A block triangular preconditioner for a class of three-by-three block saddle point problems

TL;DR

This paper introduces a new block upper triangular preconditioner for three-by-three block saddle point problems, demonstrating improved convergence and performance through theoretical analysis and numerical experiments.

Contribution

A novel block upper triangular preconditioner specifically designed for three-by-three saddle point systems, with proven convergence properties.

Findings

The proposed preconditioner converges faster than existing methods.

Numerical experiments show improved efficiency and robustness.

Theoretical analysis confirms the effectiveness of the preconditioning approach.

Abstract

This paper deals with solving a class of three-by-three block saddle point problems. The systems are solved by preconditioning techniques. Based on an iterative method, we construct a block upper triangular preconditioner. The convergence of the presented method is studied in details. Finally, some numerical experiments are given to demonstrate the superiority of the proposed preconditioner over some existing ones.