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An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation. (English) Zbl 1022.78012
Summary: The iterative algorithm proposed by A. V. Kozlov, V. G. Maz’ya and A. V. Fomin [Comput. Math. Math. Phys. 31, 45-52 (1991; Zbl 0774.65069)] for obtaining approximate solutions to the ill-posed Cauchy problem for the Helmholtz equation is analysed. The technique is then numerically implemented using the boundary element method (BEM). The numerical results confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularising criterion is also proposed.

MSC:
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R25 Ill-posed problems for PDEs
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