A boundary-field formulation for elastodynamic scattering. (English) Zbl 1518.35586
The objective of the article is the study of the elastic fields that are obtained in an infinite medium after an elastic wave collides with an obstacle and becomes embedded in the medium. To this end, the authors apply a Boundary Field Equation method. This allows to formulate a Nonlocal Boundary Problem in the domain of the Laplace transform by using the equations inside and outside the obstacle.
The basic qualitative results are obtained later, such as the existence, uniqueness and stability of the solution of the Nonlocal Boundary Problem in suitable Sobolev spaces for two integral representations. Subsequently, these results are transferred to the time domain and the stability bounds are also transferred to this domain.
These results represent the starting point for a numerical discretization based on the Convolution Quadrature.
The basic qualitative results are obtained later, such as the existence, uniqueness and stability of the solution of the Nonlocal Boundary Problem in suitable Sobolev spaces for two integral representations. Subsequently, these results are transferred to the time domain and the stability bounds are also transferred to this domain.
These results represent the starting point for a numerical discretization based on the Convolution Quadrature.
Reviewer: Ramón Quintanilla De Latorre (Barcelona)
MSC:
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 35A15 | Variational methods applied to PDEs |
| 35L05 | Wave equation |
| 45A05 | Linear integral equations |
| 74J05 | Linear waves in solid mechanics |
| 74J20 | Wave scattering in solid mechanics |
| 74B10 | Linear elasticity with initial stresses |
| 65D32 | Numerical quadrature and cubature formulas |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65R20 | Numerical methods for integral equations |
Keywords:
transient wave scattering; elastodynamics; time-dependent boundary integral equations; convolution quadratureReferences:
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