The use of generalized finite difference method in perfectly matched layer analysis

Date

2018-08-01

Author

Korkut, Fuat
Tokdemir, Turgut
Mengi, Yalcin

Metadata

Show full item record

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

Item Usage Stats

222
views

0
downloads

This study deals with the use of Generalized Finite Difference Method (GFDM) in Perfectly Matched layer (PML) analysis. There are two options for performing PML analysis. First option is to express PML equations in terms of real coordinates of the points in actual (real) PML region; the second is to use governing equations (expressed in terms of complex stretching coordinates) as they are in complex PML region. The first option is implemented in this study; the implementation of the second option is under way and will be reported in another study. For the integration of PML equations, the use of GFDM is proposed. Finally, the suggested procedure is assessed computationally by considering the compliance functions of surface and embedded rigid strip foundations. GFDM with PML results are compared to those obtained by using Finite Element Method (FEM) with PML and Boundary Element Method (BEM). Excellent matches in results showed the reliability of the proposed procedure in PML analysis.

Subject Keywords

Generalized finite difference methods, Rigid strip foundation, Compliance functions, Perfectly matched layer

URI

https://hdl.handle.net/11511/48436

Journal

APPLIED MATHEMATICAL MODELLING

DOI

https://doi.org/10.1016/j.apm.2018.03.014

Collections

Department of Engineering Sciences, Article

Suggestions

OpenMETU
Core

Generalized finitedifference method in elastodynamics using perfectly matched layer Korkut, Fuat; Tokdemir, Turgut; Department of Engineering Sciences (2012) This study deals with the use of the generalized finite difference method (GFDM) in perfectly matched layer (PML) analysis of the problems in wave mechanics, in particular, in elastodynamics. It is known that PML plays the role of an absorbing layer, for an unbounded domain, eliminating reflections of waves for all directions of incidence and frequencies. The study is initiated for purpose of detecting any possible advantages of using GFDM in PML analysis: GFDM is a meshless method suitable for any geometry...
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 (2022-01-01) 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-e...
An fMRI segmentation method under markov random fields for brain decoding Aksan, Emre; Yarman Vural, Fatoş Tunay; Department of Computer Engineering (2015) In this study, a specially tailored segmentation method for partitioning the fMRI data into a set of "homogenous" regions with respect to a predefined cost function is proposed. The proposed method, referred as f-MRF, employs univariate and multivariate fMRI data analysis techniques under Markov Random Fields to estimate the segments by resolving a mixture density. The univariate approach helps identifying activation pattern of a voxel independently from other voxels. In order to capture local interactions ...
Probabilistic Slope Stability Analyses Using Limit Equilibrium and Finite Element Methods Akbas, Burak; Huvaj Sarıhan, Nejan (2015-10-16) This paper compares the results of different probabilistic approaches and emphasizes the necessity of probabilistic analyses in slope stability studies. To do that, Limit Equilibrium Method (LEM) and Finite Element Method (FEM) are utilized and their outputs are compared in terms of probability of failure (PF), reliability index (RI), factor of safety (FS) and the failure surface. Lastly, concept of Random Finite Element Method (RFEM) is studied and effects of spatial correlation distance are investigated.
The general lot sizing and scheduling problem with sequence dependent changeovers Koçlar, Ayşe; Süral, Haldun; Department of Industrial Engineering (2005) In this study, we consider the General Lot Sizing and Scheduling Problem in single level capacitated environments with sequence dependent item changeovers. Process industries may be regarded as suitable application areas of the problem. The focus on capacity utilization and intensively time consuming changeovers necessitate the integration of lot sizing and sequencing decisions in the production plan. We present a mathematical model which captures the essence of cases in the most generic and realistic setti...

Citation Formats

F. Korkut, T. Tokdemir, and Y. Mengi, “The use of generalized finite difference method in perfectly matched layer analysis,” APPLIED MATHEMATICAL MODELLING, pp. 127–144, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48436.