GridapROMs.ParamFESpaces

module ParamFESpaces

Parametric FE spaces and FE functions for multi-sample parameter studies.

Wraps Gridap's FESpace layer so that every DOF array can hold a full batch of parameter samples simultaneously. The module provides:

• SingleFieldParamFESpace — a single-field FE space whose free-value and Dirichlet-value arrays are ParamArrays (one block per parameter sample).
• MultiFieldParamFESpace — multi-field counterpart, holding a vector of SingleFieldParamFESpaces and forwarding the Gridap MultiFieldFESpace interface.
• TrivialParamFESpace — wraps a plain Gridap FESpace as a trivially parametric space (same DOF values for every parameter sample).
• TrialParamFESpace / HomogeneousTrialParamFESpace — trial spaces with parameter-dependent Dirichlet boundary conditions; TrialParamFESpace! mutates an existing space in-place.
• UnEvalTrialFESpace / ParamTrialFESpace — lazy (unevaluated) trial FE spaces that instantiate Dirichlet values only when a Realisation is supplied.
• ParamFEFunction (SingleFieldParamFEFunction, MultiFieldParamFEFunction) — Gridap FEFunction carrying a ParamArray of free DOF values.
• Assemblers — ParamAssemblers.jl extends Gridap's SparseMatrixAssembler to fill parametric matrices and vectors in a single assembly pass.

The AgFEM tools from GridapEmbedded are available for aggregated FE spaces on cut meshes; see Extensions for the full embedded FEM machinery.

struct MultiFieldParamFEFunction{T<:MultiFieldCellField} <: ParamFEFunction
  single_fe_functions::Vector{<:SingleFieldParamFEFunction}
  free_values::AbstractArray
  fe_space::MultiFieldFESpace
  multi_cell_field::T
end

const MultiFieldParamFESpace = MultiFieldFESpace

abstract type ParamFEFunction <: FEFunction end

Parametric extension of a FEFunction in Gridap. Subtypes:

• SingleFieldParamFEFunction
• MultiFieldParamFEFunction

const ParamTrialFESpace = UnEvalTrialFESpace

struct SingleFieldParamFEFunction{T<:CellField} <: ParamFEFunction
  cell_field::T
  cell_dof_values::AbstractArray{<:ParamBlock}
  free_values::AbstractParamVector{<:Number}
  dirichlet_values::AbstractParamVector{<:Number}
  fe_space::SingleFieldFESpace
end

abstract type SingleFieldParamFESpace{S} <: SingleFieldFESpace end

Parametric extension of a SingleFieldFESpace in Gridap. The FE spaces inhereting are (trial) spaces on which we can easily define a ParamFEFunction.

Subtypes:

• TrivialParamFESpace
• TrialParamFESpace

TrialParamFESpace{S} <: SingleFieldParamFESpace{S}

Trial FE space equipped with parametric dirichlet values

TrivialParamFESpace{S} <: SingleFieldParamFESpace{S}

Wrapper for non-parametric FE spaces that we wish assumed a parametric length

struct UnEvalTrialFESpace{A,B} <: SingleFieldFESpace
  space::A
  space0::B
  dirichlet::Union{Function,AbstractVector{<:Function}}
end

Struct representing trial FE spaces that are not evaluated yet. This may include FE spaces representing transient problems (although the implementation in Gridap, called TransientTrialFESpace, does not fall into this category), parametric problems, and transient-parametric problems.

parameterise(a::SparseMatrixAssembler,plength::Int) -> SparseMatrixAssembler

Returns an assembler that also stores the parametric length of r. This function is to be used to assemble parametric residuals and Jacobians. The assembly routines follow the same pipeline as in Gridap

HomogeneousTrialParamFESpace(U::SingleFieldFESpace,plength::Int) -> TrialParamFESpace

Returns a TrialParamFESpace equipped with homogeneous parametric dirichlet values

TrialParamFESpace!(dir_values::AbstractParamVector,space::SingleFieldFESpace,objects
  ) -> TrialParamFESpace

Allows do-block syntax for the construction of a TrialParamFESpace

get_vector_type2(f::SingleFieldParamFESpace) -> Type

Returns the vector type of the underlying un-parametric FESpace contained in f

param_zero_dirichlet_values(f::FESpace,L::Integer=param_length(f)) -> AbstractParamVector

Parametric version of the function zero_dirichlet_values in Gridap

param_zero_free_values(f::FESpace,L::Integer=param_length(f)) -> AbstractParamVector

Parametric version of the function zero_free_values in Gridap