Direct collocation method for identifying the initial conditions in the inverse wave problem using radial basis functions. Issue 12 (2nd December 2018)

• Record Type: Journal Article
• Authors: Wang, Lihua; Wang, Zhen; Qian, Zhihao; Gao, Yukui; Zhou, Yueting
• Is Part Of: Inverse problems in science and engineering. Volume 26:Issue 12(2018)
• Page Start: 1695
• Page End: 1727
• Publication Date: 2018-12-02
• Subjects: Direct collocation method -- radial basis functions -- initial conditions -- inverse wave problem -- ill-posed system; 65N21 -- 65N35 -- 35L20; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2018.1428968
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: A direct collocation method associated with explicit time integration using radial basis functions is proposed for identifying the initial conditions in the inverse problem of wave propagation. Optimum weights for the boundary conditions and additional condition are derived based on Lagrange's multiplier method to achieve the prime convergence. Tikhonov regularization is introduced to improve the stability for the ill-posed system resulting from the noise, and the L-curve criterion is employed to select the optimum regularization parameter. No iteration scheme is required during the direct collocation computation which promotes the accuracy and stability for the solutions, while Galerkin-based methods demand the iteration procedure to deal with the inverse problems. High accuracy and good stability of the solution at very high noise level make this method a superior scheme for solving inverse problems.