On a boundary integral solution of a lateral planar Cauchy problem in elastodynamics

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:367

Article

Chapko, Roman¹  Johansson, B. Tomas²  Mindrinos, Leonidas³ 

[1] Ivan Franko Natl Univ Lviv, Fac Appl Math & Informat, UA-79000 Lvov, Ukraine

[2] Aston Univ, EAS, Math, Birmingham B4 7ET, W Midlands, England

[3] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math RICAM, Linz, Austria

关键词: Boundary integral equations;    Cauchy problem;    Elastodynamics;    Laguerre transformation;    Nystrom method;    Tikhonov regularization;   

DOI  :  10.1016/j.cam.2019.112463

来源: Elsevier

【 摘 要 】

A boundary integral based method for the stable reconstruction of missing boundary data is presented for the governing hyperbolic equation of elastodynamics in annular planar domains. Cauchy data in the form of the solution and traction is reconstructed on the inner boundary curve from the similar data given on the outer boundary. The ill-posed data reconstruction problem is reformulated as a sequence of boundary integral equations using the Laguerre transform with respect to time and employing a single-layer approach for the stationary problem. Singularities of the involved kernels in the integrals are analyzed and made explicit, and standard quadrature rules are used for discretization. Tikhonov regularization is employed for the stable solution of the obtained linear system. Numerical results are included showing that the outlined approach can be turned into a practical working method for finding the missing data. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free