An Adaptive Finite Element Pml Method for the Elastic Wave Scattering Problem in Periodic Structures
نویسندگان
چکیده
ABSTRACT. An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic and rigid surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing an equivalent transparent boundary condition. Second, an a posteriori error estimate is deduced for the discrete problem and is used to determine the mesh for refinements and to determine the PML parameters. Numerical experiments are included to demonstrate the competitive behavior of the proposed adaptive method.
منابع مشابه
The Adaptive Perfectly Matched Layer Method for Time-harmonic Acoustic and Electromagnetic Scattering Problems
Abstract. The recently introduced perfectly matched layer (PML) method is an efficient method to reduce the exterior wave propagation problem which is defined in the unbounded domain to the problem in the bounded domain. Under the assumption that the exterior solution is composed of outgoing waves only, the basic idea of the PML technique is to surround the computational domain by a layer of fi...
متن کاملAnalysis of a finite PML approximation to the three dimensional elastic wave scattering problem
We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay ...
متن کاملApplication of Boundary Element Method to 3 D Submerged Structures With Open Ends (RESEARCH NOTE)
This paper presents a three dimensional application of direct Boundary-Element Method (BEM) for computing interaction of sinusoidal waves with a large submerged open bottom structure near the floor with finite depth. The wave diffraction problem is formulated within the framework of linearized potential theory and solved numerically with direct BEM. A computer program based on BEM is developed ...
متن کاملA two dimensional Simulation of crack propagation using Adaptive Finite Element Analysis
Finite element method (FEM) is one of the most famous methods which has many applications in varies studies such as the study of crack propagation in engineering structures. However, unless extremely fine meshes are employed, problem arises in accurately modelling the singular stress field in the singular element area around the crack tip. In the present study, the crack growth simulation has b...
متن کاملAn Adaptive Uniaxial Perfectly Matched Layer Method for Time-harmonic Scattering Problems
Abstract. The uniaxial perfectly matched layer (PML) method uses rectangular domain to define the PML problem and thus provides greater flexibility and efficiency in dealing with problems involving anisotropic scatterers. In this paper an adaptive uniaxial PML technique for solving the time harmonic Helmholtz scattering problem is developed. The PML parameters such as the thickness of the layer...
متن کامل