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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

APA Style
Chang, C., Liu, C. (2013). A new optimal iterative algorithm for solving nonlinear poisson problems in heat diffusion. Computers, Materials & Continua, 34(2), 143-175. https://doi.org/10.3970/cmc.2013.034.143
Vancouver Style
Chang C, Liu C. A new optimal iterative algorithm for solving nonlinear poisson problems in heat diffusion. Comput Mater Contin. 2013;34(2):143-175 https://doi.org/10.3970/cmc.2013.034.143
IEEE Style
C. Chang and C. Liu, "A New Optimal Iterative Algorithm for Solving Nonlinear Poisson Problems in Heat Diffusion," Comput. Mater. Contin., vol. 34, no. 2, pp. 143-175. 2013. https://doi.org/10.3970/cmc.2013.034.143



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