演講公告
新聞標題： ( 2012-05-04 )
演講主題：Parallel Multilevel Polynomial Jacobi-Davidson Eigensolver for Dissipative Acoustic Problems
主講人：黃楓南 教授(中央大學數學系)
演講日期：2012年5月15日(星期二) 下午2:00 –3:00
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：
Abstract. Many scienti c and engineering applications require accurate, fast, robust, and scalable numerical solution of large sparse algebraic polynomial eigenvalue prob-lems (PEVPs) arising from some appropriate disretization of partial differential equations. The polynomial Jacobi-Davidson (PJD) algorithm has been numerically shown as a promising approach for the PEVPs to effectively find their interior spectrum and has gained its popularity.
The PJD algorithm is a subspace method, which extracts the candidate approximate eigenpair from a search space and the space undated by embedding the solution of the correction equation at the JD iteration. In this talk, we propose the multilevel PJD algorithm for PEVPs with emphasis on the application of the dissipative acoustic cubic eigenvalue problem. The proposed multilevel PJD algorithm is based on the Schwarz framework. The initial basis for the search space is constructed on the current level by using the solution of the same eigenvalue problem, but defined on the previous coarser grid. On the other hand, a parallel e cient multilevel Schwarz preconditioner is designed for the correction equation to enhance the scalability of the PJD algorithm, which plays a crucial property in parallel com-puting for large-scale problem solved by using a large number of processors. Some numerical examples obtained on a parallel cluster of computers are given to demonstrate the robustness and scalability of our PJD algorithm.
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