Solver

Solving requires a spatial and stochastic discretization. Both are connected in a special vector structure that is passed to a solve function that runs a special iterative solver for each model problem.

SGFEVector

The spatial discretization is represented by s single finite element space from ExtendableFEM.jl, while the stochastic discretization is represented by a tensorized basis for the parameter space of the stochastic coefficient. Both have to be prepared in advance.

Note

Currently it is not possible to use different finite element spaces for different multi-indices, but this feature might be added in the future.

ExtendableASGFEM.SGFEVector — Type

struct SGFEVector{T, Tv, Ti, ONBType<:ONBasis, MIType}

structure that builds upon ExtendableFEMBase.FEVector and adds information on the stochastic discretization, i.e. the used TensoriedBasis

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ExtendableASGFEM.SGFEVector — Method

SGFEVector(
    FES::Array{<:ExtendableFEMBase.FESpace{Tv, Ti}, 1},
    TB::TensorizedBasis{Tv, ONBType, MIType};
    active_modes,
    T,
    unames
) -> SGFEVector

constructs an SGFEVector for the given (spatial) finite element space FES and the (tensorized basis of the stochastic discretization) TB.

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Base.getindex — Method

getindex(
    SGFEV::SGFEVector,
    u::Int64,
    i::Int64
) -> ExtendableFEMBase.FEVectorBlock

returns the FEVectorBlock for the i-th stochastic mode of the u-th unknown

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Base.getindex — Method

getindex(
    SGFEV::SGFEVector,
    i::Int64
) -> ExtendableFEMBase.FEVectorBlock

returns the i-th stochastic mode

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Base.length — Method

length(SGFEV::SGFEVector) -> Int64

returns the length of the full vector, i.e., the total number of degrees of freedom

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Base.show — Method

show(io::IO, SGFEV::SGFEVector)

Custom show function for FEVector that prints some information on its blocks.

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Base.size — Method

size(SGFEV::SGFEVector)

returns a tuple with the number of active stochastic modes and the number of spatial degrees of freedom

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ExtendableASGFEM.fetypes — Method

fetypes(SGFEV::SGFEVector) -> Vector

returns the finite element types of the (spatial) FE spaces

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ExtendableASGFEM.num_multiindices — Method

num_multiindices(SGFEV::SGFEVector) -> Int64

returns the number of active modes (that are used from the stored tensorized basis)

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ExtendableASGFEM.set_sample! — Method

set_sample!(SGFEV::SGFEVector, S::AbstractVector)

evaluates the SGVector at that sample and stores the results in SGFEV.FEV.

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Solve function

ExtendableASGFEM.solve! — Method

solve!(
    ::Type{ExtendableASGFEM.AbstractModelProblem},
    sol::SGFEVector,
    C::AbstractStochasticCoefficient;
    rhs,
    use_iterative_solver,
    bonus_quadorder_f,
    bonus_quadorder_a,
    kwargs...
)

solves the specified model problem with the given stochastic coefficient C and right-hand side rhs and writes the solution into sol. Via this sol vector the spatial and stochastic discretization is communicated as well as initial data for the iterative solver. The boolean use_iterative_solver (default is true) determines if the iterative solver is used or if the full matrix is assembled and solved by a direct solver (very slow for larger systems). The parameters bonus_quadorder_f (default is 0) and bonus_quadorder_a (default is 2) can be used to increase the quadrature order in terms that involve the rhs or the stochastic coefficient, respectively.

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