On a three dimensional Cauchy problem for inhomogeneous Helmholtz equation associated with perturbed wave number

Hong, Phong Luu; Minh, Triet Le; Hoang, Quan Pham

doi:10.1016/j.cam.2017.11.042

Cited by 8 publications

(1 citation statement)

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“…This is certainly true for the Helmholtz equation. This Cauchy problem (1.1), which includes the Helmholtz equation [1,12,17,21], arises in many areas of science and engineering related to electromagnetic or acoustic waves. For example, in underwater acoustics [8], in medical applications [22], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations

Achieng

Berntsson

Chepkorir

et al. 2020

Bull. Iran. Math. Soc.

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The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers $$k^2$$ k 2 , in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of $$k^2$$ k 2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

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