| -ksp_ksp_type <solver> | - the type of the inner solver (GMRES or any of its variants for instance) | |
| -ksp_pc_type <preconditioner> | - the type of the preconditioner applied to the inner solver | |
| -ksp_ksp_max_it <maxits> | - the maximum number of inner iterations (iterations of the inner solver) | |
| -ksp_ksp_rtol <tol> | - sets the relative convergence tolerance of the inner solver | |
| -ksp_tsirm_cgls <number> | - if 1 use CGLS solver in the minimization step, otherwise use LSQR solver | |
| -ksp_tsirm_max_it_ls <maxits> | - the maximum number of iterations for the least-squares minimization solver | |
| -ksp_tsirm_tol_ls <tol> | - sets the convergence tolerance of the least-squares minimization solver | |
| -ksp_tsirm_size_ls <size> | - the number of residuals for the least-squares minimization step |
Notes: TSIRM is a new two-stage iteration method for solving large sparse linear systems of the form Ax=b. The main idea behind this new method is the use a least-squares residual minimization to improve the convergence of Krylov based iterative methods, typically those of GMRES variants. The principle of TSIRM algorithm is to build an outer iteration over a Krylov method, called inner solver, and to frequently store the current residual computed by the given Krylov method in a matrix of residuals S. After a few outer iterations, a least-squares minimization step is applied on the matrix composed by the saved residuals, in order to compute a better solution and to make new iterations if required. The GMRES method , or any of its variants, can potentially be used as inner solver. The minimization step consists in solving the least-squares problem min||b-ASa|| to find 'a' which minimizes the residuals (b-AS). The minimization step is performed using two solvers of linear least-squares problems: CGLS or LSQR. A new solution x with a minimal residual is computed with x=Sa.
Contributed by: Lilia Ziane Khodja