Substructuring Preconditioners for an h-p Nitsche-type method

TL;DR

This paper introduces an iterative substructuring preconditioner for an h-p Nitsche-type discretization, demonstrating quasi-optimality and validated through numerical experiments, advancing efficient solvers for complex discretizations.

Contribution

It develops a novel substructuring preconditioner for h-p Nitsche methods, extending classical approaches to more general discretizations with proven quasi-optimality.

Findings

Preconditioner achieves quasi-optimality with respect to mesh size and polynomial degree.

Numerical experiments confirm theoretical performance and efficiency.

Method improves iterative solver convergence for Nitsche-type discretizations.

Abstract

We propose and study an iterative substructuring method for an h-p Nitsche-type discretization, following the original approach introduced in [Bramble, Pasciack, Schatz (Math Comp. 1986)] for conforming methods. We prove quasi-optimality with respect to the mesh size and the polynomial degree for the proposed preconditioner. Numerical experiments asses the performance of the preconditioner and verify the theory.