Solving Linear problems

[shreyas02]

Hi all,

While using the AffineFEoperator, why doesn't something like the following work in parallel?

u, p = solve(solver,op)

Why is the extraction of matrices required?

[JordiManyer]

The vector solution is allocated using get_zero_dof_values, which returns arrays with the dof layout of the FESpace. The solver requires the dof layout of the matrix columns. In serial, these are the same (just arrays of the same size). In parallel, it is most often not the case.

[shreyas02]

Does this issue prevail while working with linear Transient problems? I have also noticed that the index partition differs in the allocated solution vector in the solve function. Is there a fix for this, especially for transient problems?

[shreyas02]

So, as a makeshift solution (especially for transient problems), I am doing something like this.

# BlockLinearSolve setup 

struct BlockLinearSolve <: LinearSolver
    ls::LinearSolver
end

struct BlockLinearSolveSymbolicSetup <: SymbolicSetup
    ls::BlockLinearSolve
    ss::SymbolicSetup
end

mutable struct BlockLinearSolveNumericalSetup{T<:AbstractMatrix} <: NumericalSetup
    ss::BlockLinearSolveSymbolicSetup
    A::T
    ns::NumericalSetup
    x_new::AbstractVector
end

function Gridap.Algebra.symbolic_setup(ls::BlockLinearSolve, mat::AbstractMatrix) 
    BlockLinearSolveSymbolicSetup(ls,Gridap.Algebra.symbolic_setup(ls.ls,mat))
end

function Gridap.Algebra.numerical_setup(ss::BlockLinearSolveSymbolicSetup,A::AbstractMatrix) 
    x_new = allocate_in_domain(A); fill!(x_new,0.0)
    BlockLinearSolveNumericalSetup(ss,A,Gridap.Algebra.numerical_setup(ss.ss,A),x_new)
end

function Gridap.Algebra.numerical_setup!(ns::BlockLinearSolveNumericalSetup,A::AbstractMatrix)
    ns.A = A
    Gridap.Algebra.numerical_setup!(ns.ns,A)
end

function Gridap.Algebra.solve!(x::AbstractVector,ns::BlockLinearSolveNumericalSetup,b::AbstractVector)
    solve!(ns.x_new,ns.ns,b)
    copy!(x, ns.x_new)
end

Is there any better way to do this to avoid the extra allocation ( x_new)? I am talking in the context of transient problems where extracting the matrix is not an option.

[JordiManyer]

Does this issue prevail while working with linear Transient problems?

So:

• First, this is not an issue. It's simply how parallel works. Depending on the integrals, the assembled matrix may contain columns that do not correspond to local dofs. This is always like this, for any assembled system of equations. This includes transient.

• The only way to circumvent this would be to use sub-assembled matrices. It comes at the cost of more communications when doing a sparse mat-vec multiply operation. This is not yet supported, although I am working on it. I am however quite busy.

[shreyas02]

Thanks for this update @JordiManyer. I'll use the makeshift solution for now and look at sub-assembled matrices later.

Also, until sub-assembled matrices are supported, we could add this piece of code to gridap solvers so that others could use block preconditioners on transient problems. As I see now, there is no direct way to use block preconditioners for transient linear problems.