Relevant bibliographies by topics / Fractal interpolation functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Fractal interpolation functions'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Fractal interpolation functions"

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Al-Jawfi, Rashad A. "3D Fractal Interpolation Functions." Nanoscience and Nanotechnology Letters 12, no. 1 (January 1, 2020): 120–23. http://dx.doi.org/10.1166/nnl.2020.3081.

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For visualizing one, two- and/or three-dimensional data, reconstruction mechanism is generally considered. In the present study, I have examined the application of iterated function systems in interpolation. I have also presented new fractal interpolation derivations for three-dimensional scalar data. The interpolations can indicate uncertainty of the data, allow tenability from the data, represent the data statistically at different scales, and may also more accurately facilitate data analysis.
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Bouboulis, P., and L. Dalla. "Fractal Interpolation Surfaces derived from Fractal Interpolation Functions." Journal of Mathematical Analysis and Applications 336, no. 2 (December 2007): 919–36. http://dx.doi.org/10.1016/j.jmaa.2007.01.112.

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Barnsley, Michael F. "Fractal functions and interpolation." Constructive Approximation 2, no. 1 (December 1986): 303–29. http://dx.doi.org/10.1007/bf01893434.

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Barnsley, M. F., J. Elton, D. Hardin, and P. Massopust. "Hidden Variable Fractal Interpolation Functions." SIAM Journal on Mathematical Analysis 20, no. 5 (September 1989): 1218–42. http://dx.doi.org/10.1137/0520080.

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DENİZ, Ali, and Yunus ÖZDEMİR. "Graph-directed fractal interpolation functions." TURKISH JOURNAL OF MATHEMATICS 41 (2017): 829–40. http://dx.doi.org/10.3906/mat-1604-39.

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Chand, A. K. B., N. Vijender, P. Viswanathan, and A. V. Tetenov. "Affine zipper fractal interpolation functions." BIT Numerical Mathematics 60, no. 2 (September 6, 2019): 319–44. http://dx.doi.org/10.1007/s10543-019-00774-3.

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Drakopoulos, V., and N. Vijender. "Univariable affine fractal interpolation functions." Theoretical and Mathematical Physics 207, no. 3 (June 2021): 689–700. http://dx.doi.org/10.1134/s0040577921060015.

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KAPOOR, G. P., and SRIJANANI ANURAG PRASAD. "CUBIC SPLINE SUPER FRACTAL INTERPOLATION FUNCTIONS." Fractals 22, no. 01n02 (March 2014): 1450005. http://dx.doi.org/10.1142/s0218348x14500054.

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In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown that, for an equidistant partition points of [x0, xN], the interpolating Cubic Spline SFIF[Formula: see text] and their derivatives [Formula: see text] converge respectively to the data generating function y(x) ≡ y(0)(x) and its derivatives y(j)(x) at the rate of h2-j+ϵ(0 < ϵ < 1), j = 0, 1, 2, as the norm h of the partition of [x0, xN] approaches zero. The convergence results for Cubic Spline SFIF found here show that any desired accuracy can be achieved in the approximation of a regular data generating function and its derivatives by a Cubic Spline SFIF and its corresponding derivatives.
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Igudesman, Konstantin, Marsel Davletbaev, and Gleb Shabernev. "New Approach to Fractal Approximation of Vector-Functions." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/278313.

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This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.
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NAVASCUÉS, M. A., S. K. KATIYAR, and A. K. B. CHAND. "MULTIVARIATE AFFINE FRACTAL INTERPOLATION." Fractals 28, no. 07 (November 2020): 2050136. http://dx.doi.org/10.1142/s0218348x20501364.

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Fractal interpolation functions capture the irregularity of some data very effectively in comparison with the classical interpolants. They yield a new technique for fitting experimental data sampled from real world signals, which are usually difficult to represent using the classical approaches. The affine fractal interpolants constitute a generalization of the broken line interpolation, which appears as a particular case of the linear self-affine functions for specific values of the scale parameters. We study the [Formula: see text] convergence of this type of interpolants for [Formula: see text] extending in this way the results available in the literature. In the second part, the affine approximants are defined in higher dimensions via product of interpolation spaces, considering rectangular grids in the product intervals. The associate operator of projection is considered. Some properties of the new functions are established and the aforementioned operator on the space of continuous functions defined on a multidimensional compact rectangle is studied.
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Dissertations / Theses on the topic "Fractal interpolation functions"

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Medišauskas, Edvinas. "Koliažu grįstos fraktalinių interpoliacinių funkcijų generavimo procedūros sudarymas ir tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2007. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2007~D_20070816_143711-31633.

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Darbe pateikiamas naujas lokaliojo koliažo principu grįstas fraktalinių interpoliacinių funkcijų generavimo algoritmas (procedūra) su pilna kompiuterine realizacija. Siūlomas įrankis orientuotas į realaus pasaulio objektų (sistem��), pasižyminčių "atsikartojimu savyje" (fraktališkumu), modeliavimą. Atlikti preliminarūs eksperimentai patvirtina metodo perspektyvumą.
In the paper, a new method (tool) for the generation of fractal interpolation functions is presented. The proposed interpolation tool is oriented to process data arrays having links with real-world objects. The interpolation process itself explores self-similiarities found within data arrays under processing, as well as exciting properties of the local collage theorem. Some preliminary experimental results are presented.
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Treifi, Muhammad. "Fractal-like finite element method and strain energy approach for computational modelling and analysis of geometrically V-notched plates." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/fractallike-finite-element-method-and-strain-energy-approach-for-computational-modelling-and-analysisof-geometrically-vnotched-plates(93e63366-8eef-4a29-88a4-0c89cf13ec1f).html.

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The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a notch-tip is modelled accurately in the FFEM using a few unknowns, leading to reduction of the computational cost.The analytical expressions of displacements and stresses around a notch tip are derived for different cases of notch problems: in-plane (modes I and II) conditions and out-of-plane (mode III) conditions for isotropic and bi-material notches. These expressions, which are eigenfunction series expansions, are then incorporated into the FFEM to carry out the transformation of the displacements of the singular nodes and to compute the notch SIFs directly without the need for post-processing. Different numerical examples of notch problems are presented and results are compared to available published results and solutions obtained by using other numerical methods.A strain energy approach (SEA) is also developed to extract the notch SIFs from finite element (FE) solutions. The approach is based on the strain energy of a control volume around the notch-tip. The strain energy may be computed using commercial FE packages, which are only capable of computing SIFs for crack problems and not for notch problems. Therefore, this approach is a strong tool for enabling analysts to compute notch SIFs using current commercial FE packages. This approach is developed for comparison of the FFEM results for notch problems where available published results are scarce especially for the bi-material notch cases.A very good agreement between the SEA results and the FFEM results is illustrated. In addition, the accuracy of the results of both procedures is shown to be very good compared to the available results in the literature. Therefore, the FFEM as a stand-alone procedure and the SEA as a post-processing technique, developed in this research, are proved to be very accurate and reliable numerical tools for computing the SIFs of a general notch in isotropic homogeneous and bi-material plates.
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Jančiukaitė, Giedrė. "Teoriniai ir praktiniai fraktalinių interpoliacinių funkcijų sudarymo aspektai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050608_161133-37268.

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This thesis introduces fractal interpolation functions, exposes advantages of fractal interpolation of real world objects and presents some newly developed procedures, associated with fractal interpolation process. The work briefly presents the context needed for introduction of fractal approach and relevant definitions. Also, the detailed description of fractal generating algorithms (deterministic, random iteration, “escape time”) as well as fractal classifications is presented. Since the research object is theoretical and practical aspects of fractal interpolation function analysis, special attention is paid to geometric fractals, obtained using systems of iterated functions (IFS). The notion of a fractal interpolation function is introduced in the work. The author shows that it is possible to generate fractal interpolation functions for various types of data. The generated functions are “close” (in the sense of Housdorf dimension) to the data under processing, i.e., it is possible to ensure that the fractal interpolation graph dimension were equal to the fractal dimension of experimental data (graph). The random iteration algorithm is used for the analysis of fractal interpolation functions, since it is relatively simple and fast enough. The author makes an attempt to analyze and solve the problem of choosing interpolation points (general case). A few approaches are proposed, namely the uniform distribution of interpolation points (for the interactive use) and collage. On... [to full text]
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Pesquet-Popescu, Béatrice. "Modélisation bidimensionnelle de processus non stationnaires et application à l'étude du fond sous-marin." Cachan, Ecole normale supérieure, 1998. http://www.theses.fr/1998DENS0021.

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Dans cette thèse, nous proposons des généralisations anisotropes des champs 2D de type fractal. Tout d'abord, nous introduisons les champs 2D à accroissements stationnaires fractionnaires et nous montrons que le mouvement brownien fractionnaire appartient à cette classe de processus. L'intérêt d'une analyse multi résolution de ces champs est démontré théoriquement et sur un exemple d'application à la localisation sous-marine. Pour la modélisation de données, un moyen efficace pour caractériser les textures à accroissements stationnaires est fourni par la fonction de structure. Nous soulignons la possibilité de contrôler l'anisotropie de ces champs par le biais de cette fonction, dont nous proposons également plusieurs modèles. La fonction de structure est aussi employée pour l'interpolation des champs non stationnaires à accroissements stationnaires. Un autre aspect de ce travail concerne les extensions bidimensionnelles des processus ARIMA fractionnaires et leurs liens avec les champs continus présentés. Finalement, nous considérons des processus auto-similaires non-gaussiens et étudions les statistiques de leurs coefficients d'ondelettes.
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Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.

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In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.
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Book chapters on the topic "Fractal interpolation functions"

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Hardin, Douglas P. "Wavelets are Piecewise Fractal Interpolation Functions." In Fractals in Multimedia, 121–35. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9244-6_6.

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Jha, Sangita, and A. K. B. Chand. "Zipper Rational Quadratic Fractal Interpolation Functions." In Advances in Intelligent Systems and Computing, 229–41. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5411-7_18.

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Chand, A. K. B., and K. R. Tyada. "Positivity Preserving Rational Cubic Trigonometric Fractal Interpolation Functions." In Mathematics and Computing, 187–202. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2452-5_13.

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Chand, A. K. B., and K. R. Tyada. "Constrained 2D Data Interpolation Using Rational Cubic Fractal Functions." In Mathematical Analysis and its Applications, 593–607. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_49.

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Chand, A. K. B., and K. M. Reddy. "Monotonicity Preserving Rational Cubic Graph-Directed Fractal Interpolation Functions." In Advances in Intelligent Systems and Computing, 253–67. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5411-7_20.

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Berkner, K. "A Wavelet-based Solution to the Inverse Problem for Fractal Interpolation Functions." In Fractals in Engineering, 81–92. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0995-2_7.

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Chand, A. K. B., P. Viswanathan, and K. M. Reddy. "A Novel Approach to Surface Interpolation: Marriage of Coons Technique and Univariate Fractal Functions." In Mathematical Analysis and its Applications, 577–92. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2485-3_48.

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Banerjee, Santo, D. Easwaramoorthy, and A. Gowrisankar. "Fractal Interpolation Function for Countable Data." In Understanding Complex Systems, 61–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62672-3_4.

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Chand, A. K. B., and N. Vijender. "$$\mathcal{C}^{1}$$ -Rational Cubic Fractal Interpolation Surface Using Functional Values." In Fractals, Wavelets, and their Applications, 349–67. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08105-2_22.

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Ri, SongIl, and Vasileios Drakopoulos. "How Are Fractal Interpolation Functions Related to Several Contractions?" In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92662.

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This chapter provides an overview of several types of fractal interpolation functions that are often studied by many researchers and includes some of the latest research made by the authors. Furthermore, it focuses on the connections between fractal interpolation functions resulting from Banach contractions as well as those resulting from Rakotch contractions. Our aim is to give theoretical and practical significance for the generation of fractal (graph of) functions in two and three dimensions for interpolation purposes that are not necessarily associated with Banach contractions.
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Conference papers on the topic "Fractal interpolation functions"

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Chand, A. K. B., and P. Viswanathan. "Cubic hermite and cubic spline fractal interpolation functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756439.

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DRAKOPOULOS, V., and L. DALLA. "SPACE-FILLING CURVES GENERATED BY FRACTAL INTERPOLATION FUNCTIONS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0080.

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Kurdila, Andrew, Tong Sun, and Praveen Grama. "Affine fractal interpolation functions and wavelet-based finite elements." In 36th Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-1410.

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ZHANG, BIN, JUNFENG WANG, and GUOXIANG SONG. "THE CONSTRUCTION OF BIORTHOGONAL MULTI-SCALING FUNCTIONS POSSESSING HIGHER APPROXIMATION ORDER WITH FRACTAL INTERPOLATION FUNCTIONS." In Proceedings of the Third International Conference on WAA. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812796769_0102.

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Craciunescu, Oana I., Shiva K. Das, Terrence Z. Wong, and Thaddeus V. Samulski. "Fractal Reconstruction of Breast Perfusion Before and After Hyperthermia Treatments." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33692.

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Thermal modeling for hyperthermia breast patients can provide relevant information to better understand the temperatures achieved during treatment. However, human breast is much perfused, making knowledge of the perfusion crucial to the accuracy of the temperature computations. It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index (RPI) determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI). It was also concluded that the 3D reconstruction of tumor perfusion can be performed using fractal interpolation functions (FIF). The technique used was called piecewise hidden variable fractal interpolation (PHVFI). Changes in the protocol parameters for the dynamic MRI sequences in breast patients allowed us to be able to acquire more spatial slices, hence the possibility to actually verify the accuracy of the fractal interpolation. The interpolated slices were compared to the imaged slices in the original set. The accuracy of the interpolation was tested on post-hyperthermia treatment data set. The difference between the reconstruction and the original slice varied from 2 to 5%. Significantly, the fractal dimension of the interpolated slices is within 2–3% from the original images, thus preserving the fractality of the perfusion maps. The use of such a method becomes crucial when tumor size and imaging restrictions limits the number of spatial slices, requiring interpolation to fill the data between the slices.
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Treifi, Muhammad, Derek K. L. Tsang, and S. Olutunde Oyadiji. "Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35563.

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The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.
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Levkovich-Maslyuk, Leonid I. "Determination of the scaling parameters of affine fractal interpolation functions with the aid of wavelet analysis." In SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Michael A. Unser, Akram Aldroubi, and Andrew F. Laine. SPIE, 1996. http://dx.doi.org/10.1117/12.255302.

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Bedabrata Chand, Arya Kumar. "Natural Bicubic Spline Coalescence Fractal Interpolation Function." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2012. http://dx.doi.org/10.5176/2251-1911_cmcgs53.

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Treifi, Muhammad, and S. Olutunde Oyadiji. "Computations of SIFs for Non-Symmetric V-Notched Plates by the FFEM." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86585.

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The present paper further develops The Fractal-like Finite Element Method (FFEM) to compute the stress intensity factors (SIFs) for non-symmetrical configurations of sharp V-notched plates. The use of global interpolation functions (GIFs) in the FFEM significantly reduces the number of unknown variables (nodal displacements) in a singular region surrounding a singular point to a small set of generalised coordinates. The same exact analytical solutions of the notch tip asymptotic field derived for a symmetrical notch case can be used as GIFs when the notch is non-symmetrical. However, appropriate local coordinate transformation in the singular region is required to obtain the correct global stiffness matrix. Neither post-processing technique to extract SIFs nor special singular elements to model the singular region are required. Any conventional finite elements can be used to model the singular region. The SIFs are directly computed because of the use of exact analytical solutions as GIFs whose coefficients (generalised coordinates) are the unknowns in the singular region. To demonstrate the accuracy and efficiency of the FFEM to compute the SIFs and model the singularity at a notch tip of non-symmetrical configurations of notched plates, various numerical examples are presented and results are validated via available published data.
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Ye, Ruisong, Yucheng Chen, and Qiulin Wu. "A Color Image Encryption Scheme Using Inverse Fractal Interpolation Function." In 2018 IEEE 4th International Conference on Computer and Communications (ICCC). IEEE, 2018. http://dx.doi.org/10.1109/compcomm.2018.8780765.

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