GridapROMs.ParamAlgebra

module ParamAlgebra

Algebraic infrastructure for parametric operators and solvers.

• NonlinearParamOperator — abstract parametric nonlinear operator; residual and Jacobian are assembled for all parameter values simultaneously.
• GenericParamNonlinearOperator — generic concrete implementation.
• ParamCache / SystemCache — caches for operator evaluations (residuals and Jacobians).
• Solver extensions: solve! overloads for LinearSolver and NewtonSolver acting on parametric operators.

abstract type AbstractParamCache <: GridapType end

struct GenericParamNonlinearOperator{A} <: NonlinearParamOperator
  op::A
  μ::AbstractRealisation
  paramcache::ParamCache
end

Fields:

• op: NonlinearParamOperator representing a parametric differential problem
• μ: AbstractRealisation representing the parameters at which the problem is solved
• paramcache: cache of the problem

struct LinNonlinParamOperator{A,B} <: NonlinearParamOperator
  op_linear::A
  op_nonlinear::B
  cache_linear::AbstractParamCache
end

Interface that allows to split the linear part of a parametric, nonlinear, differential operator from the nonlinear part. Fields:

• op_linear: linear part of the operator
• op_nonlinear: nonlinear part of the operator
• cache_linear: cache related to the linear part of the operator

abstract type NonlinearParamOperator <: NonlinearOperator end

mutable struct ParamCache <: AbstractParamCache
  trial
  ptrial
end

struct SystemCache <: AbstractParamCache
  A
  b
  x
end

allocate_paramcache(nlop::NonlinearParamOperator,μ::AbstractRealisation) -> AbstractParamCache

Similar to allocate_odecache in Gridap, when dealing with parametric problems

allocate_systemcache(nlop::NonlinearParamOperator[,x::AbstractVector]) -> SystemCache

Allocates the Jacobian, residual and solution vector of nlop

update_paramcache!(paramcache::AbstractParamCache,nlop::NonlinearParamOperator,μ::AbstractRealisation) -> AbstractParamCache

Similar to update_odecache! in Gridap, when dealing with parametric problems

update_systemcache!(nlop::NonlinearParamOperator,x::AbstractVector)

Updates the system cache stored in nlop, if any. For a LinNonlinParamOperator, assembles its linear part