A new hybrid velocity integration method applied to elastic wave propagation | Zendy

Chen Zhiyun | Zendy; Steeb Holger | Zendy; Diebels Stefan | Zendy

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A new hybrid velocity integration method applied to elastic wave propagation

Author(s) -

Chen Zhiyun,

Steeb Holger,

Diebels Stefan

Publication year - 2007

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.2167

Subject(s) - discretization , mathematics , galerkin method , convergence (economics) , mathematical analysis , displacement (psychology) , a priori and a posteriori , field (mathematics) , vector field , displacement field , discontinuous galerkin method , finite element method , geometry , physics , psychology , philosophy , epistemology , pure mathematics , economics , psychotherapist , thermodynamics , economic growth

We present a novel space–time Galerkin method for solutions of second‐order time‐dependent problems. By introducing the displacement–velocity relationship implicitly, the governing set of equations is reformulated into a first‐order single field problem with the unknowns in the velocity field. The resulting equation is in turn solved by a time‐discontinuous Galerkin approach ( Int. J. Numer. Anal. Meth. Geomech . 2006; 30 :1113–1134), in which the continuity between time intervals is weakly enforced by a special upwind flux treatment. After solving the equation for the unknown velocities, the displacement field quantities are computed a posteriori in a post‐processing step. Various numerical examples demonstrate the efficiency and reliability of the proposed method. Convergence studies with respect to the h ‐ and p ‐refinement and different discretization techniques are given. Copyright © 2007 John Wiley & Sons, Ltd.

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