Open Access

ARTICLE

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

by Chih-Wen Chang¹, Chein-Shan Liu³

1 Cloud Computing and System Integration Division, National Center for High-Performance Com-puting, Taichung 40763, Taiwan.
2 Corresponding author, Tel.:+886-4-24620202#860. E-mail address: 0903040@nchc.narl.org.tw
3 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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Keywords

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