An adaptive quadrature-based factorization method for inverse acoustic scattering problems. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Leem, Koung Hee; Liu, Jun; Pelekanos, George
• Is Part Of: Inverse problems in science and engineering. Volume 27:Issue 3(2019)
• Page Start: 299
• Page End: 316
• Publication Date: 2019-03-04
• Subjects: Adaptive Simpson quadrature -- inverse acoustic scattering -- factorization method -- linear sampling method -- multilevel methods; 65R32 -- 35P25; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2018.1459600
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: We propose a novel adaptive algorithm, which generates nonuniform sampling points that automatically concentrate near the boundary of an unknown scatterer, to dramatically speed up Kirsch's factorization method for inverse acoustic scattering problems. Built upon the widely used adaptive Simpson quadrature method, our proposed adaptive algorithm approximates the integral of an indicator function over the search domain and yields reliable and accurate reconstructions significantly faster than the standard factorization method. Numerical experiments are performed to validate the effectiveness of our proposed algorithm and make comparisons with the established multilevel linear sampling method.