Robust numerical algorithms based on analytic approximation for the solution of inverse problems in annular domains

• Published in: IMA journal of applied mathematics Vol. 74; no. 4; pp. 481 - 506
• Main Authors: Jaoua, Mohamed, Leblond, Juliette, Mahjoub, Moncef, Partington, Jonathan R.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.08.2009; Oxford Publishing Limited (England); Oxford University Press (OUP)
• Subjects: analytic functions; approximation; Cauchy problems; Exact sciences and technology; Hardy spaces; harmonic functions; inverse problems; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Partial differential equations; Sciences and techniques of general use; Several complex variables and analytic spaces; analytic functions; approximation; Cauchy problems; harmonic functions; inverse problems; Hardy spaces; Neumann problem; Approximation algorithm; Harmonic function; Cauchy problem; Inverse problem; Numerical approximation; Applied mathematics; Best approximation; Fast algorithm
• ISSN: 0272-4960; 1464-3634
• DOI: 10.1093/imamat/hxn041

We consider the Cauchy problem of recovering both Neumann and Dirichlet data on the inner part of the boundary of an annular domain from measurements of a harmonic function on some part of the outer boundary. Using tools from complex analysis and best approximation in Hardy classes, we present a family of fast data completion algorithms which are shown to provide constructive and robust identification schemes. These are applied to the computation of an impedance or Robin coefficient and are validated by a thorough numerical study.