An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Let be a bounded domain in Rn with a Lipschitz boundary Г divided into two parts Г0 and Г1 which do not intersect one another and have a common Lipschitz boundary. We consider the following Cauchy problem for the Helmholtz equation:
where k, the wave number, is a positive real constant, аv denotes the outward normal derivative, and f and g are specified Cauchy data on Г0. This problem is ill–posed in the sense that small errors in the Cauchy data f and g may blow up and cause a large error in the solution.
Alternating iterative algorithms for solving this problem are developed and studied. These algorithms are based on the alternating iterative schemes suggested by V.A. Kozlov and V. Maz’ya for solving ill–posed problems. Since these original alternating iterative algorithms diverge for large values of the constant k2 in the Helmholtz equation, we develop a modification of the alterating iterative algorithms that converges for all k2. We also perform numerical experiments that confirm that the proposed modification works.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. , 6 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1530
IdentifiersURN: urn:nbn:se:liu:diva-77300Local ID: LIU-TEK-LIC-2012:15ISBN: 978-91-7519-890-3OAI: oai:DiVA.org:liu-77300DiVA: diva2:526247
2012-05-02, Nobel (BL32), B-huset, ing°ang 23, Campus Valla, Linköpings universitet, Linköping, 15:15 (English)
Nilsson, Börje, Professor
Kozlov, Vladimir, ProfessorTuresson, Bengt-Ove, Dr.Berntsson, Fredrik, Dr.
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