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

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)9246-9268
Number of pages23
JournalJournal of Computational Physics
Volume229
Issue number24
DOIs
Publication statusPublished - 2010 Dec 10

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All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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