improve docs

Project.toml

@@ -1,7 +1,7 @@
 name = "StableSpectralElements"
 uuid = "fb992021-99c7-4c2d-a14b-5e48ac4045b2"
 authors = ["Tristan Montoya <[email protected]>"]
-version = "0.2.12"
+version = "0.2.13-DEV"
 
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"

docs/src/SpatialDiscretizations.md

@@ -1,11 +1,11 @@
 # Module `SpatialDiscretizations`
 
 ## Overview
-Discretizations in StableSpectralElements.jl are constructed by first building a local approximation on a canonical reference element, denoted generically as $\hat{\Omega} \subset \mathbb{R}^d$, and using a bijective transformation $\bm{X}^{(\kappa)} : \hat{\Omega} \rightarrow \Omega^{(\kappa)}$ to construct the approximation on each physical element of the mesh $\{ \Omega^{(\kappa)}\}_{\kappa \in \{1:N_e\}}$ in terms of the associated operators on the reference element. An example of such a mapping is shown below, where we also depict the collapsed coordinate transformation $\bm{\chi} : [-1,1]^d \to \hat{\Omega}$ which may be used to construct operators with a tensor-product structure on the reference simplex.
+Discretizations in StableSpectralElements.jl are constructed by first building a local approximation on a canonical reference element, denoted generically as $\hat{\Omega} \subset \mathbb{R}^d$, and using a bijective transformation $\bm{X}^{(\kappa)} : \hat{\Omega} \rightarrow \Omega^{(\kappa)}$ to construct the approximation on each physical element $\Omega^{(\kappa)} \subset \Omega$ of the mesh $\{ \Omega^{(\kappa)}\}_{\kappa \in \{1:N_e\}}$ in terms of the associated operators on the reference element. An example of such a mapping is shown below, where we also depict the collapsed coordinate transformation $\bm{\chi} : [-1,1]^d \to \hat{\Omega}$ which may be used to construct operators with a tensor-product structure on the reference simplex.
 
 ![Mesh mapping](./assets/meshmap.svg)
 
-In order to define the different geometric reference elements, existing subtypes of `AbstractElemShape` from StartUpDG.jl (e.g. `Line`, `Quad`, `Hex`, `Tri`, and `Tet`) are used and re-exported by StableSpectralElements.jl. For example, we have 
+In order to define the different geometric reference elements, the subtypes `Line`, `Quad`, `Hex`, `Tri`, and `Tet` of `AbstractElemShape` from StartUpDG.jl are used and re-exported by StableSpectralElements.jl, representing the following reference domains:
 ```math
 \begin{aligned}
 \hat{\Omega}_{\mathrm{line}} &= [-1,1],\\
@@ -15,9 +15,7 @@ In order to define the different geometric reference elements, existing subtypes
 \hat{\Omega}_{\mathrm{tet}} &= \big\{ \bm{\xi} \in [-1,1]^3 : \xi_1 + \xi_2 + \xi_3 \leq -1 \big\}.
 \end{aligned}
 ```
-These element types are used in the constructor for StableSpectralElements.jl's `ReferenceApproximation` type, along with a subtype of `AbstractApproximationType` specifying the nature of the local approximation (and, optionally, the associated volume and facet quadrature rules).
-
-All the information used to define the spatial discretization on the physical domain $\Omega$ is contained within a `SpatialDiscretization` structure, which is constructed using a `ReferenceApproximation` and a `MeshData` from StartUpDG.jl, which are stored as the fields `reference_approximation` and `mesh`. When the constructor for a `SpatialDiscretization` is called, the grid metrics are computed and stored in a `GeometricFactors` structure, with the corresponding field being `geometric_factors`. 
+These element types are used in the constructor for StableSpectralElements.jl's [`ReferenceApproximation`](@ref) type, along with a subtype of `AbstractApproximationType` specifying the nature of the local approximation (and, optionally, the associated volume and facet quadrature rules). All the information used to define the spatial discretization on the physical domain $\Omega$ is contained within a `SpatialDiscretization` structure, which is constructed using a [`ReferenceApproximation`](@ref) and a `MeshData` from StartUpDG.jl, which are stored as the fields `reference_approximation` and `mesh`. When the constructor for a `SpatialDiscretization` is called, the grid metrics are computed and stored in a `GeometricFactors` structure, with the corresponding field being `geometric_factors`. 
 
 ## Data types
 

src/SpatialDiscretizations/SpatialDiscretizations.jl

@@ -149,14 +149,14 @@ struct ConservativeCurlMetrics <: AbstractMetrics end
 const ChanWilcoxMetrics = ConservativeCurlMetrics
 
 @doc raw"""
-    ReferenceApproximation(approx_type, reference_element, D, V, Vf, R, W, B, V_plot,
-                           reference_mapping)
+    ReferenceApproximation(approx_type::AbstractReferenceMapping,
+                           element_type::AbstractElemShape, kwargs...)
 
 Data structure defining the discretization on the reference element, containing the
 following fields:
 - `approx_type::AbstractApproximationType`: Type of operators used for the discretization
-  on the reference element(`NodalTensor`, `ModalTensor`, `NodalMulti`, `ModalMulti`
-  `NodalMultiDiagE`, `ModalMultiDiagE`)
+  on the reference element ([`NodalTensor`](@ref), [`ModalTensor`](@ref), [`NodalMulti`]
+  (@ref), [`ModalMulti`](@ref), [`NodalMultiDiagE`](@ref), or [`ModalMultiDiagE`](@ref))
 - `reference_element::StartUpDG.RefElemData`: Data structure containing quadrature node
   positions and operators used for defining the mapping from reference to physical space;
   contains the field `element_type::StartUpDG.AbstractElemShape` which determines the shape