diff --git a/Manifest.toml b/Manifest.toml
index e5c90b75..12672e0e 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -148,7 +148,7 @@ version = "0.10.20"
 
 [[Gridap]]
 deps = ["AbstractTrees", "BSON", "BlockArrays", "Combinatorics", "DocStringExtensions", "FastGaussQuadrature", "FileIO", "FillArrays", "ForwardDiff", "JLD2", "JSON", "LineSearches", "LinearAlgebra", "NLsolve", "NearestNeighbors", "QuadGK", "Random", "SparseArrays", "SparseMatricesCSR", "StaticArrays", "Test", "WriteVTK"]
-git-tree-sha1 = "c58a6aade499e243bddc152f6acdc17d45886a94"
+git-tree-sha1 = "192cb4f55c2eeefcd7e39dd208a58e46fc9840a5"
 repo-rev = "gridap_distributed"
 repo-url = "https://github.com/gridap/Gridap.jl.git"
 uuid = "56d4f2e9-7ea1-5844-9cf6-b9c51ca7ce8e"
@@ -340,8 +340,8 @@ uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
 version = "2.0.5"
 
 [[PartitionedArrays]]
-deps = ["IterativeSolvers", "LinearAlgebra", "MPI", "Printf", "SparseArrays", "SparseMatricesCSR"]
-git-tree-sha1 = "38a986dc7298d3d2a8e993c7db7944132c757415"
+deps = ["Distances", "IterativeSolvers", "LinearAlgebra", "MPI", "Printf", "SparseArrays", "SparseMatricesCSR"]
+git-tree-sha1 = "763146e768b343fec44c521f5c7822116adc24ad"
 repo-rev = "gridap_distributed"
 repo-url = "https://github.com/fverdugo/PartitionedArrays.jl.git"
 uuid = "5a9dfac6-5c52-46f7-8278-5e2210713be9"
diff --git a/src/Algebra.jl b/src/Algebra.jl
index 8d1a3537..4e4a2b06 100644
--- a/src/Algebra.jl
+++ b/src/Algebra.jl
@@ -1,8 +1,28 @@
 
-function local_views(a::AbstractVector)
+function Algebra.fill_entries!(a::PVector,v::Number)
+  fill!(a,v)
+  a
+end
+
+function Algebra.fill_entries!(a::PSparseMatrix,v::Number)
+  map_parts(a.values) do values
+    fill_entries!(values,v)
+  end
+  a
+end
+
+function local_views(a)
   @abstractmethod
 end
 
+function local_views(a::AbstractVector,rows)
+  @notimplemented
+end
+
+function local_views(a::AbstractMatrix,rows,cols)
+  @notimplemented
+end
+
 function consistent_local_views(a,ids,isconsistent)
   @abstractmethod
 end
@@ -11,12 +31,24 @@ function local_views(a::AbstractPData)
   a
 end
 
+function local_views(a::PRange)
+  a.partition
+end
+
 function local_views(a::PVector)
   a.values
 end
 
-function local_views(a::PRange)
-  a.partition
+function local_views(a::PVector,rows::PRange)
+  PArrays.local_view(a,rows)
+end
+
+function local_views(a::PSparseMatrix)
+  a.values
+end
+
+function local_views(a::PSparseMatrix,rows::PRange,cols::PRange)
+  PArrays.local_view(a,rows,cols)
 end
 
 function change_ghost(a::PVector,ids_fespace::PRange)
@@ -45,10 +77,6 @@ function Algebra.allocate_vector(::Type{<:PVector{T,A}},ids::PRange) where {T,A}
   PVector(values,ids)
 end
 
-function local_views(a::PSparseMatrix)
-  a.values
-end
-
 struct FullyAssembledRows end
 struct SubAssembledRows end
 
@@ -94,6 +122,12 @@ function local_views(a::DistributedCounterCOO)
   a.counters
 end
 
+function local_views(a::DistributedCounterCOO,rows,cols)
+  @check rows === a.rows
+  @check cols === a.cols
+  a.counters
+end
+
 function Algebra.nz_allocation(a::DistributedCounterCOO)
   allocs = map_parts(nz_allocation,a.counters)
   DistributedAllocationCOO(a.par_strategy,allocs,a.rows,a.cols)
@@ -121,6 +155,12 @@ function local_views(a::DistributedAllocationCOO)
   a.allocs
 end
 
+function local_views(a::DistributedAllocationCOO,rows,cols)
+  @check rows === a.rows
+  @check cols === a.cols
+  a.allocs
+end
+
 function first_gdof_from_ids(ids)
   num_oids(ids)>0 ? Int(ids.lid_to_gid[ids.oid_to_lid[1]]) : 1
 end
@@ -132,6 +172,13 @@ function find_gid_and_part(hid_to_hdof,dofs)
   hid_to_gid, hid_to_part
 end
 
+function Algebra.create_from_nz(a::PSparseMatrix)
+  # For FullyAssembledRows the underlying Exchanger should
+  # not have ghost layer making assemble! do nothing (TODO check)
+  assemble!(a)
+  a
+end
+
 function Algebra.create_from_nz(a::DistributedAllocationCOO{<:FullyAssembledRows})
   f(x) = nothing
   A, = _fa_create_from_nz_with_callback(f,a)
@@ -292,17 +339,11 @@ function _sa_create_from_nz_with_callback(callback,async_callback,a)
     map_parts(wait,t2)
   end
 
-  # Build the matrix exchanger
-  # TODO for the moment, we build an empty exchanger
-  # (fine for problem that do not need to update the matrix)
-  exchanger = empty_exchanger(parts)
-
-  # TODO building a non-empty exchanger
-  # can be costly and not always needed
-  # add a more lazy initzialization of this inside PSparseMatrix
-
   # Finally build the matrix
-  A = PSparseMatrix(values,rows,cols,exchanger)
+  # A matrix exchanger will be created under the hood.
+  # Building a exchanger can be costly and not always needed.
+  # TODO add a more lazy initzialization of this inside PSparseMatrix
+  A = PSparseMatrix(values,rows,cols)
 
   A, callback_output
 end
@@ -334,6 +375,11 @@ function local_views(a::PVectorCounter)
   a.counters
 end
 
+function local_views(a::PVectorCounter,rows)
+  @check rows === a.rows
+  a.counters
+end
+
 function Arrays.nz_allocation(a::PVectorCounter)
   dofs = a.rows
   values = map_parts(nz_allocation,a.counters)
@@ -350,11 +396,16 @@ function local_views(a::PVectorAllocation)
   a.values
 end
 
-function Algebra.create_from_nz(a::PVector{<:FullyAssembledRows})
+function local_views(a::PVectorAllocation,rows)
+  @check rows === a.rows
+  a.values
+end
+
+function Algebra.create_from_nz(a::PVectorAllocation{<:FullyAssembledRows})
   @notimplemented
 end
 
-function Algebra.create_from_nz(a::PVector{<:SubAssembledRows})
+function Algebra.create_from_nz(a::PVectorAllocation{<:SubAssembledRows})
   @notimplemented
 end
 
@@ -389,6 +440,13 @@ function _rhs_callback(c_fespace,rows)
   return b
 end
 
+function Algebra.create_from_nz(a::PVector)
+  # For FullyAssembledRows the underlying Exchanger should
+  # not have ghost layer making asseble! do nothing (TODO check)
+  assemble!(a)
+  a
+end
+
 function Algebra.create_from_nz(
   a::DistributedAllocationCOO{<:FullyAssembledRows},
   c_fespace::PVectorAllocation{<:FullyAssembledRows})
diff --git a/src/CellData.jl b/src/CellData.jl
index a1b4794f..09d93469 100644
--- a/src/CellData.jl
+++ b/src/CellData.jl
@@ -117,12 +117,12 @@ end
 # Composition
 
 Base.:(∘)(f::Function,g::DistributedCellField) = Operation(f)(g)
-Base.:(∘)(f::Function,g::DistributedCellField,b::DistributedCellField) = Operation(f)(g,b)
-Base.:(∘)(f::Function,g::DistributedCellField,b::Number) = Operation(f)(g,b)
-Base.:(∘)(f::Function,g::Number,b::DistributedCellField) = Operation(f)(g,b)
-Base.:(∘)(f::Function,g::DistributedCellField,b::Function) = Operation(f)(g,b)
-Base.:(∘)(f::Function,g::Function,b::DistributedCellField) = Operation(f)(g,b)
-Base.:(∘)(f::Function,g::DistributedCellField...) = Operation(f)(g...)
+Base.:(∘)(f::Function,g::Tuple{DistributedCellField,DistributedCellField}) = Operation(f)(g[1],g[2])
+Base.:(∘)(f::Function,g::Tuple{DistributedCellField,Number}) = Operation(f)(g[1],g[2])
+Base.:(∘)(f::Function,g::Tuple{Number,DistributedCellField}) = Operation(f)(g[1],g[2])
+Base.:(∘)(f::Function,g::Tuple{DistributedCellField,Function}) = Operation(f)(g[1],g[2])
+Base.:(∘)(f::Function,g::Tuple{Function,DistributedCellField}) = Operation(f)(g[1],g[2])
+Base.:(∘)(f::Function,g::Tuple{Vararg{DistributedCellField}}) = Operation(f)(g...)
 
 # Define some of the well known arithmetic ops
 
diff --git a/src/FESpaces.jl b/src/FESpaces.jl
index 2750544e..d62f72a4 100644
--- a/src/FESpaces.jl
+++ b/src/FESpaces.jl
@@ -382,27 +382,27 @@ FESpaces.get_vector_builder(a::DistributedSparseMatrixAssembler) = a.vector_buil
 FESpaces.get_assembly_strategy(a::DistributedSparseMatrixAssembler) = a.strategy
 
 function FESpaces.symbolic_loop_matrix!(A,a::DistributedSparseMatrixAssembler,matdata)
-  map_parts(symbolic_loop_matrix!,local_views(A),a.assems,matdata)
+  map_parts(symbolic_loop_matrix!,local_views(A,a.rows,a.cols),a.assems,matdata)
 end
 
 function FESpaces.numeric_loop_matrix!(A,a::DistributedSparseMatrixAssembler,matdata)
-  map_parts(numeric_loop_matrix!,local_views(A),a.assems,matdata)
+  map_parts(numeric_loop_matrix!,local_views(A,a.rows,a.cols),a.assems,matdata)
 end
 
 function FESpaces.symbolic_loop_vector!(b,a::DistributedSparseMatrixAssembler,vecdata)
-  map_parts(symbolic_loop_vector!,local_views(b),a.assems,vecdata)
+  map_parts(symbolic_loop_vector!,local_views(b,a.rows),a.assems,vecdata)
 end
 
 function FESpaces.numeric_loop_vector!(b,a::DistributedSparseMatrixAssembler,vecdata)
-  map_parts(numeric_loop_vector!,local_views(b),a.assems,vecdata)
+  map_parts(numeric_loop_vector!,local_views(b,a.rows),a.assems,vecdata)
 end
 
 function FESpaces.symbolic_loop_matrix_and_vector!(A,b,a::DistributedSparseMatrixAssembler,data)
-  map_parts(symbolic_loop_matrix_and_vector!,local_views(A),local_views(b),a.assems,data)
+  map_parts(symbolic_loop_matrix_and_vector!,local_views(A,a.rows,a.cols),local_views(b,a.rows),a.assems,data)
 end
 
 function FESpaces.numeric_loop_matrix_and_vector!(A,b,a::DistributedSparseMatrixAssembler,data)
-  map_parts(numeric_loop_matrix_and_vector!,local_views(A),local_views(b),a.assems,data)
+  map_parts(numeric_loop_matrix_and_vector!,local_views(A,a.rows,a.cols),local_views(b,a.rows),a.assems,data)
 end
 
 # Parallel Assembly strategies
diff --git a/src/Geometry.jl b/src/Geometry.jl
index 5f560bc2..a645475d 100644
--- a/src/Geometry.jl
+++ b/src/Geometry.jl
@@ -222,6 +222,22 @@ function filter_cells_when_needed(
   remove_ghost_cells(trian,cell_gids)
 end
 
+function filter_cells_when_needed(
+  portion::FullyAssembledRows,
+  cell_gids::AbstractIndexSet,
+  trian::Triangulation)
+
+  trian
+end
+
+function filter_cells_when_needed(
+  portion::SubAssembledRows,
+  cell_gids::AbstractIndexSet,
+  trian::Triangulation)
+
+  remove_ghost_cells(trian,cell_gids)
+end
+
 # For the moment remove_ghost_cells
 # refers to the triangulation faces
 # pointing into the ghost cells
diff --git a/test/PLaplacianTests.jl b/test/PLaplacianTests.jl
new file mode 100644
index 00000000..b53d3094
--- /dev/null
+++ b/test/PLaplacianTests.jl
@@ -0,0 +1,60 @@
+module PLaplacianTests
+
+using Gridap
+using Gridap.Algebra
+using GridapDistributed
+using PartitionedArrays
+using Test
+
+function main(parts)
+  main(parts,FullyAssembledRows())
+  main(parts,SubAssembledRows())
+end
+
+function main(parts,strategy)
+
+  output = mkpath(joinpath(@__DIR__,"output"))
+
+  domain = (0,4,0,4)
+  cells = (4,4)
+  model = CartesianDiscreteModel(parts,domain,cells)
+
+  k = 1
+  u((x,y)) = (x+y)^k
+  σ(∇u) =(1.0+∇u⋅∇u)*∇u
+  dσ(∇du,∇u) = 2*∇u⋅∇du + (1.0+∇u⋅∇u)*∇du
+  f(x) = -divergence(y->σ(∇(u,y)),x)
+
+  Ω = Triangulation(strategy,model)
+  dΩ = Measure(Ω,2*k)
+  r(u,v) = ∫( ∇(v)⋅(σ∘∇(u)) - v*f )dΩ
+  j(u,du,v) = ∫( ∇(v)⋅(dσ∘(∇(du),∇(u))) )dΩ
+
+  reffe = ReferenceFE(lagrangian,Float64,k)
+  V = TestFESpace(model,reffe,dirichlet_tags="boundary")
+  U = TrialFESpace(u,V)
+
+  op = FEOperator(r,j,U,V,strategy)
+
+  uh = zero(U)
+  b,A = residual_and_jacobian(op,uh)
+  _A = copy(A)
+  _b = copy(b)
+  residual_and_jacobian!(_b,_A,op,uh)
+  @test (norm(_b-b)+1) ≈ 1
+  x = similar(b,Float64,axes(A,2))
+  fill!(x,1)
+  @test (norm(A*x-_A*x)+1) ≈ 1
+
+  nls = NLSolver(show_trace=i_am_main(parts), method=:newton)
+  solver = FESolver(nls)
+  uh = solve(solver,op)
+
+  Ωo = Triangulation(model)
+  dΩo = Measure(Ωo,2*k)
+  eh = u - uh
+  @test sqrt(sum(∫( abs2(eh) )dΩo)) < 1.0e-9
+
+end
+
+end # module
diff --git a/test/sequential/PLaplacianTests.jl b/test/sequential/PLaplacianTests.jl
new file mode 100644
index 00000000..ced09577
--- /dev/null
+++ b/test/sequential/PLaplacianTests.jl
@@ -0,0 +1,10 @@
+module PLaplacianTestsSeq
+
+using PartitionedArrays
+
+include("../PLaplacianTests.jl")
+
+parts = get_part_ids(sequential,(2,2))
+PLaplacianTests.main(parts)
+
+end # module
diff --git a/test/sequential/runtests.jl b/test/sequential/runtests.jl
index 884430d7..3ab25b6c 100644
--- a/test/sequential/runtests.jl
+++ b/test/sequential/runtests.jl
@@ -12,4 +12,6 @@ using Test
 
 @time @testset "Poisson" begin include("PoissonTests.jl") end
 
+@time @testset "PLaplacian" begin include("PLaplacianTests.jl") end
+
 end # module