Numerical studies of domain sampling methods for inverse boundary value problems by one measurement - Sun, Shiwei; Nakamura, Gen; Wang, Haibing (Journal of computational physics, 2023)
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. •We propose two improved algorithms for an inverse boundary value problem, based on the range test and no-response test methods.•We extend the algorithms to the inclusion case and show some numerical results.•We propose a two-step algorithm to reduce the computational cost.