On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics

Date

2022-01-01

Author

Korkut, Fuat
Mengi, Yalcin
Tokdemir, Turgut

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

273
views

0
downloads

In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex. The use of the proposed approach is considered in the analysis of inhomogeneous visco-elasto-dynamic system and assessed through three example problems analyzed in Fourier space: the composite and inhomogeneous tube, layer and impedance problems. The GFDM results obtained for the tube and layer problems compare very closely and coincide almost exactly with the exact solution. In the impedance problems, rigid surface or embedded footings resting on a composite inhomogeneous half-space are considered. The influences of various types of inhomogeneities, as well as, of various geometric shapes of PML-(physical region) interfaces on impedance curves are examined.

Subject Keywords

Generalized finite difference, Stretching coordinates, Perfectly matched, Inhomogeneity, Meshless, PERFECTLY MATCHED LAYER, SOIL-STRUCTURE INTERACTION, WAVE-PROPAGATION, PML, IMPLEMENTATION, MEDIA, FIELD

URI

https://hdl.handle.net/11511/95120

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

DOI

https://doi.org/10.1016/j.enganabound.2021.10.014

Collections

Department of Engineering Sciences, Article

Suggestions

OpenMETU
Core

Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations Ozgun, Ozlem; Kuzuoğlu, Mustafa (2007-12-10) In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of o...
On the Attenuation of the Perfectly Matched Layer in Electromagnetic Scattering Problems with the Spectral Element Method Mahariq, I.; Kuzuoğlu, Mustafa; Tarman, Işık Hakan (2014-09-01) Although Spectral Element Method (SEM) has been applied in the modeling of boundary value problems of electromagnetics, its usage is not as common as the Finite Element or Finite Difference approaches in this area. It is well-known that the Perfectly Matched Layer (PML) approach is a mesh/grid truncation method in scattering or radiation applications where the spatial domain is unbounded. In this paper, the PML approach in the SEM context is investigated in two-dimensional, frequency-domain scattering probl...
Recent advances in perfectly matched layers in finite element applications Ozgun, Ozlem; Kuzuoğlu, Mustafa (2008-01-01) We present a comparative evaluation of two novel and practical perfectly matched layer (PML) implementations to the problem of mesh truncation in the finite element method (FEM): locally-conformal PML, and multi-center PML techniques. The most distinguished feature of these methods is the simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. These methods are based on spec...
Recent results on Bayesian Cramér-Rao bounds for jump Markov systems Fritsche, Carsten; Orguner, Umut; Svensson, Lennart; Gustafsson, Fredrik (2016-07-08) In this paper, recent results on the evaluation of the Bayesian Cramer-Rao bound for jump Markov systems are presented. In particular, previous work is extended to jump Markov systems where the discrete mode variable enters into both the process and measurement equation, as well as where it enters exclusively into the measurement equation. Recursive approximations are derived with finite memory requirements as well as algorithms for checking the validity of these approximations are established. The tightnes...
On the Poisson sum formula for the analysis of wave radiation and scattering from large finite arrays Aydın Çivi, Hatice Özlem; Chou, HT (1999-05-01) Poisson sum formulas have been previously presented and utilized in the literature [1]-[8] for converting a finite element-by-element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation/scattering from electrically large finite periodic arrays. However, different authors [1]-[6] appear to use two different versions of the Poisson sum formula; one of these explicitly shows the end-point discontinui...

Citation Formats

F. Korkut, Y. Mengi, and T. Tokdemir, “On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, vol. 134, pp. 466–490, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/95120.