### Abstract

Numerical solution of the Helmholtz equation in an infinite domain often involves restriction of the domain to a bounded computational window where a numerical solution method is applied. On the boundary of the computational window artificial transparent boundary conditions are posed, for example, widely used perfectly matched layers (PMLs) or absorbing boundary conditions (ABCs). Recently proposed transparent-influx boundary conditions (TIBCs) resolve a number of drawbacks typically attributed to PMLs and ABCs, such as introduction of spurious solutions and the inability to have a tight computational window. Unlike the PMLs or ABCs, the TIBCs lead to a nonlinear dependence of the boundary integral operator on the frequency. Thus, a nonlinear Helmholtz eigenvalue problem arises.
This paper presents an approach for solving such nonlinear eigenproblems which is based on a truncated singular value decomposition (SVD) polynomial approximation of the nonlinearity and subsequent solution of the obtained approximate polynomial eigenproblem with the Jacobi-Davidson method.

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 14 |

Publication status | Published - Sep 2008 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1883 |

ISSN (Print) | 1874-4850 |

### Keywords

- MSC-65F15
- MSC-35J05
- MSC-65F30

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## Cite this

Botchev, M. A., Sleijpen, G. L. G., & Sopaheluwakan, A. (2008).

*An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems*. (Memorandum / Department of Applied Mathematics; No. 1883). Enschede: University of Twente, Department of Applied Mathematics.