TY - JOUR
T1 - A Boundary-Field Formulation for Elastodynamic Scattering
AU - Hsiao, George C.
AU - Sánchez-Vizuet, Tonatiuh
AU - Wendland, Wolfgang L.
N1 - Funding Information: Tonatiuh Sánchez-Vizuet was partially funded by the United States National Science Foundation through the grant NSF-DMS-2137305. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/1
Y1 - 2023/1
N2 - An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature.
AB - An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature.
KW - Convolution quadrature
KW - Elastodynamics
KW - Time-dependent boundary integral equations
KW - Transient wave scattering
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U2 - https://doi.org/10.1007/s10659-022-09964-7
DO - https://doi.org/10.1007/s10659-022-09964-7
M3 - Article
SN - 0374-3535
VL - 153
SP - 5
EP - 27
JO - Journal of Elasticity
JF - Journal of Elasticity
IS - 1
ER -