Summary
The problem of determining the shapes, sizes and material compositions of large inclusions embedded in elastic media from scattered elastic waves leads to the inverse scattering problems of the anisotropic linear elastic wave equations. Generalized Pulse-Spectrum Technique (GPST), a class of versatile and efficient Newton-like iterative algorithms with Tikhonov regularization, is used to solve this extremely difficult multi-parameter inverse problem. The summary of past and present applications of GPST to elastic inverse scattering problems are presented; in particular, the determination of shapes and sizes of large rigid near-spherical inclusions in an elastic medium from the scattered time-harmonic waves is described in detail. The future development of GPST and its tremendous potential for applications are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, Y.M.; Xie, G.Q.: A numerical method for simultaneous determination of bulk modulus, shear modulus and density variations for nondestructive evaluation, Nondestructive Testing Communications, 21 (1984) 125–135.
Xie, G.Q.; Chen, Y.M.: A modified Pulse-Spectrum Technique for solving inverse problems of two-dimensional elastic wave equation, Appl. Numer. Math., 1 (1985) 217–237.
Chen, Y.M.: Generalized Pulse-Spectrum Technique, Geophysics,50 (1985) 16641675.
Qiu, C.H.; Chen, Y.M.: Inverse problems for elastic plates with variable flexural rigidity, Int. J. Solids 81 Structures, 22 (1986) 901–908.
Chen, Y.M.; Xie, G.Q.: An iterative method for simultaneous determination of bulk and shear moduli and density variations, J. Comput. Phys., 62 (1986) 143–163.
Chen, Y.M.: Parallelism in hierarchy of GPST inversion algorithm for elastic wave equation, Appl. Numer. Math., 4 (1988) 83–95.
Wang, S.L.; Chen, Y.M.: An efficient numerical method for exterior and interior inverse problems of Helmholtz equation, Wave Motion, 13 (1991) 387–399.
Chen, Y.M.: Multi-parameter inversion by GPST with hierarchical parallelism and multigrid, Geophysical Inversion, ed. J. Bee Bednar, SIAM (1991).
Chen, Y.M.; Liu, M.S.: Efficiency improvement of GPST inversion algorithm, J. Comput. Phys., 72 (1987) 372–382.
Chen, Y.M.: High level parallelism in hierarchy of GPST algorithm for parameter identification in engineering mechanics, Computers e4 Struct, 30 (1988) 821–829.
Chen, Y.M.; Zhang, F.G.: Hierarchical multigrid strategy for efficiency improvement of the GPST inversion algorithm, Appl. Numer. Math.,6 (1989/90) 431–446.
Fan, W.; Chen, Y.M.: Scattering of a plane longitudinal elastic wave by a large convex rigid object with a statistically corrugated surface. I. Perturbation solutions, J. Math. Phys., 15 (1974) 831–841.
Fan, W.; Chen, Y.M.: Scattering of a plane longitudinal elastic wave by a large convex rigid object with a statistically corrugated surface. II. Far field solution, J. Math. Phys., 15 (1974) 950–953.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, Y.M. (1993). Determination of Shapes, Sizes and Material Compositions of Large Inclusions in Elastic Media from Scattered Waves. In: Tanaka, M., Bui, H.D. (eds) Inverse Problems in Engineering Mechanics. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52439-4_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-52439-4_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-52441-7
Online ISBN: 978-3-642-52439-4
eBook Packages: Springer Book Archive