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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.

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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.



cc 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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