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J. F. Claerbout and A. G. Johnson, “Extrapolation of Time Dependent Waveforms along Their Path of Propagation,” Geophysical Journal of the Royal Astron Society, Vol. 26, No. 1-4, 1971, pp. 285-293. doi:10.1111/j.1365-246X.1971.tb03402.x

has been cited by the following article:

• TITLE: Finite Element Analysis with Paraxial & Viscous Boundary Conditions for Elastic Wave Propagation

  AUTHORS: Hee Seok Kim

  KEYWORDS: Paraxial Boundary; Local Boundary; Penalty Functional; Viscous Boundary

  JOURNAL NAME: Engineering, Vol.4 No.12, December 26, 2012

  ABSTRACT: In this study, two studies are performed. One is to apply paraxial boundary conditions which are local boundary conditions based on paraxial approximations of the one-way wave equations to finite element analysis. To do this, a penalty functional is proposed and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The other is to improve the capacity of viscous boundary conditions using dashpots. To do this, customary viscous boundary conditions are modified to maximize the efficiency according to angles of incidence and materials. For the numerical analysis of elasticity with paraxial boundary conditions and the modified viscous boundary conditions, the coding of the finite element models is implemented, and the efficiency of those boundary conditions is investigated.