Fast iterative solver for convection-diffusion systems with spectral elements

✍ Scribed by P. Aaron Lott; Howard Elman

• Book ID: 102554830
• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 394 KB
• Volume: 27
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.20518

✦ Synopsis

Abstract

We introduce a solver and preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection–diffusion equation. The method is based on a Robin–Robin interface preconditioner coupled to a fast diagonalization solver which is used to efficiently eliminate the interior degrees of freedom and perform subsidiary subdomain solves. Using a spectral element discretization, we first apply our technique to constant wind problems, and then propose a means for applying the technique as a preconditioner for variable wind problems. We demonstrate that iteration counts are mildly dependent on changes in mesh size and convection strength. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011