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gridap / Gridap.jl

Grid-based approximation of partial differential equations in Julia
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FEs in the physical space #200

Closed santiagobadia closed 4 years ago

santiagobadia commented 4 years ago

I want to create a new kind of FESpace that does not rely on a ReferenceFE but transforms the prebasis into the FE basis by making use of DOFs defined in the physical space.

It seems that we must re-think the function compute_cell_space in https://github.com/gridap/Gridap.jl/blob/10b35b22d20f5091eee0f0c95bf59fba0a0de51f/src/FESpaces/ConformingFESpaces.jl#L87-L97

and more specifically the part related to dof_basis, which should be combined with cell_map

fverdugo commented 4 years ago

Just to complement your post. It is not needed to create a new FESpace struct. It is only needed to create a new constructor function that eventually creates a UnconstrainedFESpace object as it is done in GradConformingFESpace and DivConformingFESpace.

santiagobadia commented 4 years ago

Hi @fverdugo

I have been thinking how to implement FEs in the physical space, and create a simple code with what I think we must implement here.

I think that we need a new type of array of shape functions that will involve the computation of the change of basis per cell. We cannot use BasisFromChangeOfBasis anymore. I have just wrote in this file the steps needed to compute such change of basis function at every cell.

I was wondering which is the best way to implement this new CellBasis object, probably called CellBasisFromChangeOfBasis, probably using as much as possible existing code and structs we already have in Gridap. Another important issue is efficiency, so I think this CellBasis should be iterable, certainly making use of a cache array, etc.

If you have some time, and you want to tell me what you think should be the best way to implement it, it would be perfect. In any case, I will think about it.

fverdugo commented 4 years ago

I am not sure if I understand 100% correctly. Your inputs are the arrays cell_prebasis and cell_dof_basis, right?.

cell_matrix = evaluate_dof_array(cell_dof_basis,cell_prebasis)
cell_matrix_inv = apply(inv,cell_matrix)

Then, you want to apply all the change of bases in cell_matrix_inv cell-wise to all the entries in cell_prebasis.

If you are not worried about performance, this can be done as

cell_shapefuns = apply(change_basis,cell_prebasis,cell_matrix_inv)

If you are worried about performance, instead of applying inv and change_basis you need to define two new kernels that better handles the caches.

santiagobadia commented 4 years ago

I'm trying to do what you propose, but there is an error in https://github.com/gridap/Gridap.jl/blob/a826fc8c4f3cc70cf5956431a1c6b6413adbbdc4/test/FESpacesTests/PhysicalBasesTests.jl#L51 related to the zero method for the cell_prebasis type argument.

fverdugo commented 4 years ago

I have to take a look into this, but it shouldn't be very difficult to fix.

fverdugo commented 4 years ago

I have fixed this and pushed to the physical-fes branch.

santiagobadia commented 4 years ago

Hi @fverdugo Can you help me with this error https://github.com/gridap/Gridap.jl/blob/152df55e4ee378827d053e11d315eff4e2f2dee2/test/FESpacesTests/PhysicalBasesTests.jl#L72-L76 I cannot evaluate the gradient in an array of points. I am trying to understand where do I need to implement the gradient method, but the stack is pretty deep and complicated. Any insight that could help me here?

Btw, I have been playing with the Juno debugger, which I think starts to be needed to navigate through the code.

fverdugo commented 4 years ago

Is this the error you get??

julia> include("test/FESpacesTests/PhysicalBasesTests.jl")
ERROR: LoadError: type Array has no field value
Stacktrace:
 [1] getproperty(::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}, ::Symbol) at ./Base.jl:20
 [2] (::Gridap.Arrays.var"#21#22"{Array{Int8,1},Int64})(::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at ./none:0
 [3] iterate(::Base.Generator{FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}},Gridap.Arrays.var"#21#22"{Array{Int8,1},Int64}}) at ./generator.jl:47
 [4] top-level scope at /home/fverdugo/Code/jl/Gridap.jl/test/FESpacesTests/PhysicalBasesTests.jl:70
 [5] include at ./boot.jl:328 [inlined]
 [6] include_relative(::Module, ::String) at ./loading.jl:1105
 [7] include(::Module, ::String) at ./Base.jl:31
 [8] include(::String) at ./client.jl:424
 [9] top-level scope at REPL[2]:1
in expression starting at /home/fverdugo/Code/jl/Gridap.jl/test/FESpacesTests/PhysicalBasesTests.jl:70
santiagobadia commented 4 years ago

No the error is

julia> include("test/FESpacesTests/PhysicalBasesTests.jl")
ERROR: LoadError: This function belongs to an interface definition and cannot be used.
Stacktrace:
 [1] macro expansion at /home/santiago/github-repos/Gridap/Gridap.jl/src/Helpers/Macros.jl:9 [inlined]
 [2] gradient_cache(::Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}}, ::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldInterface.jl:161
 [3] gradient_cache(::Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}, ::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Polynomials/ChangeBasis.jl:63
 [4] field_cache at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldInterface.jl:126 [inlined]
 [5] evaluate_field(::Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}}, ::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldInterface.jl:293
 [6] field_return_type(::Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}}, ::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldInterface.jl:102
 [7] kernel_return_type(::Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}}, ::Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldInterface.jl:181
 [8] Gridap.Arrays.AppliedArray(::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Arrays/Apply.jl:176
 [9] apply(::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Arrays/Apply.jl:105
 [10] _evaluate_field_array(::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:36
 [11] kernel_evaluate(::Gridap.Fields.Grad, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}, ::Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:99
 [12] evaluate_field_array(::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:79
 [13] _evaluate_field_arrays(::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}, ::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Gridap.Fields.AffineMapGrad{1,Float64,1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:51
 [14] evaluate_field_arrays(::Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}},FillArrays.Fill{Gridap.Fields.AffineMapGrad{1,Float64,1},1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:47
 [15] kernel_evaluate(::Gridap.Fields.Valued{Gridap.Fields.PhysGrad}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}, ::Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Gridap.Fields.AffineMapGrad{1,Float64,1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:274
 [16] evaluate_field_array(::Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.PhysGrad,Tuple{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},Gridap.Fields.AffineMapGrad{1,Float64,1}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}},FillArrays.Fill{Gridap.Fields.AffineMapGrad{1,Float64,1},1,Tuple{Base.OneTo{Int64}}}},FillArrays.Fill{Gridap.Fields.Valued{Gridap.Fields.PhysGrad},1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:79
 [17] evaluate(::Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.PhysGrad,Tuple{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},Gridap.Fields.AffineMapGrad{1,Float64,1}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.FieldGrad{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Polynomials.BasisFromChangeOfBasis{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},Array{Float64,2}},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}},Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Array{Float64,2},1,Tuple{Gridap.Arrays.AppliedArray{Gridap.Fields.AppliedField{Gridap.Fields.MapGrad,Tuple{MonomialBasis{1,Float64},AffineMap{1,Float64,1}}},1,Tuple{CompressedArray{MonomialBasis{1,Float64},1,Array{MonomialBasis{1,Float64},1},Array{Int8,1}},Gridap.Geometry.CartesianMap{1,Float64,1}},FillArrays.Fill{Gridap.Fields.AddMap,1,Tuple{Base.OneTo{Int64}}}}},CompressedArray{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1,Array{LagrangianDofBasis{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},Int64},1},Array{Int8,1}}}},FillArrays.Fill{typeof(inv),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{typeof(change_basis),1,Tuple{Base.OneTo{Int64}}}}},FillArrays.Fill{Gridap.Fields.Grad,1,Tuple{Base.OneTo{Int64}}}},FillArrays.Fill{Gridap.Fields.AffineMapGrad{1,Float64,1},1,Tuple{Base.OneTo{Int64}}}},FillArrays.Fill{Gridap.Fields.Valued{Gridap.Fields.PhysGrad},1,Tuple{Base.OneTo{Int64}}}}, ::FillArrays.Fill{Array{Gridap.TensorValues.MultiValue{Tuple{1},Float64,1,1},1},1,Tuple{Base.OneTo{Int64}}}) at /home/santiago/github-repos/Gridap/Gridap.jl/src/Fields/FieldArrays.jl:72
 [18] top-level scope at /home/santiago/github-repos/Gridap/Gridap.jl/test/FESpacesTests/PhysicalBasesTests.jl:75
 [19] include at ./boot.jl:328 [inlined]
 [20] include_relative(::Module, ::String) at ./loading.jl:1094
 [21] include(::Module, ::String) at ./Base.jl:31
 [22] include(::String) at ./client.jl:431
 [23] top-level scope at none:0
in expression starting at /home/santiago/github-repos/Gridap/Gridap.jl/test/FESpacesTests/PhysicalBasesTests.jl:75

I have pushed my last version just in case I left some unintended thing.

fverdugo commented 4 years ago

I copy here the sketch of how to create lagrangian interpolations in the physical space


# Physical cell dof basis
reffes = [LagrangianRefFE(T,p,order) for p in polytopes]
ctype_to_refnodes= map(get_node_coordinates,reffes)
cell_to_refnodes = CompressedArray(ctype_to_refnodes,cell_to_ctype)
cell_physnodes = evaluate(cell_map,cell_to_refnodes)
cell_dof_basis = apply( nodes -> LagrangianDofBasis(T,nodes), cell_physnodes )

# Prebasis

## I think we don't want to attach the cell_map since the distance between
## the nodes at the physical space will already lead to the correct
## gradient wrt the physical coordinate
ctype_to_prebasis= map(get_prebasis,reffes)
cell_prebasis = CompressedArray(ctype_to_prebasis,cell_to_ctype)

# Shape functions (evaluable at physical space)
cell_matrix = evaluate_dof_array(cell_dof_basis,cell_prebasis)
cell_matrix_inv = apply(inv,cell_matrix)
cell_physshapefuns = apply(change_basis,cell_prebasis,cell_matrix_inv)

# Shape functions (evaluable at reference space in order to use standard quadratures)
cell_physshapefuns_evaluable_at_refgp = compose(cell_physshapefuns,cell_map)
santiagobadia commented 4 years ago

Hi @fverdugo

The creation of a FE Space part for DOFs in the physical space is working.

The problem now is 

function interpolate(fs::SingleFieldFESpace,object)
  cell_map = get_cell_map(fs)
  cell_field = convert_to_cell_field(object,cell_map)
  # Here we have a problem because the nodes are in the physical space!!!
  free_values = compute_free_values(fs,cell_field)
  FEFunction(fs,free_values)
end

Do you have an easy CellField constructor that takes a function as argument, without a cell_map?

I think we need a new CellField concrete struct that takes a function in its constructor, infers the result type for a Point and checks that it is a Field, and implements all the required methods of a CellFieldLike.

Another option would be to create a mock CellMap that would represent the identity. The problem is that it is assumed in the code that a CellField must have a method that provides a CellMap.

santiagobadia commented 4 years ago

I have already solved the previous issue by generating new interpolation methods

fverdugo commented 4 years ago

The problem is that So far we assume that cell fields are evaluated at the reference space, good for integrating them, but this does not work for interpolation in general as you have noticed when trying to interpolate...

Perhaps we can circunvent the problem with new interpolation methods, but not sure if it will work always...eg with zero mean fe spaces, restricted fe spaces etc.

We need to discuss this face to face since it is not an obvious topic.

santiagobadia commented 4 years ago

Hi @fverdugo

You can check what I have done by comparing branches.

As you will see, I have created a FunctionField that I have used in the interpolation methods in the physical space. See https://github.com/gridap/Gridap.jl/blob/51eda45e59d541ec889d97cff8108f32aed990ac/src/FESpaces/SingleFieldFESpaces.jl#L218

I have also included the dofspace argument in the FE space factories.

I think that it is still missing

What else?

fverdugo commented 4 years ago

closed via PR #216 and PR #218