BCGS – Biconjugate gradient squared – Bi-CGStab
Usage:
-ksp_type bcgs
Options: none
A Combination of BICG and repeated GMRES. The Biconjugate Gradient Stabilized method is a variant of BiCG, like CGS, but using different updates for the At-sequence in order to obtain smoother convergence than CGS.
Locally, a residual vector is minimized, which leads to a considerably smoother convergence behavior. On the other hand, if the local GMRES step stagnates, then the Krylov subspace is not expanded, and BCGSTAB will break down.
Drawbacks: The algorithm slows down often during the GMRES(1) part. This may occur in hyperbolic PDEs (waves).
Costs: Requires two extra inner products at each step compared with CGS.
Remarks: BCGS (with a Jacobi preconditioner) is the solver utilized when applying ADH without PETSc.