Numerical studies of domain sampling methods for inverse boundary value problems by one measurement

We consider an inverse boundary value problem for the Laplace equation, which discusses the reconstruction of an unknown target inside the background medium from one boundary measurement. We are interested in two domain sampling methods, i.e., the range test and no-response test, whose convergences are justified theoretically in previous work [17]. As a continuation of this work, we study the numerical realizations of these methods. Some new techniques are proposed to set up efficient algorithms, which yield reasonably good numerical reconstructions. To demonstrate the performance of proposed algorithms, we show several numerical examples for different shapes of unknown targets with noisy measurement data. Some key ingredients of numerical implementations are discussed in detail. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This article investigates an inverse boundary value problem for the Laplace equation, focusing on reconstructing an unknown target from a single boundary measurement. Two domain sampling methods, the range test and no-response test, are studied and their numerical realizations are explored using new techniques. Numerical examples are provided to demonstrate the performance of the proposed algorithms for different shapes of unknown targets with noisy data.