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

Korkut, Fuat
Mengi, Yalcin
Tokdemir, Turgut
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.


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...
On the Representation of Finite Fields
Akleylek, Sedat; Özbudak, Ferhun; Department of Cryptography (2010)
The representation of field elements has a great impact on the performance of the finite field arithmetic. In this thesis, we give modified version of redundant representation which works for any finite fields of arbitrary characteristics to design arithmetic circuits with small complexity. Using our modified redundant representation, we improve many of the complexity values. We then propose new representations as an alternative way to represent finite fields of characteristic two by using Charlier and Herm...
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...
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.