Efficient assembly of L2 Mass Matrix and its inverse using Gridap/GridapGeoScience Tools

assemble_L2MM_invL2MM.jl

using Gridap
using GridapGeosciences

order=1
degree=4

model = CubedSphereDiscreteModel(1; radius=rₑ)


# Forward integration of the shallow water equations
Ω = Triangulation(model)
dΩ = Measure(Ω, degree)
dω = Measure(Ω, degree, ReferenceDomain())

reffe_lgn = ReferenceFE(lagrangian, Float64, order)
Q = FESpace(model, reffe_lgn; conformity=:L2)
P = TrialFESpace(Q)

function assemble_L2MM_invL2MM(U,V,dΩ)
  a(a,b) = ∫(a⋅b)dΩ
  v = get_fe_basis(V)
  u = get_trial_fe_basis(U)
  assemblytuple    = Gridap.FESpaces.collect_cell_matrix(U,V,a(u,v))
  cell_matrix_MM   = collect(assemblytuple[1][1]) # This result is no longer a LazyArray
  newassemblytuple = ([cell_matrix_MM],assemblytuple[2],assemblytuple[3])
  a=SparseMatrixAssembler(U,V)
  L2MM=assemble_matrix(a,newassemblytuple)
  for i in eachindex(cell_matrix_MM)
     cell_matrix_MM[i]=inv(cell_matrix_MM[i])
  end
  invL2MM=similar(L2MM)
  Gridap.FESpaces.assemble_matrix!(invL2MM, a, newassemblytuple)
  L2MM, invL2MM
end

A,B=assemble_L2MM_invL2MM(P,Q,dΩ)
println(A*B)