Exterior Dirichlet and Neumann Problems in Domains with Random Boundaries
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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.
KeywordsDirichlet and Neumann problems Random surfaces Statistical moments Shape derivative
Mathematics Subject Classification65N30 65N38 65N15 65N50
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.