演講公告

新聞標題：　( 2016-05-03 )

• 演講主題：Asynchronous Optimized Schwarz Methods for the solution of PDEs

• 主講人：Daniel B. Szyld 教授(美國Temple University 數學系)

• 演講日期：2016 年5 月17 日(星期二) 14:00 - 15:00

• 演講地點：(光復校區) 科學一館223 室

• 茶會時間：當天下午1:30 (科學一館205 室)

• 摘要內容：
  

  摘要：
  Asynchronous methods refer to parallel iterative procedures where each process performs its task without waiting for other processes to be completed, i.e., with whatever information it has locally available and with no synchronizations with other processes. For the numerical solution of a general partial differential equaition on a domain, Schwarz iterative methods use a decomposition of the domain into two or more (possibly overlapping) subdomains.
  In essence one is introducing new artificial boundary conditions on the interfaces between these subdomains. In the classical formulation, these artificial boundary conditions are of Dirichlet type. Given an initial approximation, the method progresses by solving for the PDE restricted to each subdomain using as boundary data on the artificial interfaces the values of the solution on the neighboring subdomain from the previous step. This procedure is inherently parallel, since the (approximate) solutions on each subdomain can be performed by a different processor. In the case of optimized Schwarz, the boundary conditions on the artificial interfaces are of Robin or mixed type.
  In this way one can optimize the Robin parameter(s) and obtain a very fast method.
  In this talk, an asynchronous version of the optimized Schwarz method is presented for the solution of differential equations on a parallel computational environment. In a one-way subdivision of the computational domain, with overlap, the method is shown to converge when the optimal artificial interface conditions are used. Convergence is also proved under very mild conditions on the size of the subdomains, when approximate (nonoptimal) interface conditions are utilized. Numerical results are presented on large three-dimensional problems illustrating the efficiency of the proposed asynchronous parallel implementation of the method. The main application shown is the calculation of the gravitational potential in the area around the Chicxulub crater, in Yucatan, where an asteroid is believed to have landed 66 million years ago contributing to the extintion of the dinosaurs. (Joint work with Fréderic Magoués and Cedric Venet).

• 相關檔案：Talk_1050517.pdf

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