Linear Solvers

This section describes the interface for linear solvers.

Input File Syntax Example

Below is an example input file block for a direct solver with an LDLT factorization.

linear solvers:
  direct:
    type: DirectLinearSolver
    factorization method: ldl

General methods and abstract types

Cthonios.AbstractLinearSolver — Type

abstract type AbstractLinearSolver

A linear solver simply needs to define the following methods

residual_norm
solve!

solve! method which has the following signature solve!(ΔUu, solver::DirectSolver, obj, Uu, p) where ΔUu is the increment for a nonlinear solver solver is the solver, obj is the objective, Uu is the current guess of the solution, and p is the set of parameters

Direct Solver

Cthonios.DirectSolver — Type

assembler::Any
linsolve::Any
timer::Any

Direct linear solver

Cthonios.DirectSolver — Method

DirectSolver(
    obj::Objective,
    p,
    timer
) -> DirectSolver{A, L} where {A<:(FiniteElementContainers.StaticAssembler{Float64, Int64, _A, _B, _C, _D, _E, _F, _G, _H, _I, _J, _K, Vector{Int64}, Vector{Int64}, Vector{Float64}} where {_A<:AbstractVector{Int64}, _B<:AbstractVector{Int64}, _C<:AbstractVector{Int64}, _D<:AbstractVector{Int64}, _E<:AbstractVector{Int64}, _F<:FiniteElementContainers.NodalField, _G<:AbstractVector{Float64}, _H, _I, _J, _K}), L<:(LinearSolve.LinearCache{LinearAlgebra.Symmetric{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}}, _A, _B, SciMLBase.NullParameters, LinearSolve.DefaultLinearSolver, LinearSolve.DefaultLinearSolverInit{LinearAlgebra.LU{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}, Vector{Int64}}, LinearAlgebra.QR{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}, Vector{Float64}}, Nothing, Nothing, Sparspak.SpkSparseSolver.SparseSolver{Int64, Float64}, Nothing, Nothing, _A1, LinearAlgebra.LU{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}, Vector{Int64}}, Tuple{LinearAlgebra.LU{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}, Vector{Int64}}, Vector{Int64}}, Nothing, Nothing, SparseArrays.CHOLMOD.Factor{Float64, Int64}, Nothing, SparseArrays.CHOLMOD.Factor{Float64, Int64}, SparseArrays.CHOLMOD.Factor{Float64, Int64}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int32}}, Base.RefValue{Int32}}, Tuple{LinearAlgebra.LU{Float64, Matrix{Float64}, Vector{Int64}}, Base.RefValue{Int64}}, LinearAlgebra.QR{Float64, SparseArrays.SparseMatrixCSC{Float64, Int64}, Vector{Float64}}, _B1, _C}, SciMLOperators.IdentityOperator, SciMLOperators.IdentityOperator, _C1, Bool} where {_A, _B, _A1, _B1, _C, _C1})}

Direct linear solver constructor from a Domain

Cthonios.gradient! — Method

gradient!(
    solver::DirectSolver,
    obj::Objective,
    Uu,
    p::ObjectiveParameters
)

Cthonios.hessian! — Method

hessian!(solver::DirectSolver, obj, Uu, p)

Cthonios.residual_norm — Method

residual_norm(solver::DirectSolver, obj, Uu, p) -> Any

Cthonios.solve! — Method

solve!(ΔUu, solver::DirectSolver, obj, Uu, p)

Preconditioners

Cthonios.AbstractPreconditioner — Type

abstract type AbstractPreconditioner

Abstract base preconditioner type.

Cthonios.CholeskyPreconditioner — Type

mutable struct CholeskyPreconditioner{A, P, T} <: Cthonios.AbstractPreconditioner

assembler::Any
preconditioner::Any
timer::Any

Cthonios.CholeskyPreconditioner — Method

CholeskyPreconditioner(
    obj::Objective,
    p,
    timer
) -> CholeskyPreconditioner{A, SparseArrays.CHOLMOD.Factor{Float64, Int64}} where A<:(FiniteElementContainers.StaticAssembler{Float64, Int64, _A, _B, _C, _D, _E, _F, _G, _H, _I, _J, _K, Vector{Int64}, Vector{Int64}, Vector{Float64}} where {_A<:AbstractVector{Int64}, _B<:AbstractVector{Int64}, _C<:AbstractVector{Int64}, _D<:AbstractVector{Int64}, _E<:AbstractVector{Int64}, _F<:FiniteElementContainers.NodalField, _G<:AbstractVector{Float64}, _H, _I, _J, _K})

Cthonios.LDLPreconditioner — Type

struct LDLPreconditioner{A, P, T} <: Cthonios.AbstractPreconditioner

assembler::Any
preconditioner::Any
timer::Any

Cthonios.LDLPreconditioner — Method

LDLPreconditioner(
    obj::Objective,
    p,
    timer
) -> LDLPreconditioner{A, LDLFactorizations.LDLFactorization{Float64, Int64, Int64, Int64}} where A<:(FiniteElementContainers.StaticAssembler{Float64, Int64, _A, _B, _C, _D, _E, _F, _G, _H, _I, _J, _K, Vector{Int64}, Vector{Int64}, Vector{Float64}} where {_A<:AbstractVector{Int64}, _B<:AbstractVector{Int64}, _C<:AbstractVector{Int64}, _D<:AbstractVector{Int64}, _E<:AbstractVector{Int64}, _F<:FiniteElementContainers.NodalField, _G<:AbstractVector{Float64}, _H, _I, _J, _K})

Cthonios.LimitedLDLPreconditioner — Type

mutable struct LimitedLDLPreconditioner{A, P, T} <: Cthonios.AbstractPreconditioner

assembler::Any
preconditioner::Any
timer::Any

Cthonios.LimitedLDLPreconditioner — Method

LimitedLDLPreconditioner(
    obj::Objective,
    p,
    timer
) -> LimitedLDLPreconditioner{A, LimitedLDLFactorizations.LimitedLDLFactorization{Float64, Int64, Vector{Int64}, Vector{Int64}}} where A<:(FiniteElementContainers.StaticAssembler{Float64, Int64, _A, _B, _C, _D, _E, _F, _G, _H, _I, _J, _K, Vector{Int64}, Vector{Int64}, Vector{Float64}} where {_A<:AbstractVector{Int64}, _B<:AbstractVector{Int64}, _C<:AbstractVector{Int64}, _D<:AbstractVector{Int64}, _E<:AbstractVector{Int64}, _F<:FiniteElementContainers.NodalField, _G<:AbstractVector{Float64}, _H, _I, _J, _K})

LinearAlgebra.ldiv! — Method

ldiv!(y, P::CholeskyPreconditioner, v)