This PR implements the flexible generalized minimal residual method for refinement of the solution of the primal-dual system.
The main changes/additions in this PR are:
The FGMRES solver, a preconditioned Krylov method. FGMRES should be more robust than the current iterative refinement. The flexible version is also more robust than the regular restarted version of GMRES, see for instance https://doi.org/10.1137/060661545.
An option to enable/disable this FGMRES refinement. In the PR FGMRES is enabled by default. If FGMRES is disabled, iterative refinement is used as before.
The ComputeResidualRatio method is modified to now compute the Infinity norm-wise relative backward error, which is used in the stopping criterion for FGMRES and iterative refinement.
New routine PDFullSpaceSolver::NrmInf to compute the Inf-norm of the primal-dual system, which is used to compute the relative backward error.
Added routines ComputeRowA1 and ComputeColA1 in IpMatrix to compute the 1-norm of the rows/columns in the matrix. This is implemented in the derived classes.
Modified PDFullSpaceSolver::ComputeResiduals to use the alpha and beta parameters so it can be used to compute a matrix vector product (or the residual).
Our tests show improvements in convergence when using FGMRES compared to iterative refinement, for select problems, with minimal runtime overhead.
This PR implements the flexible generalized minimal residual method for refinement of the solution of the primal-dual system. The main changes/additions in this PR are:
ComputeResidualRatio
method is modified to now compute the Infinity norm-wise relative backward error, which is used in the stopping criterion for FGMRES and iterative refinement.PDFullSpaceSolver::NrmInf
to compute the Inf-norm of the primal-dual system, which is used to compute the relative backward error.ComputeRowA1
andComputeColA1
inIpMatrix
to compute the 1-norm of the rows/columns in the matrix. This is implemented in the derived classes.PDFullSpaceSolver::ComputeResiduals
to use thealpha
andbeta
parameters so it can be used to compute a matrix vector product (or the residual).Our tests show improvements in convergence when using FGMRES compared to iterative refinement, for select problems, with minimal runtime overhead.
@bknueven @k1nshuk