A class of block alternating splitting implicit iteration methods for double saddle point linear systems

Abstract

AbstractIn the framework of a special block alternating splitting implicit (BASI) iteration scheme for generalized saddle point problems, we establish some new iteration methods for solving double saddle point problems by means of a suitable partitioning strategy. Convergence analysis of the corresponding BASI iteration methods indicates that they are convergent unconditionally under certain weak requirements for the related matrix splittings, which are satisfied directly for our specific application to double saddle point problems. Numerical examples for liquid crystal director and time‐harmonic eddy current models are presented to demonstrate the efficiency of the proposed BASI preconditioners to accelerate the GMRES method.