arXiv subjects

Ajith Gunaratne

Publications and source records attributed to Ajith Gunaratne.

3 recordsLinked to original sources

arXiv2022

Analysis and simulation of a variational stabilization for the Helmholtz equation with noisy Cauchy data

This article considers a Cauchy problem of Helmholtz equations whose solution is well known to be exponentially unstable with respect to the inputs. In the framework of variational quasi-reversibility method, a Fourier truncation is applied to appropriately perturb the underlying problem, which allows us to obtain a stable approximate solution. The corresponding approximate problem is of a hyperbolic equation, which is also a crucial aspect of this approach. Error estimates between the approximate and true solutions are derived with respect to the noise level. From this analysis, the Lipschitz stability with respect to the noise level follows. Some numerical examples are provided to see how our numerical algorithm works well.

math.NA↗

arXiv2019

A logarithmic estimate for inverse source scattering problem with attenuation in a two-layered medium

The paper aims a logarithmic stability estimate for the inverse source problem of the one-dimensional Helmholtz equation with attenuation factor in a two layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions.

math.AP↗

arXiv2019

Increasing stability of the inverse source problem for one dimensional domain

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end points. Our main result is a stability estimate consists of two parts: the data discrepancy and the high frequency tail.

math.AP↗