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A New Optimal Iterative Algorithm for Solving Nonlinear Poisson Problems in Heat Diffusion

Chih-Wen Chang1,2, Chein-Shan Liu3
Cloud Computing and System Integration Division, National Center for High-Performance Com-puting, Taichung 40763, Taiwan.
Corresponding author, Tel.:+886-4-24620202#860. E-mail address: 0903040@nchc.narl.org.tw
Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan.

Computers, Materials & Continua 2013, 34(2), 143-175. https://doi.org/10.3970/cmc.2013.034.143

Abstract

The nonlinear Poisson problems in heat diffusion governed by elliptic type partial differential equations are solved by a modified globally optimal iterative algorithm (MGOIA). The MGOIA is a purely iterative method for searching the solution vector x without using the invert of the Jacobian matrix D. Moreover, we reveal the weighting parameter αc in the best descent vector w = αcE + DTE and derive the convergence rate and find a criterion of the parameter γ. When utilizing αc and γ, we can further accelerate the convergence speed several times. Several numerical experiments are carefully discussed and validated the proposed method.

Keywords

Nonlinear algebraic equations, Nonlinear Poisson equation, Iterative algorithm, Modified globally optimal iterative algorithm (MGOIA) Invariant manifold.

Cite This Article

C. . Chang and C. . Liu, "A new optimal iterative algorithm for solving nonlinear poisson problems in heat diffusion," Computers, Materials & Continua, vol. 34, no.2, pp. 143–175, 2013.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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