HR: 17:00h
AN: S22G-05    [PDF]
TI: Absorbing Boundaries in Frequency-Space and Wavenumber-Time Domains
AU: * Sanchez-Sesma, F J
EM: sesma@servidor.unam.mx
AF: Instituto de Ingenieria, UNAM, Cd. Universitaria, Circuito Escolar s/n, Coyoacan, DF 04510 Mexico
AU: Villa-Velazquez, C I
AF: Instituto de Ingenieria, UNAM, Cd. Universitaria, Circuito Escolar s/n, Coyoacan, DF 04510 Mexico
AB: Absorbing boundary conditions are used in a variety of disciplines to simulate the radiation of energy to the exterior of a numerically-studied interior domain. The scattering of sound, elastic or electromagnetic waves by arbitrary shaped objects may require terminating the interior domain with adequate boundary conditions. In this work a perfect absorbing boundary condition for 2D elastic wave propagation is formulated in the frequency-wavenumber spectral domain (f-k). Using Fourier transformations, the corresponding results are obtained in both the frequency-space (f-x) and the wavenumber-time domains, respectively. The singular results in the space-time (x-t) domain are discussed as well. The absorbing boundary condition can be regarded as an interface operator that gives the normal derivative in terms of boundary values. Thus it is called Dirichlet to Neumann (DtN) operator, a term that has been coined in the mathematical community. Within the framework of elasticity and from physical considerations, this condition can be expressed in terms of tractions and displacements and the DtN operator is simply the stiffness of the exterior region. This term comes from engineering usage. Most of the results presented here correspond to the 2D antiplane SH case but the ideas discussed have their vector counterparts for the in-plane P and SV waves and the 3D problems. It is found that our expressions in the space-time (x-t) domain appear naturally in the classical dynamic rupture problem. Partial support is acknowledged to DGAPA-UNAM under grant IN121202 and CONACYT-Mexico under project NC204.
DE: 7200 SEISMOLOGY
DE: 7260 Theory and modeling
SC: Seismology [S]
MN: 2003 Fall Meeting