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Exterior Dirichlet and Neumann Problems in Domains with Random Boundaries

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Abstract

An approximation of statistical moments of solutions to exterior Dirichlet and Neumann problems with random boundary surfaces is investigated. A rigorous shape calculus approach has been used to approximate these statistical moments by those of the corresponding shape derivatives, which are computed by boundary integral equation methods. Examples illustrate our theoretical results.

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Acknowledgements

Duong Thanh Pham and Dũng Dinh’s research was funded by the Department of Science and Technology–Ho Chi Minh City (HCMC-DOST), and the Institute for Computational Science and Technology (ICST) at Ho Chi Minh city, Vietnam, under Contract 21/2017/HD-KHCNTT on 21/09/2017. A part of this paper was done when Duong Pham and Dũng Dinh were working at and Thanh Tran was visiting Vietnam Institute for Advanced Study in Mathematics (VIASM). These authors thank VIASM for providing a fruitful research environment and working condition. Thanh Tran was partially supported by the Australian Research Council under the Grant DP160101755.

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Authors and Affiliations

  1. Institute for Computational Science and Technology, SBI Building, Quang Trung Software City, Tan Chanh Hiep Ward, District 12, Ho Chi Minh City, Vietnam

    Duong Thanh Pham

  2. Vietnamese German University, Le Lai Street, Binh Duong New City, Binh Duong Province, Vietnam

    Duong Thanh Pham

  3. School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia

    Thanh Tran

  4. Information Technology Institute, Vietnam National University, Hanoi, 144 Xuan Thuy, Hanoi, Vietnam

    Dũng Dinh

  5. Institute for Mathematics, Carl von Ossietzky University, 26111, Oldenburg, Germany

    Alexey Chernov

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  1. Duong Thanh Pham
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  2. Thanh Tran
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  3. Dũng Dinh
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  4. Alexey Chernov
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Correspondence to Duong Thanh Pham.

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Communicated by Ahmad Izani Md. Ismail.

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Pham, D.T., Tran, T., Dinh, D. et al. Exterior Dirichlet and Neumann Problems in Domains with Random Boundaries. Bull. Malays. Math. Sci. Soc. 43, 1311–1342 (2020). https://doi.org/10.1007/s40840-019-00741-9

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  • DOI: https://doi.org/10.1007/s40840-019-00741-9

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