Added MappedDofBasis

src/ReferenceFEs/Pullbacks.jl

@@ -57,6 +57,18 @@ Represents the inverse of a pushforward map F*, defined as
 where 
   - V̂ is a function space on the reference cell K̂ and 
   - V is a function space on the physical cell K.
+
+# Note: 
+
+Given a pushforward F*, we provide a default implementation for the inverse (F*)^-1 that 
+is not optimal (and I think wrong for nonlinear geometries???). 
+
+For better performance, the user should overload the following methods for each 
+specific pushforward type:  
+
+- `return_cache(k::InversePushforward{PF}, v_phys::Number, args...)`
+- `evaluate!(cache, k::InversePushforward{PF}, v_phys::Number, args...)`
+
 """
 struct InversePushforward{PF} <: Map
   pushforward::PF
@@ -98,6 +110,58 @@ function evaluate!(
   Broadcasting(Operation(k))(f_phys,args...)
 end
 
+# MappedDofBasis
+
+"""
+    struct MappedDofBasis{T<:Dof,MT,BT} <: AbstractVector{T}
+      F :: MT
+      σ :: BT
+      args
+    end
+
+Represents η = σ∘F, evaluated as η(φ) = σ(F(φ,args...))
+
+  - σ : V* -> R is a dof basis
+  - F : W  -> V is a map between function spaces
+
+Intended combinations would be: 
+
+- σ : V* -> R dof basis in the physical domain and F* : V̂ -> V is a pushforward map.
+- ̂σ : V̂* -> R dof basis in the reference domain and (F*)^-1 : V -> V̂ is an inverse pushforward map.
+
+"""
+struct MappedDofBasis{T<:Dof,MT,BT,A} <: AbstractVector{T}
+  F    :: MT
+  dofs :: BT
+  args :: A
+
+  function MappedDofBasis(F::Map, dofs::AbstractVector{<:Dof}, args...)
+    T  = eltype(dofs)
+    MT = typeof(F)
+    BT = typeof(dofs)
+    A  = typeof(args)
+    new{T,MT,BT,A}(F,dofs,args)
+  end
+end
+
+Base.size(b::MappedDofBasis) = size(b.dofs)
+
+# Technically wrong, but the individual dofs are fake anyway
+Base.getindex(b::MappedDofBasis, i) = getindex(b.dofs,i)
+
+function Arrays.return_cache(b::MappedDofBasis, fields)
+  f_cache = return_cache(b.F,fields,b.args...)
+  ffields = evaluate!(f_cache,b.F,fields,b.args...)
+  dofs_cache = return_cache(b.dofs,ffields)
+  return f_cache, dofs_cache
+end
+
+function Arrays.evaluate!(cache, b::MappedDofBasis, fields)
+  f_cache, dofs_cache = cache
+  ffields = evaluate!(f_cache,b.F,fields,b.args...)
+  evaluate!(dofs_cache,b.dofs,ffields)
+end
+
 # Pullback
 
 """
@@ -131,8 +195,7 @@ end
 function evaluate!(
   cache, k::Pullback, σ_phys::AbstractVector{<:Dof}, args...
 )
-  pf(f_ref) = evaluate(k.pushforward,f_ref,args...) # TODO: Can we avoid this? 
-  return Arrays.OperationMap(σ_phys,pf)
+  return MappedDofBasis(k.pushforward,σ_phys,args...)
 end
 
 # InversePullback
@@ -171,8 +234,7 @@ end
 function evaluate!(
   cache, k::InversePullback, σ_ref::AbstractVector{<:Dof}, args...
 )
-  ipf(f_phys) = evaluate(inverse_map(k.pushforward),f_phys,args...) # TODO: Can we avoid this? 
-  return Arrays.OperationMap(σ_ref,ipf)
+  return MappedDofBasis(inverse_map(k.pushforward),σ_ref,args...)
 end
 
 # ContraVariantPiolaMap
@@ -184,7 +246,21 @@ function evaluate!(
 )
   sign  = (-1)^sign_flip
   idetJ = 1. / meas(Jt)
-  return (sign*v_ref)⋅(idetJ*Jt)
+  return sign * idetJ * (v_ref⋅Jt)
+end
+
+function return_cache(
+  ::InversePushforward{ContraVariantPiolaMap}, v_phys::Number, Jt::Number, sign_flip::Bool
+)
+  nothing
+end
+
+function evaluate!(
+  cache, ::InversePushforward{ContraVariantPiolaMap}, v_phys::Number, Jt::Number, sign_flip::Bool
+)
+  sign  = (-1)^sign_flip
+  detJ = meas(Jt)
+  return sign * detJ * (inv(Jt)⋅v_phys)
 end
 
 # CoVariantPiolaMap
@@ -197,3 +273,15 @@ function evaluate!(
   # we right-multiply to compute the gradient correctly
   return v_ref⋅transpose(inv(Jt))
 end
+
+function return_cache(
+  ::InversePushforward{CoVariantPiolaMap}, v_phys::Number, Jt::Number
+)
+  return nothing
+end
+
+function evaluate!(
+  cache, ::InversePushforward{CoVariantPiolaMap}, v_phys::Number, Jt::Number
+)
+  return transpose(Jt)⋅v_phys
+end