--- a/src/Grids/Grids.jl	Wed Apr 24 13:26:30 2024 +0200
+++ b/src/Grids/Grids.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -1,3 +1,4 @@
+# TODO: Double check that the interfaces for indexing and iterating are fully implemented and tested for all grids.
 module Grids
 
 using Sbplib.RegionIndices
@@ -47,6 +48,15 @@
 export equidistant_grid
 
 
+# MappedGrid
+export MappedGrid
+export jacobian
+export logicalgrid
+export mapped_grid
+export jacobian_determinant
+export geometric_tensor
+export geometric_tensor_inverse
+
 abstract type BoundaryIdentifier end
 
 include("manifolds.jl")
@@ -54,5 +64,6 @@
 include("tensor_grid.jl")
 include("equidistant_grid.jl")
 include("zero_dim_grid.jl")
+include("mapped_grid.jl")
 
 end # module

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Grids/mapped_grid.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -0,0 +1,81 @@
+struct MappedGrid{T,D, GT<:Grid{<:Any,D}, CT<:AbstractArray{T,D}, JT<:AbstractArray{<:AbstractArray{<:Any, 2}, D}} <: Grid{T,D}
+    logicalgrid::GT
+    physicalcoordinates::CT
+    jacobian::JT
+end
+
+jacobian(g::MappedGrid) = g.jacobian
+logicalgrid(g::MappedGrid) = g.logicalgrid
+
+
+# Indexing interface
+Base.getindex(g::MappedGrid, I::Vararg{Int}) = g.physicalcoordinates[I...]
+Base.eachindex(g::MappedGrid) = eachindex(g.logicalgrid)
+
+Base.firstindex(g::MappedGrid, d) = firstindex(g.logicalgrid, d)
+Base.lastindex(g::MappedGrid, d) = lastindex(g.logicalgrid, d)
+
+# Iteration interface
+
+Base.iterate(g::MappedGrid) = iterate(g.physicalcoordinates)
+Base.iterate(g::MappedGrid, state) = iterate(g.physicalcoordinates, state)
+
+Base.IteratorSize(::Type{<:MappedGrid{<:Any, D}}) where D = Base.HasShape{D}()
+Base.length(g::MappedGrid) = length(g.logicalgrid)
+Base.size(g::MappedGrid) = size(g.logicalgrid)
+Base.size(g::MappedGrid, d) = size(g.logicalgrid, d)
+
+boundary_identifiers(g::MappedGrid) = boundary_identifiers(g.logicalgrid)
+boundary_indices(g::MappedGrid, id::TensorGridBoundary) = boundary_indices(g.logicalgrid, id)
+
+function boundary_grid(g::MappedGrid, id::TensorGridBoundary)
+    b_indices = boundary_indices(g.logicalgrid, id)
+
+    # Calculate indices of needed jacobian components
+    D = ndims(g)
+    all_indices = SVector{D}(1:D)
+    free_variable_indices = deleteat(all_indices, grid_id(id))
+    jacobian_components = (:, free_variable_indices)
+
+    # Create grid function for boundary grid jacobian
+    boundary_jacobian = componentview((@view g.jacobian[b_indices...])  , jacobian_components...)
+    boundary_physicalcoordinates = @view g.physicalcoordinates[b_indices...]
+
+    return MappedGrid(
+        boundary_grid(g.logicalgrid, id),
+        boundary_physicalcoordinates,
+        boundary_jacobian,
+    )
+end
+
+# TBD: refine and coarsen could be implemented once we have a simple manifold implementation.
+# Before we do, we should consider the overhead of including such a field in the mapped grid struct.
+
+function mapped_grid(x, J, size...)
+    D = length(size)
+    lg = equidistant_grid(size, ntuple(i->0., D), ntuple(i->1., D))
+    return MappedGrid(
+        lg,
+        map(x,lg),
+        map(J,lg),
+    )
+end
+
+function jacobian_determinant(g::MappedGrid)
+    return map(jacobian(g)) do ∂x∂ξ
+        det(∂x∂ξ)
+    end
+end
+
+function geometric_tensor(g::MappedGrid)
+    return map(jacobian(g)) do ∂x∂ξ
+        ∂x∂ξ'*∂x∂ξ
+    end
+end
+
+function geometric_tensor_inverse(g::MappedGrid)
+    return map(jacobian(g)) do ∂x∂ξ
+        inv(∂x∂ξ'*∂x∂ξ)
+    end
+end
+

--- a/src/Grids/tensor_grid.jl	Wed Apr 24 13:26:30 2024 +0200
+++ b/src/Grids/tensor_grid.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -1,3 +1,5 @@
+# TODO: Check this file and other grids for duplicate implementation of general methods implemented for Grid
+
 """
     TensorGrid{T,D} <: Grid{T,D}
 

--- a/src/SbpOperators/volumeops/laplace/laplace.jl	Wed Apr 24 13:26:30 2024 +0200
+++ b/src/SbpOperators/volumeops/laplace/laplace.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -52,3 +52,25 @@
     return Δ
 end
 laplace(g::EquidistantGrid, stencil_set) = second_derivative(g, stencil_set)
+
+
+function laplace(g::MappedGrid, stencil_set)
+    J = jacobian_determinant(g)
+    J⁻¹ = map(inv, J)
+
+    Jḡ = map(*, J, ggeometric_tensor_inverse(g))
+    lg = logicalgrid(g)
+
+    return mapreduce(+, CartesianIndices(first(ḡ))) do I
+        i,j = I[1], I[2]
+        Jgⁱʲ = componentview(Jḡ, I[1], I[2])
+
+        if i == j
+            J⁻¹∘second_derivative_variable(lg, Jgⁱʲ, stencil_set, i)
+        else
+            Dᵢ = first_derivative(lg, stencil_set, i)
+            Dⱼ = first_derivative(lg, stencil_set, j)
+            J⁻¹∘Dᵢ∘DiagonalTensor(Jgⁱʲ)∘Dⱼ
+        end
+    end
+end

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/Grids/mapped_grid_test.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -0,0 +1,186 @@
+using Sbplib.Grids
+using Sbplib.RegionIndices
+using Test
+using StaticArrays
+
+@testset "MappedGrid" begin
+    lg = equidistant_grid((11,11), (0,0), (1,1)) # TODO: Change dims of the grid to be different
+    x̄ = map(ξ̄ -> 2ξ̄, lg)
+    J = map(ξ̄ -> @SArray(fill(2., 2, 2)), lg)
+    mg = MappedGrid(lg, x̄, J)
+
+    # TODO: Test constructor for different dims of range and domain for the coordinates
+    # TODO: Test constructor with different type than TensorGrid. a dummy type?
+
+    @test_broken false # @test_throws ArgumentError("Sizes must match") MappedGrid(lg, map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg), rand(SMatrix{2,3,Float64},15,11))
+
+
+    @test mg isa Grid{SVector{2, Float64},2}
+
+    @test jacobian(mg) isa Array{<:AbstractMatrix}
+    @test logicalgrid(mg) isa Grid
+
+    @testset "Indexing Interface" begin
+        mg = MappedGrid(lg, x̄, J)
+        @test mg[1,1] == [0.0, 0.0]
+        @test mg[4,2] == [0.6, 0.2]
+        @test mg[6,10] == [1., 1.8]
+
+        @test mg[begin, begin] == [0.0, 0.0]
+        @test mg[end,end] == [2.0, 2.0]
+        @test mg[begin,end] == [0., 2.]
+
+        @test eachindex(mg) == CartesianIndices((11,11))
+
+        @testset "cartesian indexing" begin
+            cases = [
+                 (1,1) ,
+                 (3,5) ,
+                 (10,6),
+                 (1,1) ,
+                 (3,2) ,
+            ]
+
+            @testset "i = $is" for (lg, is) ∈ cases
+                @test mg[CartesianIndex(is...)] == mg[is...]
+            end
+        end
+
+        @testset "eachindex" begin
+            @test eachindex(mg) == CartesianIndices((11,11))
+        end
+
+        @testset "firstindex" begin
+            @test firstindex(mg, 1) == 1
+            @test firstindex(mg, 2) == 1
+        end
+
+        @testset "lastindex" begin
+            @test lastindex(mg, 1) == 11
+            @test lastindex(mg, 2) == 11
+        end
+    end
+    # TODO: Test with different types of logical grids
+
+    @testset "Iterator interface" begin
+        sg = MappedGrid(
+            equidistant_grid((15,11), (0,0), (1,1)),
+            map(ξ̄ -> @SArray[ξ̄[1], ξ̄[2], -ξ̄[1]], lg), rand(SMatrix{2,3,Float64},15,11)
+        )
+
+        @test eltype(mg) == SVector{2,Float64}
+        @test eltype(sg) == SVector{3,Float64}
+
+        @test eltype(typeof(mg)) == SVector{2,Float64}
+        @test eltype(typeof(sg)) == SVector{3,Float64}
+
+        @test size(mg) == (11,11)
+        @test size(sg) == (15,11)
+
+        @test size(mg,2) == 11
+        @test size(sg,2) == 11
+
+        @test length(mg) == 121
+        @test length(sg) == 165
+
+        @test Base.IteratorSize(mg) == Base.HasShape{2}()
+        @test Base.IteratorSize(typeof(mg)) == Base.HasShape{2}()
+
+        @test Base.IteratorSize(sg) == Base.HasShape{2}()
+        @test Base.IteratorSize(typeof(sg)) == Base.HasShape{2}()
+
+        element, state = iterate(mg)
+        @test element == lg[1,1].*2
+        element, _ =  iterate(mg, state)
+        @test element == lg[2,1].*2
+
+        element, state = iterate(sg)
+        @test element == sg.physicalcoordinates[1,1]
+        element, _ = iterate(sg, state)
+        @test element == sg.physicalcoordinates[2,1]
+
+        @test collect(mg) == 2 .* lg
+    end
+
+    @testset "Base" begin
+        @test ndims(mg) == 2
+    end
+
+    @testset "boundary_identifiers" begin
+        @test boundary_identifiers(mg) == boundary_identifiers(lg)
+    end
+
+    @testset "boundary_indices" begin
+        @test boundary_indices(mg, CartesianBoundary{1,Lower}()) == boundary_indices(lg,CartesianBoundary{1,Lower}())
+        @test boundary_indices(mg, CartesianBoundary{2,Lower}()) == boundary_indices(lg,CartesianBoundary{2,Lower}())
+        @test boundary_indices(mg, CartesianBoundary{1,Upper}()) == boundary_indices(lg,CartesianBoundary{1,Upper}())
+    end
+
+    @testset "boundary_grid" begin
+        x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
+        J((ξ, η)) = @SMatrix[
+            1         0;
+            η*(2ξ-1)  1+ξ*(ξ-1);
+        ]
+
+        mg = mapped_grid(x̄, J, 10, 11)
+        J1((ξ, η)) = @SMatrix[
+            1       ;
+            η*(2ξ-1);
+        ]
+        J2((ξ, η)) = @SMatrix[
+            0;
+            1+ξ*(ξ-1);
+        ]
+
+        function test_boundary_grid(mg, bId, Jb)
+            bg = boundary_grid(mg, bId)
+
+            lg = logicalgrid(mg)
+            expected_bg = MappedGrid(
+                boundary_grid(lg, bId),
+                map(x̄, boundary_grid(lg, bId)),
+                map(Jb, boundary_grid(lg, bId)),
+            )
+
+            @testset let bId=bId, bg=bg, expected_bg=expected_bg
+                @test collect(bg) == collect(expected_bg)
+                @test logicalgrid(bg) == logicalgrid(expected_bg)
+                @test jacobian(bg) == jacobian(expected_bg)
+                # TODO: Implement equality of a curvilinear grid and simlify the above
+            end
+        end
+
+        @testset test_boundary_grid(mg, TensorGridBoundary{1, Lower}(), J2)
+        @testset test_boundary_grid(mg, TensorGridBoundary{1, Upper}(), J2)
+        @testset test_boundary_grid(mg, TensorGridBoundary{2, Lower}(), J1)
+        @testset test_boundary_grid(mg, TensorGridBoundary{2, Upper}(), J1)
+    end
+
+    @testset "jacobian_determinant" begin
+        @test_broken false
+    end
+
+    @testset "geometric_tensor" begin
+        @test_broken false
+    end
+
+    @testset "geometric_tensor_inverse" begin
+        @test_broken false
+    end
+
+end
+
+@testset "mapped_grid" begin
+    x̄((ξ, η)) = @SVector[ξ, η*(1+ξ*(ξ-1))]
+    J((ξ, η)) = @SMatrix[
+        1         0;
+        η*(2ξ-1)  1+ξ*(ξ-1);
+    ]
+    mg = mapped_grid(x̄, J, 10, 11)
+    @test mg isa MappedGrid{SVector{2,Float64}, 2}
+
+    lg = equidistant_grid((10,11), (0,0), (1,1))
+    @test logicalgrid(mg) == lg
+    @test collect(mg) == map(x̄, lg)
+end

--- a/test/SbpOperators/volumeops/laplace/laplace_test.jl	Wed Apr 24 13:26:30 2024 +0200
+++ b/test/SbpOperators/volumeops/laplace/laplace_test.jl	Thu Apr 25 10:20:43 2024 +0200
@@ -72,12 +72,12 @@
     g_1D = equidistant_grid(0.0, 1., 101)
     g_3D = equidistant_grid((0.0, -1.0, 0.0), (1., 1., 1.), 51, 101, 52)
 
-    @testset "1D" begin
+    @testset "EquidistantGrid" begin
         Δ = laplace(g_1D, stencil_set)
         @test Δ == second_derivative(g_1D, stencil_set)
         @test Δ isa LazyTensor{Float64,1,1}
     end
-    @testset "3D" begin
+    @testset "TensorGrid" begin
         Δ = laplace(g_3D, stencil_set)
         @test Δ isa LazyTensor{Float64,3,3}
         Dxx = second_derivative(g_3D, stencil_set, 1)
@@ -86,5 +86,9 @@
         @test Δ == Dxx + Dyy + Dzz
         @test Δ isa LazyTensor{Float64,3,3}
     end
+
+    @testset "MappedGrid" begin
+        @test_broken false
+    end
 end