### Abstract

Original language | English |
---|---|

Pages (from-to) | 1783-1819 |

Number of pages | 37 |

Journal | Mathematics of Computation |

Volume | 87 |

Issue number | 312 |

Early online date | 4 Oct 2017 |

DOIs | |

Publication status | Published - 2018 |

### Fingerprint

### Keywords

- math.NA
- 65M38, 65M12, 65R20

### Cite this

*Mathematics of Computation*,

*87*(312), 1783-1819 . https://doi.org/10.1090/mcom/3279

}

*Mathematics of Computation*, vol. 87, no. 312, pp. 1783-1819 . https://doi.org/10.1090/mcom/3279

**Convolution quadrature for the wave equation with a nonlinear impedance boundary condition.** / Banjai, Lehel; Rieder, Alexander.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Convolution quadrature for the wave equation with a nonlinear impedance boundary condition

AU - Banjai, Lehel

AU - Rieder, Alexander

PY - 2018

Y1 - 2018

N2 - A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a bounded obstacle with a nonlinear impedance boundary condition. We describe a boundary integral formulation of the problem and prove without any smoothness assumptions on the solution the convergence of a full discretization: Galerkin in space and convolution quadrature in time. If the solution is sufficiently regular, we prove that the discrete method converges at optimal rates. Numerical evidence in 3D supports the theory.

AB - A rarely exploited advantage of time-domain boundary integral equations compared to their frequency counterparts is that they can be used to treat certain nonlinear problems. In this work we investigate the scattering of acoustic waves by a bounded obstacle with a nonlinear impedance boundary condition. We describe a boundary integral formulation of the problem and prove without any smoothness assumptions on the solution the convergence of a full discretization: Galerkin in space and convolution quadrature in time. If the solution is sufficiently regular, we prove that the discrete method converges at optimal rates. Numerical evidence in 3D supports the theory.

KW - math.NA

KW - 65M38, 65M12, 65R20

U2 - 10.1090/mcom/3279

DO - 10.1090/mcom/3279

M3 - Article

VL - 87

SP - 1783

EP - 1819

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 312

ER -