--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/test/SbpOperators/volumeops/laplace/laplace_test.jl	Fri Mar 19 16:52:53 2021 +0100
@@ -0,0 +1,205 @@
+using Test
+
+using Sbplib.SbpOperators
+using Sbplib.Grids
+using Sbplib.LazyTensors
+using Sbplib.RegionIndices
+
+"""
+    cmp_fields(s1,s2)
+
+Compares the fields of two structs s1, s2, using the == operator.
+"""
+function cmp_fields(s1::T,s2::T) where T
+    f = fieldnames(T)
+    return getfield.(Ref(s1),f) == getfield.(Ref(s2),f)
+end
+
+@testset "Laplace" begin
+    g_1D = EquidistantGrid(101, 0.0, 1.)
+    g_3D = EquidistantGrid((51,101,52), (0.0, -1.0, 0.0), (1., 1., 1.))
+    op = read_D2_operator(sbp_operators_path()*"standard_diagonal.toml"; order=4)
+    @testset "Constructors" begin
+
+        @testset "1D" begin
+            # Create all tensor mappings included in Laplace
+            Δ = laplace(g_1D, op.innerStencil, op.closureStencils)
+            H = inner_product(g_1D, op.quadratureClosure)
+            Hi = inverse_inner_product(g_1D, op.quadratureClosure)
+
+            (id_l, id_r) = boundary_identifiers(g_1D)
+
+            e_l = boundary_restriction(g_1D,op.eClosure,id_l)
+            e_r = boundary_restriction(g_1D,op.eClosure,id_r)
+            e_dict = Dict(Pair(id_l,e_l),Pair(id_r,e_r))
+
+            d_l = normal_derivative(g_1D,op.dClosure,id_l)
+            d_r = normal_derivative(g_1D,op.dClosure,id_r)
+            d_dict = Dict(Pair(id_l,d_l),Pair(id_r,d_r))
+
+            H_l = inner_product(boundary_grid(g_1D,id_l),op.quadratureClosure)
+            H_r = inner_product(boundary_grid(g_1D,id_r),op.quadratureClosure)
+            Hb_dict = Dict(Pair(id_l,H_l),Pair(id_r,H_r))
+
+            L = Laplace(g_1D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+            @test cmp_fields(L,Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict))
+            @test L isa TensorMapping{T,1,1}  where T
+            @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
+        end
+        @testset "3D" begin
+            # Create all tensor mappings included in Laplace
+            Δ = laplace(g_3D, op.innerStencil, op.closureStencils)
+            H = inner_product(g_3D, op.quadratureClosure)
+            Hi = inverse_inner_product(g_3D, op.quadratureClosure)
+
+            (id_l, id_r, id_s, id_n, id_b, id_t) = boundary_identifiers(g_3D)
+
+            e_l = boundary_restriction(g_3D,op.eClosure,id_l)
+            e_r = boundary_restriction(g_3D,op.eClosure,id_r)
+            e_s = boundary_restriction(g_3D,op.eClosure,id_s)
+            e_n = boundary_restriction(g_3D,op.eClosure,id_n)
+            e_b = boundary_restriction(g_3D,op.eClosure,id_b)
+            e_t = boundary_restriction(g_3D,op.eClosure,id_t)
+            e_dict = Dict(Pair(id_l,e_l),Pair(id_r,e_r),
+                          Pair(id_s,e_s),Pair(id_n,e_n),
+                          Pair(id_b,e_b),Pair(id_t,e_t))
+
+            d_l = normal_derivative(g_3D,op.dClosure,id_l)
+            d_r = normal_derivative(g_3D,op.dClosure,id_r)
+            d_s = normal_derivative(g_3D,op.dClosure,id_s)
+            d_n = normal_derivative(g_3D,op.dClosure,id_n)
+            d_b = normal_derivative(g_3D,op.dClosure,id_b)
+            d_t = normal_derivative(g_3D,op.dClosure,id_t)
+            d_dict = Dict(Pair(id_l,d_l),Pair(id_r,d_r),
+                          Pair(id_s,d_s),Pair(id_n,d_n),
+                          Pair(id_b,d_b),Pair(id_t,d_t))
+
+            H_l = inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure)
+            H_r = inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure)
+            H_s = inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure)
+            H_n = inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure)
+            H_b = inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure)
+            H_t = inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure)
+            Hb_dict = Dict(Pair(id_l,H_l),Pair(id_r,H_r),
+                          Pair(id_s,H_s),Pair(id_n,H_n),
+                          Pair(id_b,H_b),Pair(id_t,H_t))
+
+            L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+            @test cmp_fields(L,Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict))
+            @test L isa TensorMapping{T,3,3} where T
+            @inferred Laplace(Δ,H,Hi,e_dict,d_dict,Hb_dict)
+        end
+    end
+
+    @testset "laplace" begin
+        @testset "1D" begin
+            L = laplace(g_1D, op.innerStencil, op.closureStencils)
+            @test L == second_derivative(g_1D, op.innerStencil, op.closureStencils)
+            @test L isa TensorMapping{T,1,1}  where T
+        end
+        @testset "3D" begin
+            L = laplace(g_3D, op.innerStencil, op.closureStencils)
+            @test L isa TensorMapping{T,3,3} where T
+            Dxx = second_derivative(g_3D, op.innerStencil, op.closureStencils,1)
+            Dyy = second_derivative(g_3D, op.innerStencil, op.closureStencils,2)
+            Dzz = second_derivative(g_3D, op.innerStencil, op.closureStencils,3)
+            @test L == Dxx + Dyy + Dzz
+            @test L isa TensorMapping{T,3,3} where T
+        end
+    end
+
+    @testset "inner_product" begin
+        L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+        @test inner_product(L) == inner_product(g_3D,op.quadratureClosure)
+    end
+
+    @testset "inverse_inner_product" begin
+        L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+        @test inverse_inner_product(L) == inverse_inner_product(g_3D,op.quadratureClosure)
+    end
+
+    @testset "boundary_restriction" begin
+        L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+        id_l = CartesianBoundary{1,Lower}()
+        id_r = CartesianBoundary{1,Upper}()
+        id_s = CartesianBoundary{2,Lower}()
+        id_n = CartesianBoundary{2,Upper}()
+        id_b = CartesianBoundary{3,Lower}()
+        id_t = CartesianBoundary{3,Upper}()
+        @test boundary_restriction(L,id_l) == boundary_restriction(g_3D,op.eClosure,id_l)
+        @test boundary_restriction(L,id_r) == boundary_restriction(g_3D,op.eClosure,id_r)
+        @test boundary_restriction(L,id_s) == boundary_restriction(g_3D,op.eClosure,id_s)
+        @test boundary_restriction(L,id_n) == boundary_restriction(g_3D,op.eClosure,id_n)
+        @test boundary_restriction(L,id_b) == boundary_restriction(g_3D,op.eClosure,id_b)
+        @test boundary_restriction(L,id_t) == boundary_restriction(g_3D,op.eClosure,id_t)
+    end
+
+    @testset "normal_derivative" begin
+        L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+        id_l = CartesianBoundary{1,Lower}()
+        id_r = CartesianBoundary{1,Upper}()
+        id_s = CartesianBoundary{2,Lower}()
+        id_n = CartesianBoundary{2,Upper}()
+        id_b = CartesianBoundary{3,Lower}()
+        id_t = CartesianBoundary{3,Upper}()
+        @test normal_derivative(L,id_l) == normal_derivative(g_3D,op.dClosure,id_l)
+        @test normal_derivative(L,id_r) == normal_derivative(g_3D,op.dClosure,id_r)
+        @test normal_derivative(L,id_s) == normal_derivative(g_3D,op.dClosure,id_s)
+        @test normal_derivative(L,id_n) == normal_derivative(g_3D,op.dClosure,id_n)
+        @test normal_derivative(L,id_b) == normal_derivative(g_3D,op.dClosure,id_b)
+        @test normal_derivative(L,id_t) == normal_derivative(g_3D,op.dClosure,id_t)
+    end
+
+    @testset "boundary_quadrature" begin
+        L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+        id_l = CartesianBoundary{1,Lower}()
+        id_r = CartesianBoundary{1,Upper}()
+        id_s = CartesianBoundary{2,Lower}()
+        id_n = CartesianBoundary{2,Upper}()
+        id_b = CartesianBoundary{3,Lower}()
+        id_t = CartesianBoundary{3,Upper}()
+        @test boundary_quadrature(L,id_l) == inner_product(boundary_grid(g_3D,id_l),op.quadratureClosure)
+        @test boundary_quadrature(L,id_r) == inner_product(boundary_grid(g_3D,id_r),op.quadratureClosure)
+        @test boundary_quadrature(L,id_s) == inner_product(boundary_grid(g_3D,id_s),op.quadratureClosure)
+        @test boundary_quadrature(L,id_n) == inner_product(boundary_grid(g_3D,id_n),op.quadratureClosure)
+        @test boundary_quadrature(L,id_b) == inner_product(boundary_grid(g_3D,id_b),op.quadratureClosure)
+        @test boundary_quadrature(L,id_t) == inner_product(boundary_grid(g_3D,id_t),op.quadratureClosure)
+    end
+
+    # Exact differentiation is measured point-wise. In other cases
+    # the error is measured in the l2-norm.
+    @testset "Accuracy" begin
+        l2(v) = sqrt(prod(spacing(g_3D))*sum(v.^2));
+        polynomials = ()
+        maxOrder = 4;
+        for i = 0:maxOrder-1
+            f_i(x,y,z) = 1/factorial(i)*(y^i + x^i + z^i)
+            polynomials = (polynomials...,evalOn(g_3D,f_i))
+        end
+        v = evalOn(g_3D, (x,y,z) -> sin(x) + cos(y) + exp(z))
+        Δv = evalOn(g_3D,(x,y,z) -> -sin(x) - cos(y) + exp(z))
+
+        # 2nd order interior stencil, 1st order boundary stencil,
+        # implies that L*v should be exact for binomials up to order 2.
+        @testset "2nd order" begin
+            L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=2)
+            @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
+            @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
+            @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
+            @test L*v ≈ Δv rtol = 5e-2 norm = l2
+        end
+
+        # 4th order interior stencil, 2nd order boundary stencil,
+        # implies that L*v should be exact for binomials up to order 3.
+        @testset "4th order" begin
+            L = Laplace(g_3D, sbp_operators_path()*"standard_diagonal.toml"; order=4)
+            # NOTE: high tolerances for checking the "exact" differentiation
+            # due to accumulation of round-off errors/cancellation errors?
+            @test L*polynomials[1] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
+            @test L*polynomials[2] ≈ zeros(Float64, size(g_3D)...) atol = 5e-9
+            @test L*polynomials[3] ≈ polynomials[1] atol = 5e-9
+            @test L*polynomials[4] ≈ polynomials[2] atol = 5e-9
+            @test L*v ≈ Δv rtol = 5e-4 norm = l2
+        end
+    end
+end