Split values into geometric mapping and function values

[KnutAM]

This PR splits Values into geometric values and function values, the main advantages are

• Reuse code for reinit! for FaceValues and CellValues
  • This solves #616
  • When different mappings are added in the future (cf WIP: New vector interpolations and mappings #798) re-use becomes more important since we get more reinit! methods.
  • For making the MultiCellValues type (cf. MultiCellValues #680) this allows using only a single geometry cache
• The new parameterization is free to allow e.g. GPU-arrays

For a more complete picture, please see #798.

For normal use, this is not breaking wrt. master (i.e. no direct field access).
However, CellValues{<:VectorInterpolation} cannot be dispatched on anymore. This can be added if required, but in that case perhaps (re-)introducing CellVectorValues and CellScalarValues as aliases is cleaner.

Description of internal changes

Description of internal changes

struct CellValues{FV, GV, QR, detT<:AbstractVector} <: AbstractCellValues
    fun_values::FV # FunctionValues
    geo_values::GV # GeometryValues
    qr::QR         # QuadratureRule
    detJdV::detT   # AbstractVector{<:Number}
end

struct FaceValues{FV, GV, QR, detT, nT, V_FV<:AbstractVector{FV}, V_GV<:AbstractVector{GV}} <: AbstractFaceValues
    fun_values::V_FV # AbstractVector{FunctionValues}
    geo_values::V_GV # AbstractVector{GeometryValues}
    qr::QR           # FaceQuadratureRule
    detJdV::detT     # AbstractVector{<:Number}
    normals::nT      # AbstractVector{<:Vec}
    current_face::ScalarWrapper{Int}
end

where

QuadratureRule/FaceQuadratureRule: No changes, contains the location and
weights for the quadrature on the reference element.

GeometryValues contain information about the geometric interpolation on
the reference element. These are used to calculate the required quantities
for (1) mapping mutable parts of FunctionValues from the reference element to the
actual element and (2) calculating properties for the current cell, such as the detJdV
for each quadrature point and the face normals.

struct GeometryValues{IP, M_t, dMdξ_t, d2Mdξ2_t}
    ip::IP             # ::Interpolation                Geometric interpolation 
    M::M_t             # ::AbstractVector{<:Number}     Values of geometric shape functions
    dMdξ::dMdξ_t       # ::AbstractVector{<:Vec}        Gradients of geometric shape functions in ref-domain
    d2Mdξ2::d2Mdξ2_t   # ::AbstractVector{<:Tensor{2}}  Hessians of geometric shape functions in ref-domain
                       # ::Nothing                      When hessians are not required
end

FunctionValues contain information about the function interpolation on
the reference element, as well as caches for the value and gradient on the
current element.

struct FunctionValues{IP, N_t, dNdx_t, dNdξ_t}
    ip::IP          # ::Interpolation
    N_x::N_t        # ::AbstractMatrix{Union{<:Tensor,<:Number}}
    N_ξ::N_t        # ::AbstractMatrix{Union{<:Tensor,<:Number}}
    dNdx::dNdx_t    # ::AbstractMatrix{Union{<:Tensor,<:StaticArray}}
    dNdξ::dNdξ_t    # ::AbstractMatrix{Union{<:Tensor,<:StaticArray}}
end

Construction

The function interpolation (type parameter to FunctionValues) decides how
it should be mapped, by defining get_mapping_type(::Interpolation), possible
options are currently IdentityMapping() (same as what currently is in Ferrite),
CovariantPiolaMapping() (H(curl)), and ContravariantPiolaMapping() (H(div)).

The type of mapping determines what information is required to be precalculated in
GeometryValues, specifically if the hessian, d²M/dξ² must be calculated or not.

reinit! (Calculation and application of mapping)

First, mapping::MappingValues is calculated for the current quadrature point,
q_point, by using the precalculated values for the geometric interpolation in
geometry_values and the cell's coordinates, x:

mapping = calculate_mapping(geometry_values, q_point, x)

This mapping object can be querried for information required to perform the mapping,
specifically the jacobian and the hessian. If the latter should be calculated is determined
by whether d²M/dξ² is calculated in GeometryValues (which in turn was decided on construction based on the needs of the mapping type requested by the function interpolation).

We use this mapping to first calculate the detJdV (+ normals in FaceValues)
and later in apply_mapping! to update the values in FunctionValues appropriately fulling the requested mapping type.

[codecov-commenter]

Codecov Report

Attention: 6 lines in your changes are missing coverage. Please review.

Comparison is base (2dfcaf9) 93.08% compared to head (a255614) 93.15%.

Files	Patch %	Lines
src/FEValues/face_values.jl	95.77%	3 Missing ⚠️
src/FEValues/cell_values.jl	96.66%	2 Missing ⚠️
src/FEValues/FunctionValues.jl	98.79%	1 Missing ⚠️

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #764      +/-   ##
==========================================
+ Coverage   93.08%   93.15%   +0.06%     
==========================================
  Files          34       36       +2     
  Lines        5163     5229      +66     
==========================================
+ Hits         4806     4871      +65     
- Misses        357      358       +1     

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[KnutAM]

Seems to fix #616 (At least the example provided by @termi-official is not erroring, but tests are needed)

[termi-official]

Sorry for the late review! I think this looks really good already. I left some questions on the design.

[fredrikekre]

LGTM, just some stylistic nits that you don't have to fix if you don't agree. Can also merge and then do smaller clean ups later to make it easier to review.

Please squash-merge (and use a better commit message than the default message containing all commits in the branch).

[termi-official]

I think @AbdAlazezAhmed just had a good point on slack. Should we also update the new InterfaceValues in this PR or in a separate one?

[KnutAM]

I think @AbdAlazezAhmed just had a good point on slack. Should we also update the new InterfaceValues in this PR or in a separate one?

Thanks - did it now with 2cbd2b9