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• W2143906881 abstract "The robust and reliable solution of large-scale nonlinear eigenvalue problems (NEPs) in computational science and engineering is recognized to be a challenging task. This paper proposes a new algorithm, denoted by CIRR(S), that utilizes the Rayleigh-Ritz procedure to compute all eigenvalues (and the corresponding eigenvectors) lying within a given contour in the complex plane. The main novelties are the following. First and foremost, the eigenspace is directly constructed by using the values of the resolvent at a series of sampling points on the contour, as such the unreliability caused by the use of high order contour moments of the resolvent in the current scheme can be effectively circumvented. Next, the projected NEP is solved by using the Sakurai-Sugiura algorithm. To enhance the reliability and accuracy, the user-defined probing matrix in the original algorithm is avoided and strategies for automatically determining the number of eigenvalues are provided. Finally, the CIRR(S) is extended to solve NEPs in the boundary element method which are hard to solve due to the densely populated matrix and high computational cost. The Chebyshev interpolation technique is used for approximating the projected matrix. The good performance of the CIRR(S) algorithm is verified by a variety of NEPs in real applications, with the degrees of freedom ranging from several hundreds to around one million. The algorithm is suitable for parallelization and easy to be implemented in conjunction with other programs and softwares." @default.
• W2143906881 created "2016-06-24" @default.
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• W2143906881 date "2015-10-26" @default.
• W2143906881 modified "2023-09-27" @default.
• W2143906881 title "Contour integral based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems" @default.
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