Summary
For the numerical solution of inverse Helmholtz problems the boundary value problem for a Helmholtz equation with spatially variable wave number has to be solved repeatedly. For large wave numbers this is a challenge. In the paper we reformulate the inverse problem as an initial value problem, and describe a marching scheme for the numerical computation that needs only n2 log n operations on an n × n grid. We derive stability and error estimates for the marching scheme. We show that the marching solution is close to the low-pass filtered true solution. We present numerical examples that demonstrate the efficacy of the marching scheme.
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Natterer, F., Wübbeling, F. Marching schemes for inverse acoustic scattering problems. Numer. Math. 100, 697–710 (2005). https://doi.org/10.1007/s00211-004-0580-3
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DOI: https://doi.org/10.1007/s00211-004-0580-3