Block triangular preconditioning for elliptic boundary optimal control with mixed boundary conditions

TL;DR

This paper introduces a block triangular preconditioning technique for saddle point problems in elliptic boundary optimal control with mixed boundary conditions, improving computational efficiency.

Contribution

It proposes a novel block triangular preconditioning method based on permutations and Schur complement approximations for saddle point systems.

Findings

Spectral analysis shows improved eigenvalue distribution.

Numerical experiments confirm enhanced convergence.

Preconditioning reduces computational time.

Abstract

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of the saddle point problem and approximations of the corresponding Schur complement. The spectral properties of the preconditioned matrix is analyzed. Numerical experiments are conducted to demonstrate the effectiveness of the proposed preconditioning method.