Multiscale seamless‐domain method for solving nonlinear problems using statistical estimation methodology |
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| Authors: | Yoshiro Suzuki |
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| Affiliation: | Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japan |
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| Abstract: | This article presents a nonlinear solver combining regression analysis and a multiscale simulation scheme. First, the proposed method repeats microscopic analysis of a local simulation domain, which is extracted from the entire global domain, to statistically estimate the relation(s) between the value of a dependent variable at a point and values at surrounding points. The relation is called regression function. Subsequent global analysis reveals the behavior of the global domain with only coarse‐grained points using the regression function quickly at low computational cost, which can be accomplished using a multiscale numerical solver, called the seamless‐domain method. The objective of the study is to solve a nonlinear problem accurately and at low cost by combining the 2 techniques. We present an example problem of a nonlinear steady‐state heat conduction analysis of a heterogeneous material. The proposed model using fewer than 1000 points generates a solution with precision similar to that of a standard finite‐element solution using hundreds of thousands of nodes. To investigate the relationship between the accuracy and computational time, we apply the seamless‐domain method under varying conditions such as the number of iterations of the prior analysis for statistical data learning. |
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| Keywords: | elliptic multiscale nonlinear solvers partial differential equations regression analysis |
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