Nonoverlapping domain decomposition method with preconditioner from asymptotic analysis of steady flow in high contrast media. Issue 10 (3rd October 2021)

• Record Type: Journal Article
• Authors: Borcea, Liliana; Riviere, Beatrice; Wang, Yingpei
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 10(2021)
• Page Start: 2008
• Page End: 2024
• Publication Date: 2021-10-03
• Subjects: preconditioner -- domain decomposition method -- asymptotic analysis -- high contrast media -- nonoverlapping; 65N08 -- 65N20 -- 65N55; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1870681
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: We present a nonoverlapping domain decomposition method for steady flow in high contrast heterogeneous media modelled by an elliptic equation with coefficients that have very large amplitude variations on a small spatial scale. The linear system of equations resulting from matching the solution trace and the fluxes through the boundary of the subdomains is ill-conditioned, especially for fine meshes needed to capture the rapid variations of the solution. Our main contribution is to show with analysis and numerical simulations how to use an asymptotic approximation of the Dirichlet to Neumann map of the sub-domain problems to obtain a preconditioner for an efficient domain decomposition algorithm.