A multiple-scale MQ-RBF for solving the inverse Cauchy problems in arbitrary plane domain. (July 2016)

• Record Type: Journal Article
• Authors: Liu, Chein-Shan; Chen, Wen; Fu, Zhuojia
• Is Part Of: Engineering analysis with boundary elements. Volume 68(2016:Jul.)
• Page Start: 11
• Page End: 16
• Publication Date: 2016-07
• Subjects: Multiple-scale radial basis function expansion -- Elliptic PDEs -- Inverse Cauchy problem -- Post-conditioner; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2016.02.011
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The method of radial basis function (RBF) is popularly used in the solution of partial differential equations (PDEs). We propose a multiple-scale MQ-RBF method to solve the linear elliptic PDEs and the corresponding inverse Cauchy problems in simply- and doubly-connected domains, where the multiple scales are automatically determined a priori by the collocation points and source points, which play a role of post-conditioner of linear system to determine the unknown expansion coefficients. In the solution of inverse Cauchy problems the multiple-scale MQ-RBF is quite accurate and stable against large noise level up to 10–30%. Even for a case with only a quarter of boundary being imposed over-specified data, the multiple-scale MQ-RBF can still recover 75% unknown data very well.