The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Abdulmajid Wazwaz - One of the best experts on this subject based on the ideXlab platform.
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solving coupled lane emden boundary value problems in catalytic diffusion reactions by the adomian Decomposition Method
Journal of Mathematical Chemistry, 2014Co-Authors: Randolph Rach, Junsheng Duan, Abdulmajid WazwazAbstract:In this paper, we consider the coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian Decomposition Method. First, we utilize systems of Volterra integral forms of the Lane–Emden equations and derive the modified recursion scheme for the components of the Decomposition series solutions. The numerical results display that the Adomian Decomposition Method gives reliable algorithm for analytic approximate solutions of these systems. The error analysis of the sequence of the analytic approximate solutions can be performed by using the error remainder functions and the maximal error remainder parameters, which demonstrate an approximate exponential rate of convergence.
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adomian Decomposition Method for solving the volterra integral form of the lane emden equations with initial values and boundary conditions
Applied Mathematics and Computation, 2013Co-Authors: Abdulmajid Wazwaz, Randolph Rach, Junsheng DuanAbstract:In this paper, we use the systematic Adomian Decomposition Method to handle the integral form of the Lane-Emden equations with initial values and boundary conditions. The Volterra integral form of the Lane-Emden equation overcomes the singular behavior at the origin x=0. We confirm our belief that the Adomian Decomposition Method provides efficient algorithm for analytic approximate solutions of the equation. Our results are supported by investigating several numerical examples that include initial value problems and boundary value problems as well. Finally we consider the modified Decomposition Method of Rach, Adomian and Meyers for the Volterra integral form.
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comparison of the adomian Decomposition Method and the variational iteration Method for solving the lane emden equations of the first and second kinds
Kybernetes, 2011Co-Authors: Abdulmajid Wazwaz, Randolph RachAbstract:Purpose – The purpose of this paper is to provide a comparison of the Adomian Decomposition Method (ADM) with the variational iteration Method (VIM) for solving the Lane‐Emden equations of the first and second kinds.Design/Methodology/approach – The paper examines the theoretical framework of the Adomian Decomposition Method and compares it with the variational iteration Method. The paper seeks to determine the relative merits and computational benefits of both the Adomian Decomposition Method and the variational iteration Method in the context of the important physical models of the Lane‐Emden equations of the first and second kinds.Findings – The Adomian Decomposition Method is shown to readily solve the Lane‐Emden equations of both the first and second kinds for all positive real values of the system coefficient α and for all positive real values of the nonlinear exponent m. The Decomposition series solution of these nonlinear differential equations requires the calculation of the Adomian polynomials a...
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the combined laplace transform adomian Decomposition Method for handling nonlinear volterra integro differential equations
Applied Mathematics and Computation, 2010Co-Authors: Abdulmajid WazwazAbstract:In this work, a combined form of the Laplace transform Method with the Adomian Decomposition Method is developed for analytic treatment of the nonlinear Volterra integro-differential equations. The combined Method is capable of handling both equations of the first and second kind. Illustrative examples will be examined to support the proposed analysis.
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a comparison between the variational iteration Method and adomian Decomposition Method
Journal of Computational and Applied Mathematics, 2007Co-Authors: Abdulmajid WazwazAbstract:In this paper, we present a comparative study between the variational iteration Method and Adomian Decomposition Method. The study outlines the significant features of the two Methods. The analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems.
Taisuke Ozaki - One of the best experts on this subject based on the ideXlab platform.
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a three dimensional domain Decomposition Method for large scale dft electronic structure calculations
Computer Physics Communications, 2014Co-Authors: Taisuke OzakiAbstract:Abstract With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational Methods are required to take advantage of such extreme-scale machines. In this paper, we present a three-dimensional domain Decomposition scheme for enabling large-scale electronic structure calculations based on density functional theory (DFT) on massively parallel computers. It is composed of two Methods: (i) the atom Decomposition Method and (ii) the grid Decomposition Method. In the former Method, we develop a modified recursive bisection Method based on the moment of inertia tensor to reorder the atoms along a principal axis so that atoms that are close in real space are also close on the axis to ensure data locality. The atoms are then divided into sub-domains depending on their projections onto the principal axis in a balanced way among the processes. In the latter Method, we define four data structures for the partitioning of grid points that are carefully constructed to make data locality consistent with that of the clustered atoms for minimizing data communications between the processes. We also propose a Decomposition Method for solving the Poisson equation using the three-dimensional FFT in Hartree potential calculation, which is shown to be better in terms of communication efficiency than a previously proposed parallelization Method based on a two-dimensional Decomposition. For evaluation, we perform benchmark calculations with our open-source DFT code, OpenMX, paying particular attention to the O ( N ) Krylov subspace Method. The results show that our scheme exhibits good strong and weak scaling properties, with the parallel efficiency at 131,072 cores being 67.7% compared to the baseline of 16,384 cores with 131,072 atoms of the diamond structure on the K computer.
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A three-dimensional domain Decomposition Method for large-scale DFT electronic structure calculations
arXiv: Materials Science, 2012Co-Authors: Taisuke OzakiAbstract:With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational Methods are required to take advantage of such extreme-scale machines. In this paper, we present a three-dimensional domain Decomposition scheme for enabling large-scale electronic calculations based on density functional theory (DFT) on massively parallel computers. It is composed of two Methods: (i) atom Decomposition Method and (ii) grid Decomposition Method. In the former, we develop a modified recursive bisection Method based on inertia tensor moment to reorder the atoms along a principal axis so that atoms that are close in real space are also close on the axis to ensure data locality. The atoms are then divided into sub-domains depending on their projections onto the principal axis in a balanced way among the processes. In the latter, we define four data structures for the partitioning of grids that are carefully constructed to make data locality consistent with that of the clustered atoms for minimizing data communications between the processes. We also propose a Decomposition Method for solving the Poisson equation using three-dimensional FFT in Hartree potential calculation, which is shown to be better than a previously proposed parallelization Method based on a two-dimensional Decomposition in terms of communication efficiency. For evaluation, we perform benchmark calculations with our open-source DFT code, OpenMX, paying particular attention to the O(N) Krylov subspace Method. The results show that our scheme exhibits good strong and weak scaling properties, with the parallel efficiency at 131,072 cores being 67.7% compared to the baseline of 16,384 cores with 131,072 diamond atoms on the K computer.
Chen Gaojie - One of the best experts on this subject based on the ideXlab platform.
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domain Decomposition Method for variational inequalities with robin boundary condition
Computer Simulation, 2007Co-Authors: Chen GaojieAbstract:Nonoverlapping additive domain Decomposition Method for a kind of elliptic variational inequalities with Robin boundary condition was developed and analyzed. In the Method, the unknown values at the common interface between adjacent subdomains were updated by Robin transmission conditions. Convergence was established for the proposed Methods. This kind of domain Decomposition Methods have been widely used to solve the boundary value problems of partial differential equation and many convergence theorems have been obtianed. Numerical experiments appeared that a greater acceleration of the Method could be obtained by choosing the Robin parameter suitably.
Dejie Yu - One of the best experts on this subject based on the ideXlab platform.
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sparse signal Decomposition Method based on multi scale chirplet and its application to the fault diagnosis of gearboxes
Mechanical Systems and Signal Processing, 2011Co-Authors: Fuqiang Peng, Dejie YuAbstract:Abstract Based on the chirplet path pursuit and the sparse signal Decomposition Method, a new sparse signal Decomposition Method based on multi-scale chirplet is proposed and applied to the Decomposition of vibration signals from gearboxes in fault diagnosis. An over-complete dictionary with multi-scale chirplets as its atoms is constructed using the Method. Because of the multi-scale character, this Method is superior to the traditional sparse signal Decomposition Method wherein only a single scale is adopted, and is more applicable to the Decomposition of non-stationary signals with multi-components whose frequencies are time-varying. When there are faults in a gearbox, the vibration signals collected are usually AM–FM signals with multiple components whose frequencies vary with the rotational speed of the shaft. The meshing frequency and modulating frequency, which vary with time, can be derived by the proposed Method and can be used in gearbox fault diagnosis under time-varying shaft-rotation speed conditions, where the traditional signal processing Methods are always blocked. Both simulations and experiments validate the effectiveness of the proposed Method.
Saha S Ray - One of the best experts on this subject based on the ideXlab platform.
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analytical solution for the space fractional diffusion equation by two step adomian Decomposition Method
Communications in Nonlinear Science and Numerical Simulation, 2009Co-Authors: Saha S RayAbstract:Abstract Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical superdiffusive problems in fluid flow, finance and other areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by two-step Adomian Decomposition Method (TSADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form and then their solutions have been represented graphically. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present technique. The solutions obtained by the standard Decomposition Method have been numerically evaluated and presented in the form of tables and then compared with those obtained by TSADM. The present TSADM performs extremely well in terms of efficiency and simplicity.
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an approximate solution of a nonlinear fractional differential equation by adomian Decomposition Method
Applied Mathematics and Computation, 2005Co-Authors: Saha S Ray, Rati Kanta BeraAbstract:The aim of the present analysis is to apply Adomian Decomposition Method for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Decomposition Method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series Method. A good agreement of the results is observed.
