A Schwarz preconditioner for the smoothed lowest-order virtual element method

Abstract

In this paper we introduce a novel virtual smoothed method that is spectrally equivalent to the virtual element method. Furthermore, we design a robust two-level Schwarz preconditioner tailored for irregular subdomains, applicable to extended smoothed finite element methods, smoothed strain element methods, and the proposed smoothed virtual element method. Theoretical proofs are provided for the new method, including spectral estimates of the preconditioned system. Numerical experiments validate the effectiveness, scalability, and practical applicability of the approach in addressing irregular subdomains.