ADI, LOD and Modern Decomposition Methods for Certain Multiphysics Applications. Issue 1 (March 2015)

• Record Type: Journal Article
• Authors: Sheng, Qin
• Is Part Of: Journal of algorithms & computational technology. Volume 9:Issue 1(2015)
• Page Start: 105
• Page End: 120
• Publication Date: 2015-03
• Subjects: Decomposition methods -- partial differential equations -- beam propagation -- multiscale -- multiphysics -- eikonal transformation -- stability and asymptotic stability; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1260/1748-3018.9.1.105
• Languages: English
• ISSNs: 1748-3018

Abstract

This paper explores applications of several traditional and latest decomposition methods for approximating solutions of linear and nonlinear partial differential equations in multiphysical computations. Differences and similarities between concerned ADI and LOD strategies are discussed and analyzed. Eikonal transformation based splitting realizations are introduced for solving highly oscillatory paraxial Helmholtz problems on micro and macro scaled domains. It is found that modern decomposition algorithms developed achieve not only anticipated accuracy and efficiency, but also stabilities. Therefore required high reliability is ensured throughout multiphysical and multiscaled computations.