Numerical Solution of the Cauchy Problem for the Helmholtz Equation
2014 (English)Report (Other academic)
The Cauchy problem for the Helmholtz equation appears in applications related to acoustic or electromagnetic wave phenomena. The problem is ill–posed in the sense that the solution does not depend on the data in a stable way. In this paper we give a detailed study of the problem. Specifically we investigate how the ill–posedness depends on the shape of the computational domain and also on the wave number. Furthermore, we give an overview over standard techniques for dealing with ill–posed problems and apply them to the problem.
Place, publisher, year, edition, pages
Linköping University Electronic Press, 2014. , 16 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2014:04
Helmholtz equation, Cauchy Problem, Ill-Posed, Regularization, Numerical Methods.
Computational Mathematics Mathematics
IdentifiersURN: urn:nbn:se:liu:diva-105707ISRN: LiTH-MAT-R--2014/04--SEOAI: oai:DiVA.org:liu-105707DiVA: diva2:709791