A multiscale domain decomposition approach for chemical vapor deposition
type: Item
instance of: scholarly article
title: A multiscale domain decomposition approach for chemical vapor deposition
zbMATH Open document ID: 1268.80007
author: J. Bogers
author: K. Kumar
author: P. H. L. Notten
author: J. F. M. Oudenhoven
author: I. S. Pop
published in: Journal of Computational and Applied Mathematics
publication date: 2013-04-22T00:00:00Z
review text: The authors present a numerical scheme for a chemical vapor deposition process on a trenched \(\mathrm{Si}\) substrate. They introduce three scales occurring in three domains \(\Omega _{j}\), \(j=1,2,3\). The boundaries of the domains \( \Omega _{j}\) are decomposed in the two parts \(\Omega _{j,R}\), where the deposition reaction occurs, and the interfaces between the domains, where coupling boundary conditions are imposed. In the first part of their paper, the authors write the balance equations for continuity and momentum and the convection-diffusion equations in the domains \(\Omega _{j}\), \(j=1,2,3\). They also write the coupling boundary conditions on the interfaces and the reactive boundary conditions on the \(\Omega _{j,R}\). Initial data are imposed for the non-steady convection-diffusion equations. The main part of the paper presents a numerical scheme for this problem. The authors first write a weak formulation of the problem using an Euler implicit scheme with respect to the time parameter. The main result proves the convergence of the approximate solutions built using a domain decomposition scheme in the weak topology of \(H^{1}(\Omega _{j})\).
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80A32
Mathematics Subject Classification ID: 65M55
Mathematics Subject Classification ID: 76V05
zbMATH DE Number: 6156325
zbMATH Keywords: domain decomposition
zbMATH Keywords: reactive flows
zbMATH Keywords: chemical vapor deposition
zbMATH Keywords: multiscale
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: numerical scheme
MaRDI profile type: Publication
full work available at URL: j.cam.2012.10.018
OpenAlex ID: W1975681917
DOI: 10.1016/J.CAM.2012.10.018
description: scientific article; zbMATH DE number 6156325