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International Journal for Multiscale Computational Engineering
MULTISCALE SEAMLESS-DOMAIN METHOD FOR NONPERIODIC FIELDS: NONLINEAR HEAT CONDUCTION ANALYSIS
Tokyo Institute of Technology, Department of Mechanical Sciences and Engineering, Tokyo
A multiscale numerical solver called the seamless-domain method (SDM) consists of macroscopic global analysis and
microscopic local analysis. Previous work presented a nonlinear solver using the SDM technique that does not couple these two analyses interactively. In addition, the practicality of this solver was verified only for use with periodic fields. In this work, we present another nonlinear SDM solver that couples the multiple scales completely interactively. We solve an example problem of a nonlinear heat conduction analysis of a nonperiodic field using the presented SDM, the standard finite difference method, and the conventional domain decomposition method (DDM). The target temperature field has thermal conductivity distribution that is nonuniform, nonperiodic, and has temperature dependency. This problem thus has material nonlinearity. The accuracy of the SDM solution is very high, and the root mean squared error in temperature is less than 0.044% of the maximum temperature in the field. In contrast, the error of the DDM is 0.10%–0.18%, which is larger than twice the error of the SDM. The finite difference method requires 7–36 times the computation time of the SDM to generate a solution as accurate as that of the SDM.
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