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.
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