Open this publication in new window or tab >>2021 (English)In: Bulletin of the Iranian Mathematical Society, ISSN 1735-8515, Vol. 47, p. 1681-1699Article in journal (Refereed) Published
Abstract [en]
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}, 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} in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.
Place, publisher, year, edition, pages
Springer, 2021
Keywords
Helmholtz equation, Cauchy problem, Inverse problem, Ill-posed problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-170834 (URN)10.1007/s41980-020-00466-7 (DOI)000575739300001 ()2-s2.0-85092146699 (Scopus ID)
2020-10-262020-10-262024-02-22Bibliographically approved