A multiscale domain decomposition approach for chemical vapor deposition
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 \(H^{1}(\Omega _{j})\).
scientific article; zbMATH DE number 6156325