An optimal two-side Robin-Robin domain decomposition method for H(div)-elliptic problem

TL;DR

This paper introduces a new two-side Robin-Robin domain decomposition method for H(div)-elliptic problems, demonstrating convergence rate dependence on subdomain size and mesh, with stable iterative solutions via MINRES.

Contribution

The paper presents a novel domain decomposition algorithm with proven convergence properties and a stable algebraic system solution approach for H(div)-elliptic problems.

Findings

Convergence rate depends only on the ratio H/h.

Derived algebraic Robin boundary system solved by MINRES.

Achieved asymptotically stable iteration numbers.

Abstract

In this paper, we develop a new two-side Robin-Robin domain decomposition method for H(div)-elliptic problem. Numerical results show that the convergence rate of the new algorithm only depends on $H/h$, where $H$ is diameter of subdomains and $h$ is the mesh size. Besides, an algebraic system of Robin boundary conditions is derived from the iterative method. We solve it by MINRES and get asymptotically stable iteration numbers as well.