Linear solvers

Description

ExaPF allows to solve linear systems with either direct and indirect linear algebra, both on CPU and on GPU. To solve a linear system $Ax = b$, ExaPF uses the function ldiv!.

ExaPF.LinearSolvers.ldiv! — Function
ldiv!(solver, x, A, y)
ldiv!(solver, x, y)
  • solver::AbstractLinearSolver: linear solver to solve the system
  • x::AbstractVector: Solution
  • A::AbstractMatrix: Input matrix
  • y::AbstractVector: RHS

Solve the linear system $A x = y$ using the algorithm specified in solver. If A is not specified, the function will used directly the factorization stored inside solver.

source

Direct solvers

ExaPF wraps UMFPACK (shipped with SuiteSparse.jl) on the CPU, and CUSPARSE on CUDA device.

ExaPF.LinearSolvers.DirectSolver — Type
DirectSolver <: AbstractLinearSolver

Solve linear system $A x = y$ with direct linear algebra.

  • On the CPU, DirectSolver uses UMFPACK to solve the linear system
  • On CUDA GPU, DirectSolver redirects the resolution to the method CUSOLVER.csrlsvqr
source

Iterative solvers

ExaPF.LinearSolvers.Bicgstab — Type
Bicgstab <: AbstractIterativeLinearSolver
Bicgstab(precond; verbose=0, rtol=1e-10, atol=1e-10)

Wrap Krylov.jl's BICGSTAB algorithm to solve iteratively the linear system $A x = y$.

source
ExaPF.LinearSolvers.Dqgmres — Type
Dqgmres <: AbstractIterativeLinearSolver
Dqgmres(precond; verbose=false, memory=4)

Wrap Krylov.jl's Dqgmres algorithm to solve iteratively the linear system $A x = y$.

source

Available linear solvers can be queried with

A default solver is provided for each vendor backend.