Adomian’s decomposition method to modeling power functionally graded thermoelastic materials in heat transfer and thermal stress analysis

This work deals with an iteration method for numerical solving the problem of one-dimensional coupled thermoelasticity under given boundary conditions. This iteration based on the Adomian’s decomposition method. All the material properties have been considered variable on position with a power law. The numerical results have been calculated for different cases of the gradient parameter and the gradient index. The numerical results have been shown in figures. The gradient parameter and the gradient index have significant effects on the temperature increment, the strain, the stress, and the displacement

Additional degrees of parallelism within the Adomian decomposition method

4th International Conference on Computational Engineering (ICCE 2017), 28-29 September 2017, DarmstadtThis is the author accepted manuscript. The final version is available from Springer via the DOI in this record.The trend of future massively parallel computer architectures challenges the exploration of additional degrees of parallelism also in the time dimension when solving continuum mechanical partial differential equations. The Adomian decomposition method (ADM) is investigated to this respects in the present work. This is accomplished by comparison with the Runge-Kutta (RK) time integration and put in the context of the viscous Burgers equation. Our studies show that both methods have similar restrictions regarding their maximal time step size. Increasing the order of the schemes leads to larger errors for the ADM compared to RK. However, we also discuss a parallelization within the ADM, reducing its runtime complexity from O(n^2) to O(n). This indicates the possibility to make it a viable competitor to RK, as fewer function evaluations have to be done in serial, if a high order method is desired. Additionally, creating ADM schemes of high-order is less complex as it is with RK.The work of Andreas Schmitt is supported by the ’Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universit¨at Darmstadt

Approximate Method for Studying the Waves Propagating along the Interface between Air-Water

This paper is devoted to consider the approximate solutions of the nonlinear water wave problem for a fluid layer of finite depth in the presence of gravity. The method of multiple-scale expansion is employed to obtain the Korteweg-de Vries (KdV) equations for solitons, which describes the behavior of the system for free surface between air and water in a nonlinear approach. The solutions of the water wave problem split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as the solutions of KdV equations. The solution of KdV equations is obtained analytically by using a reliable modification of Laplace decomposition method (LDM), namely, the modified Laplace decomposition method (MLDM) is presented. This procedure is a powerful tool for solving large amount of nonlinear problems. The proposed method provides the solution as a series which may converge to the exact solution of the problem. Also, the convergence analysis of the proposed method is given. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves. The horizontal and vertical of the velocity components have nonlinear characters