Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients

Yu Chen Shu, Chiu Yen Kao, I. Liang Chern, Chien C. Chang

研究成果: Article同行評審

4 引文 斯高帕斯(Scopus)

摘要

In this paper, we propose an augmented coupling interface method on a Cartesian grid for solving eigenvalue problems with sign-changed coefficients. The underlying idea of the method is the correct local construction near the interface which incorporates the jump conditions. The method, which is very easy to implement, is based on finite difference discretization. The main ingredients of the proposed method comprise (i) an adaptive-order strategy of using interpolating polynomials of different orders on different sides of interfaces, which avoids the singularity of the local linear system and enables us to handle complex interfaces; (ii) when the interface condition involves the eigenvalue, the original problem is reduced to a quadratic eigenvalue problem by introducing an auxiliary variable and an interfacial operator on the interface; (iii) the auxiliary variable is discretized uniformly on the interface, the rest of variables are discretized on an underlying rectangular grid, and a proper interpolation between these two grids are designed to reduce the number of stencil points. Several examples are tested to show the robustness and accuracy of the schemes.

原文English
頁(從 - 到)9246-9268
頁數23
期刊Journal of Computational Physics
229
發行號24
DOIs
出版狀態Published - 2010 12月 10

All Science Journal Classification (ASJC) codes

  • 數值分析
  • 建模與模擬
  • 物理與天文學(雜項)
  • 一般物理與天文學
  • 電腦科學應用
  • 計算數學
  • 應用數學

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