Domain Decomposition Learning Methods (区域分解法)




报告题目 (Title):Domain Decomposition Learning Methods (区域分解法)

报告人 (Speaker):许学军 教授(同济大学)

报告时间 (Time):2023年5月24日(周三) 16:00-17:00

报告地点 (Place):校本部 F309



报告摘要:With the aid of hardware and software developments, there has been a surge of interests in solving partial differential equations by deep learning techniques, and the integration with domain decomposition strategies has recently attracted considerable attention due to its enhanced representation and parallelization capacity of the network solution. In this talk, a novel learning approach, i.e., the compensated deep Ritz method, is proposed to enable the flux transmission across subregion interfaces with guaranteed accuracy, thereby allowing us to construct effective learning algorithms for realizing the more general non-overlapping domain decomposition methods in the presence of overfitted interface conditions. Numerical experiments on a series of elliptic boundary value problems including the regular and irregular interfaces, low and high dimensions, smooth and high-contrast coefficients on multidomains are carried out to validate the effectiveness of our proposed domain decomposition learning algorithms.

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