Dirichlet-to-Neumann map for three-dimensional elastic waves

✍ Scribed by Günter K. Gächter; Marcus J. Grote

• Book ID: 104293927
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 242 KB
• Volume: 37
• Category: Article
• ISSN: 0165-2125
• DOI: 10.1016/s0165-2125(02)00091-4

✦ Synopsis

An exact nonreflecting boundary condition is derived for time-harmonic elastic waves in three space dimensions. This condition holds on a spherical surface, B, which separates the computational domain from the surrounding unbounded region. It establishes an exact relation between the displacement field and its normal and tangential tractions, and thus defines a Dirichlet-to-Neumann (DtN) map on B. Then a modified DtN condition (MDtN) is derived to remove the difficulties that arise when the exact DtN condition is truncated for use in computation, by modifying the truncated condition. Uniqueness of the solution to the boundary-value problem with the MDtN condition imposed on B is proved. Both the DtN and the MDtN conditions naturally fit into the variational formulation for use with the finite element method. Numerical results with a finite difference method demonstrate the high improvement in accuracy over standard methods.