector)

Return the physical coordinates of a point in an element elem of mesh. The position of the point can either be a vertex number vert or the coordinates ξ in the reference element.

elem = Meshes.containing_element(mesh::AbstractMesh, coord)

The element elem in mesh containing the coordinate coord. If the coordinate falls on the boundary between two or more elements, an arbitrary element is chosen.

ξ = Meshes.reference_coordinates(mesh::AbstractMesh, elem, coord)

An SVector of coordinates in the reference element such that

Meshes.coordinates(mesh, elem, ξ) == coord

This can be used for interpolation to a specific point.

Meshes.SharedVertices(mesh, elem, vert)

An iterator over (element, vertex) pairs that are shared with (elem,vert).

M = Meshes.face_connectivity_matrix(mesh, elemorder = elements(mesh))

Construct a Bool-valued SparseCSCMatrix containing the face connections of mesh. Elements are indexed according to elemorder.

Note that M[i,i] == true only if two distinct faces of element i are connected.

M = Meshes.vertex_connectivity_matrix(mesh, elemorder = elements(mesh))

Construct a Bool-valued SparseCSCMatrix containing the vertex connections of mesh. Elements are indexed according to elemorder.

Note that M[i,i] == true only if two distinct vertices of element i are connected.

Meshes.linearindices(elemorder)

Given a data structure elemorder[i] = elem that orders elements, construct the inverse map from orderindex = linearindices(elemorder) such that orderindex[elem] = i.

This will try to use the most efficient structure available.

Meshes.element_horizontal_length_scale(mesh::AbstractMesh)

The approximate length scale (in units of distance) of the elements of the mesh.

AbstractTopology

Subtypes of AbstractHorizontalTopology define connectiveness of a mesh in the horizontal domain.

Interfaces

• nelems
• domain(topology::AbstractTopology)
• mesh
• nlocalelems
• nneighbors
• nsendelems
• nghostelems
• localelemindex
• vertex_coordinates
• opposing_face
• face_node_index
• interior_faces
• ghost_faces
• vertex_node_index
• local_neighboring_elements
• ghost_neighboring_elements
• local_vertices
• ghost_vertices
• neighbors
• boundary_tags
• boundary_tag
• boundary_faces

IntervalTopology([context::SingletonCommsContext,] mesh::IntervalMesh)

A sequential topology on an Meshes.IntervalMesh.

Topology2D(mesh::AbstractMesh2D, elemorder=Mesh.elements(mesh))

This is a distributed topology for 2D meshes. elemorder is a vector or other linear ordering of the Mesh.elements(mesh). elempid is a sorted vector of the same length as elemorder, each element of which contains the pid of the owning process.

Internally, we can refer to elements in several different ways:

• elem: an element of the mesh. Often a CartesianIndex object.
• gidx: "global index": an enumeration of all elements:
  • elemorder[gidx] == elem
  • orderindex[elem] == gidx
• lidx: "local index": an enumeration of local elements.
  • local_elem_gidx[lidx] == gidx
• sidx: "send index": an index into the send buffer of a local element. A single local element may have multiple sidxs if it needs to be send to multiple processes.
  • send_elem_lidx[sidx] == lidx
• ridx: "receive index": an index into the receive buffer of a ghost element.
  • recv_elem_gidx[ridx] == gidx

spacefillingcurve(mesh::Meshes.AbstractCubedSphere)

Generate element ordering, elemorder, based on a space filling curve for a CubedSphere mesh.

spacefillingcurve(mesh::Meshes.RectilinearMesh)

Generate element ordering, elemorder, based on a space filling curve for a Rectilinear mesh.

nelems(topology)

The total number of elements in topology.

nneighbors(topology)

The number of neighbors of this process in topology.

nsendelems(topology)

The number of elements to send to neighbors in topology.

nghostelems(topology)

The number of ghost elements in topology.

localelemindex(topology, elem)

The local index for the specified element; useful for distributed topologies.

i,j = face_node_index(face, Nq, q, reversed=false)

The node indices of the qth node on face face, where Nq is the number of face nodes in each direction.

ghost_faces(topology::AbstractTopology)

An iterator over the ghost faces of topology. Each element of the iterator is a 5-tuple the form

(elem1, face1, elem2, face2, reversed)

where elemX, faceX are the element and face numbers, and reversed indicates whether they have opposing orientations.

i,j = vertex_node_index(vertex_num, Nq)

The node indices of vertex_num, where Nq is the number of face nodes in each direction.

local_vertices(topology)

An iterator over the interior vertices of topology. Each vertex is an iterator over (lidx, vert) pairs.

ghost_vertices(topology)

An iterator over the ghost vertices of topology. Each vertex is an iterator over (isghost, lidx/ridx, vert) pairs.

neighbors(topology)

Returns an array of the PIDs of the neighbors of this process.

mesh(topology)

Returns the mesh underlying the topology

nlocalelems(topology)

The number of local elements in topology.

(c1,c2,c3,c4) = vertex_coordinates(topology, elem)

The coordinates of the 4 vertices of element elem.

(opelem, opface, reversed) = opposing_face(topology, elem, face)

The opposing face of face number face of element elem in topology.

• opelem is the opposing element number, 0 for a boundary, negative for a ghost element
• opface is the opposite face number, or boundary face number if a boundary
• reversed indicates whether the opposing face has the opposite orientation.

interior_faces(topology::AbstractTopology)

An iterator over the interior faces of topology. Each element of the iterator is a 5-tuple the form

(elem1, face1, elem2, face2, reversed)

where elemX, faceX are the element and face numbers, and reversed indicates whether they have opposing orientations.

boundary_tags(topology)

A Tuple or NamedTuple of the boundary tags of the topology. A boundary tag is an integer that uniquely identifies a boundary.

boundary_tag(topology, name::Symbol)

The boundary tag of the topology for boundary name name. A boundary tag is an integer that uniquely identifies a boundary.

boundary_faces(topology, boundarytag)

An iterator over the faces of topology which face the boundary with tag boundarytag. Each element of the iterator is an (elem, face) pair.

local_neighboring_elements(topology::AbstractTopology, lidx::Integer)

An iterator of the local element indices (lidx) of the local elements which are neighbors of the local element lidx in topology (excluding lidx itself).

ghost_neighboring_elements(topology::AbstractTopology, ridx::Integer)

An iterator of the receive buffer indices (ridx) of the ghost elements which are neighbors of the local element lidx in topology.

CellFace()

Cell face location

CellCenter()

Cell center location

ColumnGrid(
    full_grid :: ExtrudedFiniteDifferenceGrid, 
    colidx    :: ColumnIndex,
)

A view into a column of a ExtrudedFiniteDifferenceGrid. This can be used as an

FiniteDifferenceGrid(topology::Topologies.IntervalTopology)
FiniteDifferenceGrid(device::ClimaComms.AbstractDevice, mesh::Meshes.IntervalMesh)

Construct a FiniteDifferenceGrid from an IntervalTopology (or an IntervalMesh).

This is an object which contains all the necessary geometric information.

To avoid unnecessary duplication, we memoize the construction of the grid.

ExtrudedFiniteDifferenceGrid(
    horizontal_space::AbstractSpace,
    vertical_space::FiniteDifferenceSpace,
    hypsography::HypsographyAdaption = Flat(),
)

Construct an ExtrudedFiniteDifferenceGrid from the horizontal and vertical spaces.

SpectralElementGrid1D(mesh::Meshes.IntervalMesh, quadrature_style::Quadratures.QuadratureStyle)

A one-dimensional space: within each element the space is represented as a polynomial.

SpectralElementSpace2D <: AbstractSpace

A two-dimensional space: within each element the space is represented as a polynomial.

Flat()

No surface hypsography.

CommonGrids

CommonGrids contains convenience constructors for common grids. Constructors in this module are sometimes dynamically created. You may want to use a different constructor if you're making the object in a performance-critical section, and if you know the type parameters at compile time.

If no convenience constructor exists, then you may need to create a custom grid using our low-level compose-able API.

Transitioning to using CommonGrids

You may have constructed a grid in the following way:

using ClimaComms
using ClimaCore: DataLayouts, Geometry, Topologies, Quadratures, Domains, Meshes, Grids
FT = Float64
z_elem = 63
z_min = FT(0)
z_max = FT(1)
radius = FT(6.371229e6)
h_elem = 15
n_quad_points = 4
device = ClimaComms.device()
context = ClimaComms.context(device)
hypsography = Grids.Flat()
global_geometry = Geometry.ShallowSphericalGlobalGeometry(radius)
quad = Quadratures.GLL{n_quad_points}()
h_mesh = Meshes.EquiangularCubedSphere(Domains.SphereDomain{FT}(radius), h_elem)
h_topology = Topologies.Topology2D(context, h_mesh)
z_boundary_names = (:bottom, :top)
z_domain = Domains.IntervalDomain(
    Geometry.ZPoint{FT}(z_min),
    Geometry.ZPoint{FT}(z_max);
    boundary_names = z_boundary_names,
)
z_mesh = Meshes.IntervalMesh(z_domain; nelems = z_elem)
h_grid = Grids.SpectralElementGrid2D(h_topology, quad)
z_topology = Topologies.IntervalTopology(context, z_mesh)
z_grid = Grids.FiniteDifferenceGrid(z_topology)
grid = Grids.ExtrudedFiniteDifferenceGrid(
    h_grid,
    z_grid,
    hypsography,
    global_geometry,
)

You may re-write this as:

using ClimaCore.CommonGrids: ExtrudedCubedSphereGrid
grid = ExtrudedCubedSphereGrid(;
    z_elem = 63,
    z_min = 0,
    z_max = 1,
    radius = 6.371229e6,
    h_elem = 15,
    n_quad_points = 4,
)

ExtrudedCubedSphereGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    z_min::Real,
    z_max::Real,
    radius::Real,
    h_elem::Integer,
    n_quad_points::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.ShallowSphericalGlobalGeometry(radius),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    h_mesh = Meshes.EquiangularCubedSphere(Domains.SphereDomain{FT}(radius), h_elem),
    h_topology::Topologies.AbstractDistributedTopology = Topologies.Topology2D(context, h_mesh),
    horizontal_layout_type = DataLayouts.IJFH,
    z_mesh::Meshes.IntervalMesh = DefaultZMesh(FT; z_min, z_max, z_elem, stretch),
    enable_bubble::Bool = false
)

A convenience constructor, which builds an Grids.ExtrudedFiniteDifferenceGrid, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• radius the radius of the cubed sphere
• h_elem the number of horizontal elements per side of every panel (6 panels in total)
• n_quad_points the number of quadrature points per horizontal element
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_mesh the horizontal mesh (defaults to Meshes.EquiangularCubedSphere)
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch
• enable_bubble enables the "bubble correction" for more accurate element areas when computing the spectral element space. See Grids.SpectralElementGrid2D for more information.

Example usage

using ClimaCore.CommonGrids
grid = ExtrudedCubedSphereGrid(;
    z_elem = 10,
    z_min = 0,
    z_max = 1,
    radius = 10,
    h_elem = 10,
    n_quad_points = 4,
)

CubedSphereGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    radius::Real,
    h_elem::Integer,
    n_quad_points::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    h_mesh = Meshes.EquiangularCubedSphere(Domains.SphereDomain{FT}(radius), h_elem),
    h_topology::Topologies.AbstractDistributedTopology = Topologies.Topology2D(context, h_mesh),
    horizontal_layout_type = DataLayouts.IJFH,
)

A convenience constructor, which builds a Grids.SpectralElementGrid2D given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• radius the radius of the cubed sphere
• h_elem the number of horizontal elements per side of every panel (6 panels in total)
• n_quad_points the number of quadrature points per horizontal element
• device the ClimaComms.device
• context the ClimaComms.context
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_mesh the horizontal mesh (defaults to Meshes.EquiangularCubedSphere)
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.

Example usage

using ClimaCore.CommonGrids
grid = CubedSphereGrid(; radius = 10, n_quad_points = 4, h_elem = 10)

ColumnGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    z_min::Real,
    z_max::Real,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    z_mesh::Meshes.IntervalMesh = DefaultZMesh(FT; z_min, z_max, z_elem, stretch),
)

A convenience constructor, which builds a Grids.FiniteDifferenceGrid given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch

Example usage

using ClimaCore.CommonGrids
grid = ColumnGrid(; z_elem = 10, z_min = 0, z_max = 10)

Box3DGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    x_min::Real,
    x_max::Real,
    y_min::Real,
    y_max::Real,
    z_min::Real,
    z_max::Real,
    periodic_x::Bool,
    periodic_y::Bool,
    n_quad_points::Integer,
    x_elem::Integer,
    y_elem::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    horizontal_layout_type = DataLayouts.IJFH,
    [h_topology::Topologies.AbstractDistributedTopology], # optional
    [z_mesh::Meshes.IntervalMesh], # optional
    enable_bubble::Bool = false,
)

A convenience constructor, which builds a Grids.ExtrudedFiniteDifferenceGrid with a Grids.FiniteDifferenceGrid vertical grid and a Grids.SpectralElementGrid2D horizontal grid, given:

• z_elem the number of z-points
• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• y_min the domain minimum along the y-direction.
• y_max the domain maximum along the y-direction.
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• periodic_y Bool indicating to use periodic domain along y-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• y_elem the number of y-points
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch
• enable_bubble enables the "bubble correction" for more accurate element areas when computing the spectral element space. See Grids.SpectralElementGrid2D for more information.
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.

Example usage

using ClimaCore.CommonGrids
grid = Box3DGrid(;
    z_elem = 10,
    x_min = 0,
    x_max = 1,
    y_min = 0,
    y_max = 1,
    z_min = 0,
    z_max = 10,
    periodic_x = false,
    periodic_y = false,
    n_quad_points = 4,
    x_elem = 3,
    y_elem = 4,
)

SliceXZGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    x_min::Real,
    x_max::Real,
    z_min::Real,
    z_max::Real,
    periodic_x::Bool,
    n_quad_points::Integer,
    x_elem::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
)

A convenience constructor, which builds a Grids.ExtrudedFiniteDifferenceGrid with a Grids.FiniteDifferenceGrid vertical grid and a Grids.SpectralElementGrid1D horizontal grid, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})

Example usage

using ClimaCore.CommonGrids
grid = SliceXZGrid(;
    z_elem = 10,
    x_min = 0,
    x_max = 1,
    z_min = 0,
    z_max = 1,
    periodic_x = false,
    n_quad_points = 4,
    x_elem = 4,
)

RectangleXYGrid(
    ::Type{<:AbstractFloat}; # defaults to Float64
    x_min::Real,
    x_max::Real,
    y_min::Real,
    y_max::Real,
    periodic_x::Bool,
    periodic_y::Bool,
    n_quad_points::Integer,
    x_elem::Integer, # number of horizontal elements
    y_elem::Integer, # number of horizontal elements
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    hypsography::Grids.HypsographyAdaption = Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
)

A convenience constructor, which builds a Grids.SpectralElementGrid2D with a horizontal RectilinearMesh mesh, given:

• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• y_min the domain minimum along the y-direction.
• y_max the domain maximum along the y-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• periodic_y Bool indicating to use periodic domain along y-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• y_elem the number of y-points
• device the ClimaComms.device
• context the ClimaComms.context
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})

Example usage

using ClimaCore.CommonGrids
grid = RectangleXYGrid(;
    x_min = 0,
    x_max = 1,
    y_min = 0,
    y_max = 1,
    periodic_x = false,
    periodic_y = false,
    n_quad_points = 4,
    x_elem = 3,
    y_elem = 4,
)

Meshes

• domain
• topology
• coordinates
• metric terms (inverse partial derivatives)
• quadrature rules and weights

References / notes

• ceed
• QA

Δz_data(space::AbstractSpace)

A DataLayout containing the Δz on a given space space.

FiniteDifferenceSpace(
    grid::Grids.FiniteDifferenceGrid,
    staggering::Staggering
)

A 1D finite-difference space, that lives on either:

• cell centers (where staggering is Grids.CellCenter) or
• cell faces (where staggering is Grids.CellFace)

Δz_metric_component(::Type{<:Goemetry.AbstractPoint})

The index of the z-component of an abstract point in an AxisTensor.

SpectralElementSpace1D(grid::SpectralElementGrid1D)
SpectralElementSpace1D(
    topology::Topologies.IntervalTopology,
    quadrature_style::Quadratures.QuadratureStyle;
    kwargs...
)

SpectralElementSpace2D(grid::SpectralElementGrid1D)
SpectralElementSpace2D(
    topology::Topologies.Topology2D,
    quadrature_style::Quadratures.QuadratureStyle;
    kwargs...,
)

SpectralElementSpaceSlab <: AbstractSpace

A view into a SpectralElementSpace2D for a single slab.

Spaces.node_horizontal_length_scale(space::AbstractSpectralElementSpace)

The approximate length scale of the distance between nodes. This is defined as the length scale of the mesh (see Meshes.element_horizontal_length_scale), divided by the number of unique quadrature points along each dimension.

ExtrudedFiniteDifferenceSpace(grid, staggering)

ExtrudedFiniteDifferenceSpace(
    horizontal_space::AbstractSpace,
    vertical_space::FiniteDifferenceSpace,
    hypsography::Grids.HypsographyAdaption = Grids.Flat(),
)

An extruded finite-difference space, where the extruded direction is staggered, containing grid information at either

• cell centers (where staggering is Grids.CellCenter) or
• cell faces (where staggering is Grids.CellFace)

CommonSpaces

CommonSpaces contains convenience constructors for common spaces, which builds off of CommonGrids and(when appropriate) requires an additional argument, staggering::Staggering to construct the desired space.

ExtrudedCubedSphereSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    z_min::Real,
    z_max::Real,
    radius::Real,
    h_elem::Integer,
    n_quad_points::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.ShallowSphericalGlobalGeometry(radius),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    h_mesh = Meshes.EquiangularCubedSphere(Domains.SphereDomain{FT}(radius), h_elem),
    h_topology::Topologies.AbstractDistributedTopology = Topologies.Topology2D(context, h_mesh),
    horizontal_layout_type = DataLayouts.IJFH,
    z_mesh::Meshes.IntervalMesh = DefaultZMesh(FT; z_min, z_max, z_elem, stretch),
    enable_bubble::Bool = false
    staggering::Staggering,
)

Construct an Spaces.ExtrudedFiniteDifferenceSpace for a cubed sphere configuration, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• radius the radius of the cubed sphere
• h_elem the number of horizontal elements per side of every panel (6 panels in total)
• n_quad_points the number of quadrature points per horizontal element
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_mesh the horizontal mesh (defaults to Meshes.EquiangularCubedSphere)
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch
• enable_bubble enables the "bubble correction" for more accurate element areas when computing the spectral element space. See Grids.SpectralElementGrid2D for more information.
• staggering vertical staggering, can be one of [Grids.CellFace, Grids.CellCenter]

Note that these arguments are all the same as CommonGrids.ExtrudedCubedSphereGrid, except for staggering.

Example usage

using ClimaCore.CommonSpaces
space = ExtrudedCubedSphereSpace(;
    z_elem = 10,
    z_min = 0,
    z_max = 1,
    radius = 10,
    h_elem = 10,
    n_quad_points = 4,
    staggering = Grids.CellCenter()
)

CubedSphereSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    radius::Real,
    h_elem::Integer,
    n_quad_points::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    h_mesh = Meshes.EquiangularCubedSphere(Domains.SphereDomain{FT}(radius), h_elem),
    h_topology::Topologies.AbstractDistributedTopology = Topologies.Topology2D(context, h_mesh),
    horizontal_layout_type = DataLayouts.IJFH,
)

Construct a Spaces.SpectralElementSpace2D for a cubed sphere configuration, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• radius the radius of the cubed sphere
• h_elem the number of horizontal elements per side of every panel (6 panels in total)
• n_quad_points the number of quadrature points per horizontal element
• device the ClimaComms.device
• context the ClimaComms.context
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_mesh the horizontal mesh (defaults to Meshes.EquiangularCubedSphere)
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.

Note that these arguments are all the same as CommonGrids.CubedSphereGrid.

Example usage

using ClimaCore.CommonSpaces
space = CubedSphereSpace(;
    radius = 10,
    n_quad_points = 4,
    h_elem = 10,
)

ColumnSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    z_min::Real,
    z_max::Real,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    z_mesh::Meshes.IntervalMesh = DefaultZMesh(FT; z_min, z_max, z_elem, stretch),
)

Construct a 1D Spaces.FiniteDifferenceSpace for a column configuration, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch
• staggering vertical staggering, can be one of [Grids.CellFace, Grids.CellCenter]

Note that these arguments are all the same as CommonGrids.ColumnGrid, except for staggering.

Example usage

using ClimaCore.CommonSpaces
space = ColumnSpace(;
    z_elem = 10,
    z_min = 0,
    z_max = 10,
    staggering = Grids.CellCenter()
)

Box3DSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    x_min::Real,
    x_max::Real,
    y_min::Real,
    y_max::Real,
    z_min::Real,
    z_max::Real,
    periodic_x::Bool,
    periodic_y::Bool,
    n_quad_points::Integer,
    x_elem::Integer,
    y_elem::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    horizontal_layout_type = DataLayouts.IJFH,
    [h_topology::Topologies.AbstractDistributedTopology], # optional
    [z_mesh::Meshes.IntervalMesh], # optional
    enable_bubble::Bool = false,
    staggering::Staggering
)

Construct a Spaces.ExtrudedFiniteDifferenceSpace for a 3D box configuration, given:

• z_elem the number of z-points
• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• y_min the domain minimum along the y-direction.
• y_max the domain maximum along the y-direction.
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• periodic_y Bool indicating to use periodic domain along y-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• y_elem the number of y-points
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• h_topology the horizontal topology (defaults to Topologies.Topology2D)
• z_mesh the vertical mesh, defaults to an Meshes.IntervalMesh along z with given stretch
• enable_bubble enables the "bubble correction" for more accurate element areas when computing the spectral element space. See Grids.SpectralElementGrid2D for more information.
• horizontal_layout_type the horizontal DataLayout type (defaults to DataLayouts.IJFH). This parameter describes how data is arranged in memory. See Grids.SpectralElementGrid2D for its use.
• staggering vertical staggering, can be one of [Grids.CellFace, Grids.CellCenter]

Note that these arguments are all the same as CommonGrids.Box3DGrid, except for staggering.

Example usage

using ClimaCore.CommonSpaces
space = Box3DSpace(;
    z_elem = 10,
    x_min = 0,
    x_max = 1,
    y_min = 0,
    y_max = 1,
    z_min = 0,
    z_max = 10,
    periodic_x = false,
    periodic_y = false,
    n_quad_points = 4,
    x_elem = 3,
    y_elem = 4,
    staggering = Grids.CellCenter()
)

SliceXZSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    z_elem::Integer,
    x_min::Real,
    x_max::Real,
    z_min::Real,
    z_max::Real,
    periodic_x::Bool,
    n_quad_points::Integer,
    x_elem::Integer,
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    stretch::Meshes.StretchingRule = Meshes.Uniform(),
    hypsography_fun = (h_grid, z_grid) -> Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
    staggering::Staggering
)

Construct a Spaces.ExtrudedFiniteDifferenceSpace for a 2D slice configuration, given:

• FT the floating-point type (defaults to Float64) [Float32, Float64]
• z_elem the number of z-points
• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• z_min the domain minimum along the z-direction.
• z_max the domain maximum along the z-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• device the ClimaComms.device
• context the ClimaComms.context
• stretch the mesh Meshes.StretchingRule (defaults to Meshes.Uniform)
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})
• staggering vertical staggering, can be one of [Grids.CellFace, Grids.CellCenter]

Note that these arguments are all the same as CommonGrids.SliceXZGrid, except for staggering.

Example usage

using ClimaCore.CommonSpaces
space = SliceXZSpace(;
    z_elem = 10,
    x_min = 0,
    x_max = 1,
    z_min = 0,
    z_max = 1,
    periodic_x = false,
    n_quad_points = 4,
    x_elem = 4,
    staggering = Grids.CellCenter()
)

RectangleXYSpace(
    ::Type{<:AbstractFloat}; # defaults to Float64
    x_min::Real,
    x_max::Real,
    y_min::Real,
    y_max::Real,
    periodic_x::Bool,
    periodic_y::Bool,
    n_quad_points::Integer,
    x_elem::Integer, # number of horizontal elements
    y_elem::Integer, # number of horizontal elements
    device::ClimaComms.AbstractDevice = ClimaComms.device(),
    context::ClimaComms.AbstractCommsContext = ClimaComms.context(device),
    hypsography::Grids.HypsographyAdaption = Grids.Flat(),
    global_geometry::Geometry.AbstractGlobalGeometry = Geometry.CartesianGlobalGeometry(),
    quad::Quadratures.QuadratureStyle = Quadratures.GLL{n_quad_points}(),
)

Construct a Spaces.SpectralElementSpace2D space for a 2D rectangular configuration, given:

• x_min the domain minimum along the x-direction.
• x_max the domain maximum along the x-direction.
• y_min the domain minimum along the y-direction.
• y_max the domain maximum along the y-direction.
• periodic_x Bool indicating to use periodic domain along x-direction
• periodic_y Bool indicating to use periodic domain along y-direction
• n_quad_points the number of quadrature points per horizontal element
• x_elem the number of x-points
• y_elem the number of y-points
• device the ClimaComms.device
• context the ClimaComms.context
• hypsography_fun a function or callable object (hypsography_fun(h_grid, z_grid) -> hypsography) for constructing the hypsography model.
• global_geometry the global geometry (defaults to Geometry.CartesianGlobalGeometry)
• quad the quadrature style (defaults to Quadratures.GLL{n_quad_points})

Note that these arguments are all the same as CommonGrids.RectangleXYGrid, except for staggering.

Example usage

using ClimaCore.CommonSpaces
space = RectangleXYSpace(;
    x_min = 0,
    x_max = 1,
    y_min = 0,
    y_max = 1,
    periodic_x = false,
    periodic_y = false,
    n_quad_points = 4,
    x_elem = 3,
    y_elem = 4,
)

QuadratureStyle

Quadrature style supertype. See sub-types:

• GLL
• GL
• Uniform

GLL{Nq}()

Gauss-Legendre-Lobatto quadrature using Nq quadrature points.

GL{Nq}()

Gauss-Legendre quadrature using Nq quadrature points.

Uniform{Nq}()

Uniformly-spaced quadrature.

degrees_of_freedom(QuadratureStyle) -> Int

Returns the degreesoffreedom of the QuadratureStyle concrete type

polynomial_degree(QuadratureStyle) -> Int

Returns the polynomial degree of the QuadratureStyle concrete type

points, weights = quadrature_points(::Type{FT}, quadrature_style)

The points and weights of the quadrature rule in floating point type FT.

barycentric_weights(x::SVector{Nq}) where {Nq}

The barycentric weights associated with the array of point locations x:

\[w_j = \frac{1}{\prod_{k \ne j} (x_i - x_j)}\]

See [11], equation 3.2.

interpolation_matrix(x::SVector, r::SVector{Nq})

The matrix which interpolates the Lagrange polynomial of degree Nq-1 through the points r, to points x. The matrix coefficients are computed using the Barycentric formula of [11], section 4:

\[I_{ij} = \begin{cases} 1 & \text{if } x_i = r_j, \\ 0 & \text{if } x_i = r_k \text{ for } k \ne j, \\ \frac{\displaystyle \frac{w_j}{x_i - r_j}}{\displaystyle \sum_k \frac{w_k}{x_i - r_k}} & \text{otherwise,} \end{cases}\]

where $w_j$ are the barycentric weights, see barycentric_weights.

differentiation_matrix(r::SVector{Nq, T}) where {Nq, T}

The spectral differentiation matrix for the Lagrange polynomial of degree Nq-1 interpolating at points r.

The matrix coefficients are computed using the [11], section 9.3:

\[D_{ij} = \begin{cases} \displaystyle \frac{w_j}{w_i (x_i - x_j)} &\text{ if } i \ne j \\ -\sum_{k \ne j} D_{kj} &\text{ if } i = j \end{cases}\]

where $w_j$ are the barycentric weights, see barycentric_weights.

differentiation_matrix(FT, quadstyle::QuadratureStyle)

The spectral differentiation matrix at the quadrature points of quadstyle, using floating point types FT.

V = orthonormal_poly(points, quad)

V_{ij} contains the j-1th Legendre polynomial evaluated at points[i]. i.e. it is the mapping from the modal to the nodal representation.

dss_transform(arg, local_geometry, weight, I)

Transfrom arg[I] to a basis for direct stiffness summation (DSS). Transformations only apply to vector quantities.

• local_geometry[I] is the relevant LocalGeometry object. If it is nothing, then no transformation is performed
• weight[I] is the relevant DSS weights. If weight is nothing, then the result is simply summation.

See ClimaCore.Spaces.weighted_dss!.

dss_transform!(
    device::ClimaComms.AbstractDevice,
    dss_buffer::DSSBuffer,
    data::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF},
    local_geometry::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF},
    weight::Union{DataLayouts.IJFH, DataLayouts.IJHF},
    perimeter::Perimeter2D,
    localelems::AbstractVector{Int},
)

Transforms vectors from Covariant axes to physical (local axis), weights the data at perimeter nodes, and stores result in the perimeter_data array. This function calls the appropriate version of dss_transform! based on the data layout of the input arguments.

Arguments:

• dss_buffer: DSSBuffer generated by create_dss_buffer function for field data
• data: field data
• local_geometry: local metric information defined at each node
• weight: local dss weights for horizontal space
• perimeter: perimeter iterator
• localelems: list of local elements to perform transformation operations on

Part of ClimaCore.Spaces.weighted_dss!.

function dss_transform!(
    ::ClimaComms.AbstractCPUDevice,
    perimeter_data::Union{DataLayouts.VIFH, DataLayouts.VIHF},
    data::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF},
    perimeter::AbstractPerimeter,
    bc,
    localelems::Vector{Int},
)

Transforms vectors from Covariant axes to physical (local axis), weights the data at perimeter nodes, and stores result in the perimeter_data array.

Arguments:

• perimeter_data: contains the perimeter field data, represented on the physical axis, corresponding to the full field data in data
• data: field data
• perimeter: perimeter iterator
• bc: A broadcasted object representing the dss transform.
• localelems: list of local elements to perform transformation operations on

Part of ClimaCore.Spaces.weighted_dss!.

dss_untransform!(
    device::ClimaComms.AbstractDevice,
    dss_buffer::DSSBuffer,
    data::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF},
    local_geometry::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF},
    perimeter::AbstractPerimeter,
)

Transforms the DSS'd local vectors back to Covariant12 vectors, and copies the DSS'd data from the perimeter_data to data. This function calls the appropriate version of dss_transform! function based on the data layout of the input arguments.

Arguments:

• dss_buffer: DSSBuffer generated by create_dss_buffer function for field data
• data: field data
• local_geometry: local metric information defined at each node
• perimeter: perimeter iterator
• localelems: list of local elements to perform transformation operations on

Part of ClimaCore.Spaces.weighted_dss!.

dss_untransform(T, targ, local_geometry, I...)

Transform targ[I...] back to a value of type T after performing direct stiffness summation (DSS).

See ClimaCore.Spaces.weighted_dss!.

dss_local_vertices!(
    perimeter_data::DataLayouts.VIFH,
    perimeter::Perimeter2D,
    topology::Topology2D,
)

Apply dss to local vertices.

function dss_local!(
    ::ClimaComms.AbstractCPUDevice,
    perimeter_data::DataLayouts.VIFH,
    perimeter::AbstractPerimeter,
    topology::AbstractTopology,
)

Performs DSS on local vertices and faces.

Part of ClimaCore.Spaces.weighted_dss!.

function dss_local_ghost!(
    ::ClimaComms.AbstractCPUDevice,
    perimeter_data::DataLayouts.VIFH,
    perimeter::AbstractPerimeter,
    topology::AbstractTopology,
)

Computes the "local" part of ghost vertex dss. (i.e. it computes the summation of all the shared local vertices of a unique ghost vertex and stores the value in each of the local vertex locations in perimeter_data)

Part of ClimaCore.Spaces.weighted_dss!.

dss_ghost!(
    device::ClimaComms.AbstractCPUDevice,
    perimeter_data::DataLayouts.VIFH,
    perimeter::AbstractPerimeter,
    topology::AbstractTopology,
)

Sets the value for all local vertices of each unique ghost vertex, in perimeter_data, to that of the representative ghost vertex.

Part of ClimaCore.Spaces.weighted_dss!.

create_dss_buffer(
    data::Union{DataLayouts.IJFH, DataLayouts.VIJFH},
    hspace::AbstractSpectralElementSpace,
)

Creates a DSSBuffer for the field data corresponding to data

Spaces.create_dss_buffer(fv::FieldVector)

Create a NamedTuple of buffers for communicating neighbour information of each Field in fv. In this NamedTuple, the name of each field is mapped to the buffer.

Spaces.create_dss_buffer(field::Field)

Create a buffer for communicating neighbour information of field.

create_dss_buffer(
    data::Union{DataLayouts.IJFH{S}, DataLayouts.IJHF{S}, DataLayouts.VIJFH{S}, DataLayouts.VIJHF{S}},
    topology::Topology2D,
    local_geometry::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF, Nothing} = nothing,
    local_weights::Union{DataLayouts.IJFH, DataLayouts.IJHF, DataLayouts.VIJFH, DataLayouts.VIJHF, Nothing} = nothing,
) where {S}

Creates a DSSBuffer for the field data corresponding to data

fill_send_buffer!(::ClimaComms.AbstractCPUDevice, dss_buffer::DSSBuffer; synchronize=true)

Loads the send buffer from perimeter_data. For unique ghost vertices, only data from the representative vertices which store result of "ghost local" DSS are loaded.

Part of ClimaCore.Spaces.weighted_dss!.

DSSBuffer{G, D, A, B}

Fields

• graph_context: ClimaComms graph context for communication
• perimeter_data: Perimeter DataLayout object: typically a VIFH{TT,Nv,Np,Nh} or VIHF{TT,Nv,Np,Nh}, where TT is the transformed type, Nv is the number of vertical levels, and Np is the length of the perimeter
• send_date: send buffer AbstractVector{FT}
• recv_data: recv buffer AbstractVector{FT}
• send_buf_idx: indexing array for loading send buffer from perimeter_data
• recv_buf_idx: indexing array for loading (and summing) data from recv buffer to
• internal_elems: internal local elements (lidx)
• perimeter_elems: local elements (lidx) located on process boundary

load_from_recv_buffer!(::ClimaComms.AbstractCPUDevice, dss_buffer::DSSBuffer)

Adds data from the recv buffer to the corresponding location in perimeter_data. For ghost vertices, this data is added only to the representative vertices. The values are then scattered to other local vertices corresponding to each unique ghost vertex in dss_local_ghost.

Part of ClimaCore.Spaces.weighted_dss!.

dss!(data, topology)

Computed unweighted/pure DSS of data.

weighted_dss_start!(
    data::Union{
        DataLayouts.IFH,
        DataLayouts.IHF,
        DataLayouts.VIFH,
        DataLayouts.VIHF,
        DataLayouts.IJFH,
        DataLayouts.IJHF,
        DataLayouts.VIJFH,
        DataLayouts.VIJHF,
    },
    space::Union{
        AbstractSpectralElementSpace,
        ExtrudedFiniteDifferenceSpace,
    },
    dss_buffer::Union{DSSBuffer, Nothing},
)

It comprises of the following steps:

1). Apply Spaces.dss_transform! on perimeter elements. This weights and tranforms vector fields to physical basis if needed. Scalar fields are weighted. The transformed and/or weighted perimeter data is stored in perimeter_data.

2). Apply Spaces.dss_local_ghost! This computes partial weighted DSS on ghost vertices, using only the information from local vertices.

3). Spaces.fill_send_buffer! Loads the send buffer from perimeter_data. For unique ghost vertices, only data from the representative ghost vertices which store result of "ghost local" DSS are loaded.

4). Start DSS communication with neighboring processes

weighted_dss_internal!(
    data::Union{
        DataLayouts.IFH,
        DataLayouts.IHF,
        DataLayouts.VIFH,
        DataLayouts.VIHF,
        DataLayouts.IJFH,
        DataLayouts.IJHF,
        DataLayouts.VIJFH,
        DataLayouts.VIJHF,
    },
    space::Union{
        AbstractSpectralElementSpace,
        ExtrudedFiniteDifferenceSpace,
    },
    dss_buffer::DSSBuffer,
)

1). Apply Spaces.dss_transform! on interior elements. Local elements are split into interior and perimeter elements to facilitate overlapping of communication with computation.

2). Probe communication

3). Spaces.dss_local! computes the weighted DSS on local vertices and faces.

weighted_dss_ghost!(
    data::Union{
        DataLayouts.IFH,
        DataLayouts.IHF,
        DataLayouts.VIFH,
        DataLayouts.VIHF,
        DataLayouts.IJFH,
        DataLayouts.IJHF,
        DataLayouts.VIJFH,
        DataLayouts.VIJHF,
    },
    space::Union{
        AbstractSpectralElementSpace,
        ExtrudedFiniteDifferenceSpace,
    },
    dss_buffer::Union{DSSBuffer, Nothing},
)

1). Finish communications.

2). Call Spaces.load_from_recv_buffer! After the communication is complete, this adds data from the recv buffer to the corresponding location in perimeter_data. For ghost vertices, this data is added only to the representative vertices. The values are then scattered to other local vertices corresponding to each unique ghost vertex in dss_local_ghost.

3). Call Spaces.dss_untransform! on all local elements. This transforms the DSS'd local vectors back to Covariant12 vectors, and copies the DSS'd data from the perimeter_data to data.

function weighted_dss!(
    data::Union{
        DataLayouts.IFH,
        DataLayouts.IHF,
        DataLayouts.VIFH,
        DataLayouts.VIHF,
        DataLayouts.IJFH,
        DataLayouts.IJHF,
        DataLayouts.VIJFH,
        DataLayouts.VIJHF,
    },
    space::Union{
        AbstractSpectralElementSpace,
        ExtrudedFiniteDifferenceSpace,
    },
    dss_buffer::Union{DSSBuffer, Nothing},
)

Computes weighted dss of data.

It comprises of the following steps:

1). Spaces.weighted_dss_start!

2). Spaces.weighted_dss_internal!

3). Spaces.weighted_dss_ghost!

Spaces.weighted_dss!(fv::FieldVector, dss_buffer = Spaces.create_dss_buffer(fv))

Apply weighted direct stiffness summation (DSS) to each field in fv. If a dss_buffer object is not provided, a buffer will be created for each field in fv. Note that using the Pair interface here parallelizes the weighted_dss! calls.

Spaces.weighted_dss!(f::Field, dss_buffer = Spaces.create_dss_buffer(field))

Apply weighted direct stiffness summation (DSS) to f. This operates in-place (i.e. it modifies the f). ghost_buffer contains the necessary information for communication in a distributed setting, see Spaces.create_dss_buffer.

This is a projection operation from the piecewise polynomial space $\mathcal{V}_0$ to the continuous space $\mathcal{V}_1 = \mathcal{V}_0 \cap \mathcal{C}_0$, defined as the field $\theta \in \mathcal{V}_1$ such that for all $\phi \in \mathcal{V}_1$

\[\int_\Omega \phi \theta \,d\Omega = \int_\Omega \phi f \,d\Omega\]

In matrix form, we define $\bar \theta$ to be the unique global node representation, and $Q$ to be the "scatter" operator which maps to the redundant node representation $\theta$

\[\theta = Q \bar \theta\]

Then the problem can be written as

\[(Q \bar\phi)^\top W J Q \bar\theta = (Q \bar\phi)^\top W J f\]

which reduces to

\[\theta = Q \bar\theta = Q (Q^\top W J Q)^{-1} Q^\top W J f\]

Spaces.weighted_dss!(field1 => ghost_buffer1, field2 => ghost_buffer2, ...)

Call Spaces.weighted_dss! on multiple fields at once, overlapping communication as much as possible.

unique_nodes(space::SpectralElementSpace2D)

An iterator over the unique nodes of space. Each node is represented by the first ((i,j), e) triple.

This function is experimental, and may change in future.

Spaces.area(space::Spaces.AbstractSpace)

The length/area/volume of space. This is computed as the sum of the quadrature weights $W_i$ multiplied by the Jacobian determinants $J_i$:

\[\sum_i W_i J_i \approx \int_\Omega \, d \Omega\]

If space is distributed, this uses a ClimaComms.allreduce operation.

Spaces.local_area(space::Spaces.AbstractSpace)

The length/area/volume of space local to the current context. See Spaces.area

RecursiveApply

This module contains operators to recurse over nested Tuples or NamedTuples.

To extend to another type T, define RecursiveApply.rmap(fn, args::T...)

Field(values, space)

A set of values defined at each point of a space.

coordinate_field(space::AbstractSpace)

Construct a Field of the coordinates of the space.

local_geometry_field(space::AbstractSpace)

Construct a Field of the LocalGeometry of the space.

zeros(space::AbstractSpace)

Construct a field on space that is zero everywhere.

ones(space::AbstractSpace)

Construct a field on space that is one everywhere.

sum([f=identity,] v::Field)

Approximate integration of v or f.(v) over the domain. In an AbstractSpectralElementSpace, an integral over the entire space is computed by summation over the elements of the integrand multiplied by the Jacobian determinants and the quadrature weights at each node within an element. Hence, sum is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights:

\[\sum_i f(v_i) W_i J_i \approx \int_\Omega f(v) \, d \Omega\]

where $v_i$ is the value at each node, and $f$ is the identity function if not specified.

If v is a distributed field, this uses a ClimaComms.allreduce operation.

Fields.local_sum(v::Field)

Compute the approximate integral of v over the domain local to the current context.

See sum for the integral over the full domain.

mean([f=identity, ]v::Field)

The mean value of field or f.(field) over the domain, weighted by area. Similar to sum, in an AbstractSpectralElementSpace, this is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights:

\[\frac{\sum_i f(v_i) W_i J_i}{\sum_i W_i J_i} \approx \frac{\int_\Omega f(v) \, d \Omega}{\int_\Omega \, d \Omega}\]

where $v_i$ is the Field value at each node, and $f$ is the identity function if not specified.

If v is a distributed field, this uses a ClimaComms.allreduce operation.

norm(v::Field, p=2; normalize=true)

The approximate $L^p$ norm of v, where $L^p$ represents the space of measurable functions for which the p-th power of the absolute value is Lebesgue integrable, that is:

\[\| v \|_p = \left( \int_\Omega |v|^p d \Omega \right)^{1/p}\]

where $|v|$ is defined to be the absolute value if $v$ is a scalar-valued Field, or the 2-norm if it is a vector-valued Field or composite Field (see LinearAlgebra.norm). Similar to sum and mean, in an AbstractSpectralElementSpace, this is computed by summation of the field values multiplied by the Jacobian determinants and quadrature weights. If normalize=true (the default), then internally the discrete norm is divided by the sum of the Jacobian determinants and quadrature weights:

\[\left(\frac{\sum_i |v_i|^p W_i J_i}{\sum_i W_i J_i}\right)^{1/p} \approx \left(\frac{\int_\Omega |v|^p \, d \Omega}{\int_\Omega \, d \Omega}\right)^{1/p}\]

If p=Inf, then the norm is the maximum of the absolute values

\[\max_i |v_i| \approx \sup_{\Omega} |v|\]

Consequently all norms should have the same units for all $p$ (being the same as calling norm on a single value).

If normalize=false, then the denominator term is omitted, and so the result will be the norm as described above multiplied by the length/area/volume of $\Omega$ to the power of $1/p$.

set!(f::Function, field::Field, args = ())

Apply function f to populate values in field field. f must have a function signature with signature f(::LocalGeometry[, args...]). Additional arguments may be passed to f with args.

ColumnIndex(ij,h)

An index into a column of a field. This can be used as an argument to getindex of a Field, to return a field on that column.

Example

colidx = ColumnIndex((1,1),1)
field[colidx]

Fields.bycolumn(fn, space)

Call fn(colidx) to every ColumnIndex colidx of space. This can be used to apply multiple column-wise operations in a single pass, making use of multiple threads.

Example

∇ = GradientF2C()
div = DivergenceC2F()

bycolumn(axes(f)) do colidx
    @. ∇f[colidx] = ∇(f[colidx])
    @. df[colidx] = div(∇f[colidx])
end

Δz_field(field::Field)
Δz_field(space::AbstractSpace)

A Field containing the Δz values on the same space as the given field.

LinearAdaption(surface::Field)

Locate the levels by linear interpolation between the surface field and the top of the domain, using the method of [12].

SLEVEAdaption(surface::Field, ηₕ::FT, s::FT)

Locate vertical levels using an exponential function between the surface field and the top of the domain, using the method of [13]. This method is modified such no warping is applied above some user defined parameter 0 ≤ ηₕ < 1.0, where the lower and upper bounds represent the domain bottom and top respectively. s governs the decay rate. If the decay-scale is poorly specified (i.e., s * zₜ is lower than the maximum surface elevation), a warning is thrown and s is adjusted such that it szₜ > maximum(z_surface).

diffuse_surface_elevation!(f::Field; κ::T, iter::Int, dt::T)

Option for 2nd order diffusive smoothing of generated terrain. Mutate (smooth) a given elevation profile f before assigning the surface elevation to the HypsographyAdaption type. A spectral second-order diffusion operator is applied with forward-Euler updates to generate profiles for each new iteration. Steps to generate smoothed terrain ( represented as a ClimaCore Field) are as follows:

• Compute discrete elevation profile f
• Compute diffusesurfaceelevation!(f, κ, iter). f is mutated.
• Define Hypsography.LinearAdaption(f)
• Define ExtrudedFiniteDifferenceSpace with new surface elevation.

Default diffusion parameters are appropriate for spherical arrangements. For zmax-zsfc == 𝒪(10^4), κ == 𝒪(10^8), dt == 𝒪(10⁻¹).

ref_z_to_physical_z(adaption::HypsographyAdaption, z_ref::ZPoint, z_surface::ZPoint, z_top::ZPoint) :: ZPoint

Convert reference zs to physical zs as prescribed by the given adaption.

This function has to be the inverse of physical_z_to_ref_z.

AbstractLimiter

Supertype for all limiters.

Interfaces

• apply_limiter!

QuasiMonotoneLimiter

This limiter is inspired by the one presented in Guba et al [14]. In the reference paper, it is denoted by OP1, and is outlined in eqs. (37)-(40). Quasimonotone here is meant to be monotone with respect to the spectral element nodal values. This limiter involves solving a constrained optimization problem (a weighted least square problem up to a fixed tolerance) that is completely local to each element.

As in HOMME, the implementation idea here is the following: we need to find a grid field which is closest to the initial field (in terms of weighted sum), but satisfies the min/max constraints. So, first we find values that do not satisfy constraints and bring these values to a closest constraint. This way we introduce some change in the tracer mass, which we then redistribute so that the l2 error is smallest. This redistribution might violate constraints; thus, we do a few iterations (until abs(Δtracer_mass) <= rtol * tracer_mass).

• ρq: tracer density Field, where q denotes tracer concentration per unit mass. This can be a scalar field, or a struct-valued field.
• ρ: fluid density Field (scalar).

Constructor

limiter = QuasiMonotoneLimiter(ρq::Field; rtol = eps(eltype(parent(ρq))))

Creates a limiter instance for the field ρq with relative tolerance rtol.

Usage

Call compute_bounds! on the input fields:

compute_bounds!(limiter, ρq, ρ)

Then call apply_limiter! on the output fields:

apply_limiter!(ρq, ρ, limiter)

compute_bounds!(limiter::QuasiMonotoneLimiter, ρq::Field, ρ::Field)

Compute the desired bounds for the tracer concentration per unit mass q, based on the tracer density, ρq, and density, ρ, fields.

This is computed by

1. compute_element_bounds!
2. starts the ghost exchange (if distributed)
3. compute_neighbor_bounds_local!
4. completes the ghost exchange (if distributed)
5. compute_neighbor_bounds_ghost! (if distributed)

apply_limiter!(ρq, ρ, limiter::QuasiMonotoneLimiter)

Apply the limiter on the tracer density ρq, using the computed desired bounds on the concentration q and density ρ as an optimal weight. This iterates over each element, calling apply_limit_slab!. If the limiter fails to converge for any element, a warning is issued.

compute_element_bounds!(limiter::QuasiMonotoneLimiter, ρq, ρ)

Given two fields ρq and ρ, computes the min and max of q in each element, storing it in limiter.q_bounds.

Part of compute_bounds!.

compute_neighbor_bounds_local!(limiter::QuasiMonotoneLimiter, topology)

Update the field limiter.q_bounds_nbr based on limiter.q_bounds in the local neighbors.

Part of compute_bounds!.

compute_neighbor_bounds_ghost!(limiter::QuasiMonotoneLimiter, topology)

Update the field limiter.q_bounds_nbr based on limiter.q_bounds in the ghost neighbors. This should be called after the ghost exchange has completed.

Part of compute_bounds!.

apply_limit_slab!(slab_ρq, slab_ρ, slab_WJ, slab_q_bounds, rtol)

Apply the computed bounds of the tracer concentration (slab_q_bounds) in the limiter to slab_ρq, given the total mass slab_ρ, metric terms slab_WJ, and relative tolerance rtol. Return whether the tolerance condition could be satisfied.

HDF5Writer(filename::AbstractString[, context::ClimaComms.AbstractCommsContext];
           overwrite::Bool = true)

An AbstractWriter for writing to HDF5-formatted files using the ClimaCore storage conventions. An internal cache is used to avoid writing duplicate domains, meshes, topologies and spaces to the file. Use HDF5Reader to load the data from the file.

The optional context can be used for writing distributed fields: in this case, the MPICommsContext used passed as an argument: this must match the context used for distributing the Field.

The writer overwrites or appends to existing files depending on the value of the overwrite keyword argument. When overwrite is false, the writer appends to filename if the file already exists, otherwise it creates a new one.

Interface

write!

Usage

writer = InputOutput.HDF5Writer(filename)
InputOutput.write!(writer, Y, "Y")
close(writer)

write!(writer::AbstractWriter, obj[, preferredname])

Write the object obj using writer. An optional preferredname can be provided, otherwise defaultname will be used to generate a name. The name of the object will be returned.

A cache of domains, meshes, topologies and spaces is kept: if one of these objects has already been written, then the file will not be modified: instead the name under which the object was first written will be returned. Note that Fields and FieldVectors are not cached, and so can be written multiple times.

write!(writer::HDF5Writer, name => value...)

Write one or more name => value pairs to writer.

write!(filename::AbstractString, name => value...)

Write one or more name => value pairs to the HDF5 file filename.

HDF5Reader(filename::AbstractString[, context::ClimaComms.AbstractCommsContext])

An AbstractReader for reading from HDF5 files created by HDF5Writer. The reader object contains an internal cache of domains, meshes, topologies and spaces that are read so that duplicate objects are not created.

The optional context can be used for reading distributed fields: in this case, the MPICommsContext used passed as an argument: resulting Fields will be distributed using this context. As with HDF5Writer, this requires a HDF5 library with MPI support.

Interface

• read_domain
• read_mesh
• read_topology
• read_space
• read_field

Usage

reader = InputOutput.HDF5Reader(filename)
Y = read_field(reader, "Y")
Y.c |> propertynames
Y.f |> propertynames
ρ_field = read_field(reader, "Y.c.ρ")
w_field = read_field(reader, "Y.f.w")
close(reader)

To explore the contents of the reader, use either

julia> reader |> propertynames

e.g, to explore the components of the space,

julia> reader.space_cache
Dict{Any, Any} with 3 entries:
  "center_extruded_finite_difference_space" => CenterExtrudedFiniteDifferenceSpace:…
  "horizontal_space"                        => SpectralElementSpace2D:…
  "face_extruded_finite_difference_space"   => FaceExtrudedFiniteDifferenceSpace:…

Once "unpacked" as shown above, ClimaCorePlots or ClimaCoreMakie can be used to visualise fields. ClimaCoreTempestRemap supports interpolation onto user-specified grids if necessary.

read_domain(reader::AbstractReader, name)

Reads a domain named name from reader. Domain objects are cached in the reader to avoid creating duplicate objects.

read_mesh(reader::AbstractReader, name)

Reads a mesh named name from reader, or from the reader cache if it has already been read.

read_topology(reader::AbstractReader, name)

Reads a topology named name from reader, or from the reader cache if it has already been read.

read_space(reader::AbstractReader, name)

Reads a space named name from reader, or from the reader cache if it has already been read.

read_field(reader, name)

Reads a Field or FieldVector named name from reader. Fields are not cached, so that reading the same field multiple times will create multiple distinct objects.

defaultname(obj)

Default name of object for InputOutput writers.

interpolate_array(field, xpts, ypts)
interpolate_array(field, xpts, ypts, zpts)

Interpolate a field to a regular array using pointwise interpolation.

This is primarily used for plotting and diagnostics.

Examples

longpts = range(Geometry.LongPoint(-180.0), Geometry.LongPoint(180.0), length = 21)
latpts = range(Geometry.LatPoint(-80.0), Geometry.LatPoint(80.0), length = 21)
zpts = range(Geometry.ZPoint(0.0), Geometry.ZPoint(1000.0), length = 21)

interpolate_array(field, longpts, latpts, zpts)

interpolate(remapper::Remapper, fields) interpolate!(dest, remapper::Remapper, fields)

Interpolate the given field(s) as prescribed by remapper.

The optimal number of fields passed is the buffer_length of the remapper. If more fields are passed, the remapper will batch work with size up to its buffer_length.

This call mutates the internal (private) state of the remapper.

Horizontally, interpolation is performed with the barycentric formula in [11], equation (3.2). Vertical interpolation is linear except in the boundary elements where it is 0th order.

interpolate! writes the output to the given destiniation. dest is expected to be defined on the root process and to be nothing for the other processes.

Note: interpolate allocates new arrays and has some internal type-instability, interpolate! is non-allocating and type-stable.

When using interpolate!, the destination has to be the same array type as the device in use (e.g., CuArray for CUDA runs).

Example

Given field1,field2, two Field defined on a cubed sphere.

longpts = range(-180.0, 180.0, 21)
latpts = range(-80.0, 80.0, 21)
zpts = range(0.0, 1000.0, 21)

hcoords = [Geometry.LatLongPoint(lat, long) for long in longpts, lat in latpts]
zcoords = [Geometry.ZPoint(z) for z in zpts]

space = axes(field1)

remapper = Remapper(space, hcoords, zcoords)

int1 = interpolate(remapper, field1)
int2 = interpolate(remapper, field2)

# Or
int12 = interpolate(remapper, [field1, field2])
# With int1 = int12[1, :, :, :]

   interpolate(field::ClimaCore.Fields, target_hcoords, target_zcoords)

Interpolate the given fields on the Cartesian product of target_hcoords with target_zcoords (if not empty).

Coordinates have to be ClimaCore.Geometry.Points.

Note: do not use this method when performance is important. Instead, define a Remapper and call interpolate(remapper, fields). Different Fields defined on the same Space can share a Remapper, so that interpolation can be optimized.

Example

Given field, a Field defined on a cubed sphere.

longpts = range(-180.0, 180.0, 21)
latpts = range(-80.0, 80.0, 21)
zpts = range(0.0, 1000.0, 21)

hcoords = [Geometry.LatLongPoint(lat, long) for long in longpts, lat in latpts]
zcoords = [Geometry.ZPoint(z) for z in zpts]

interpolate(field, hcoords, zcoords)