Efficient preconditioners for saddle point systems with trace constraints coupling 2D and 1D domains

TL;DR

This paper develops and analyzes parameter-robust preconditioners for saddle point systems that couple 2D and 1D elliptic problems through trace constraints, demonstrating their effectiveness via numerical experiments.

Contribution

The paper introduces new preconditioners specifically designed for saddle point systems with trace constraints coupling different dimensional domains, ensuring robustness and efficiency.

Findings

Preconditioners are robust with respect to problem parameters.

Numerical experiments confirm the efficiency of the proposed preconditioners.

The approach effectively handles coupling between 2D and 1D elliptic problems.

Abstract

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical experiments.