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Journal articles on the topic 'Finite difference method of analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Tang, Hui, Xiao Jun Li, Guo Liang Zhou, and Chun Ming Zhang. "Finite/Explicit Finite Element - Finite Difference Coupling Method for Analysis of Soil - Foundation System." Advanced Materials Research 838-841 (November 2013): 913–17. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.913.

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There are some coupling methods based on Finite Element Method and some other numerical methods, such as Infinite Element Method, Boundary Element Method, Finite Difference Method, etc. But these methods have their own limitations on simulation the foundation. For overcome these disadvantages, a coupling method is presented in this paper, which be proposed to analyze the effect of soil - foundation on seismic response of structures. In this coupling method, the structure and the surrounding soil are simulated with Finite Element method, and the other part of the soil with Explicit Finite Element - Finite Difference Method. Compared to other coupling methods, it is more flexible and its calculation amount is acceptable. The accuracy and effectiveness of the coupling method have been verified through Numerical experiment in this paper.

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2

Dow, John O., Michael S. Jones, and Shawn A. Harwood. "A generalized finite difference method for solid mechanics." Numerical Methods for Partial Differential Equations 6, no. 2 (1990): 137–52. http://dx.doi.org/10.1002/num.1690060204.

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3

Dow, John O., and Ian Stevenson. "Adaptive refinement procedure for the finite difference method." Numerical Methods for Partial Differential Equations 8, no. 6 (November 1992): 537–50. http://dx.doi.org/10.1002/num.1690080604.

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4

ISHIKAWA, Mikihito, Toshihito OHMI, A. Toshimitsu YOKOBORI Jr., and Masaaki NISHIMURA. "OS1010 The Hydrogen Diffusion Analysis by Finite Element Method and Finite Difference Method." Proceedings of the Materials and Mechanics Conference 2014 (2014): _OS1010–1_—_OS1010–3_. http://dx.doi.org/10.1299/jsmemm.2014._os1010-1_.

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5

Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1399–402. http://dx.doi.org/10.22214/ijraset.2021.38153.

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Abstract: Analysis of rectangular plates is common when designing the foundation of civil, traffic, and irrigation works. The current research presents the results of the analysis of rectangular plates using the finite difference method and Finite Element Method. The results of the research verify the accuracy of the FEM and are in agreement with findings in the literature. The plate is analyzed considering it to be completely solid. The ordinary finite difference method is used to solve the governing differential equation of the plate deflection. The proposed method can be easily programmed to readily apply on a plate problem. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. Keywords: rectangular plate, FEM, Finite Difference Method

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6

Gupta, Dr A. R. "Comparative analysis of Rectangular Plate by Finite element method and Finite Difference Method." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1397–98. http://dx.doi.org/10.22214/ijraset.2021.38152.

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Abstract: Plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a comparative analysis of rectangular plate is done between Finite Element Method (FEM) and Finite Difference Method (FDM). The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). FEM subdivides a large problem into smaller, simpler, parts, called finite elements. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis. The ordinary Finite Difference Method (FDM) is used to solve the governing differential equation of the plate deflection. The proposed methods can be easily programmed to readily apply on a plate problem. Keywords: Arbitrary, FEM, FDM, boundary.

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7

Ashyralyyev, Charyyar, Ayfer Dural, and Yasar Sozen. "Finite Difference Method for the Reverse Parabolic Problem." Abstract and Applied Analysis 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/294154.

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A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

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8

Yang, Dongquan, M. K. Rahman, and Yibai Chen. "Bottomhole assembly analysis by finite difference differential method." International Journal for Numerical Methods in Engineering 74, no. 9 (2008): 1495–517. http://dx.doi.org/10.1002/nme.2221.

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9

Virdi, Kuldeep S. "Finite difference method for nonlinear analysis of structures." Journal of Constructional Steel Research 62, no. 11 (November 2006): 1210–18. http://dx.doi.org/10.1016/j.jcsr.2006.06.015.

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10

Tang, X. W., and X. W. Zhang. "Seismic liquefaction analysis by a modified finite element-finite difference method." Japanese Geotechnical Society Special Publication 2, no. 33 (2016): 1204–7. http://dx.doi.org/10.3208/jgssp.chn-58.

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11

Achdou, Yves, Fabio Camilli, and Italo Capuzzo-Dolcetta. "Mean Field Games: Convergence of a Finite Difference Method." SIAM Journal on Numerical Analysis 51, no. 5 (January 2013): 2585–612. http://dx.doi.org/10.1137/120882421.

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12

Huang, Yating, and Zhe Yin. "The Compact Finite Difference Method of Two-Dimensional Cattaneo Model." Journal of Function Spaces 2020 (May 28, 2020): 1–12. http://dx.doi.org/10.1155/2020/6301757.

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In this paper, we propose and analyze the compact finite difference scheme of the two-dimensional Cattaneo model. The stability and convergence of the scheme are proved by the energy method, the convergence orders are 2 in time and 4 in space. We also use the variables separation method to find the true solution of the problem. On this basis, the validity and accuracy of the scheme are verified by numerical experiments.

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13

Junk, Michael. "A finite difference interpretation of the lattice Boltzmann method." Numerical Methods for Partial Differential Equations 17, no. 4 (2001): 383–402. http://dx.doi.org/10.1002/num.1018.

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14

Dow, J. O., and J. L. Hardaway. "Modeling of multimaterial interfaces in the finite difference method." Numerical Methods for Partial Differential Equations 8, no. 5 (September 1992): 493–503. http://dx.doi.org/10.1002/num.1690080507.

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15

Zhang, Jiansong, and Danping Yang. "Parallel characteristic finite difference method for convection-diffusion equations." Numerical Methods for Partial Differential Equations 27, no. 4 (April 11, 2011): 854–66. http://dx.doi.org/10.1002/num.20557.

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16

Roberts, J. L. "A method for calculating meshless finite difference weights." International Journal for Numerical Methods in Engineering 74, no. 2 (September 13, 2007): 321–36. http://dx.doi.org/10.1002/nme.2169.

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17

Blanchard, C. H., G. Gutierrez, J. A. White, and R. B. Roemer. "Hybrid finite element-finite difference method for thermal analysis of blood vessels." International Journal of Hyperthermia 16, no. 4 (January 2000): 341–53. http://dx.doi.org/10.1080/02656730050074104.

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18

Twyman Q., John. "Water hammer analysis using an implicit finite-difference method." Ingeniare. Revista chilena de ingeniería 26, no. 2 (June 2018): 307–18. http://dx.doi.org/10.4067/s0718-33052018000200307.

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19

Kamyabi, Ata, Vahid Kermani, and Mohammadmahdi Kamyabi. "Improvements to the meshless generalized finite difference method." Engineering Analysis with Boundary Elements 99 (February 2019): 233–43. http://dx.doi.org/10.1016/j.enganabound.2018.11.002.

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20

Bagré, Remi Guillaume, Frédéric Béré, and Vini Yves Bernadin Loyara. "Construction of a Class of Copula Using the Finite Difference Method." Journal of Function Spaces 2021 (July 23, 2021): 1–8. http://dx.doi.org/10.1155/2021/5271105.

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The definition of a copula function and the study of its properties are at the same time not obvious tasks, as there is no general method for constructing them. In this paper, we present a method that allows us to obtain a class of copula as a solution to a boundary value problem. For this, we use the finite difference method which is a common technique for finding approximate solutions of partial differential equations which consists in solving a system of relations (numerical scheme) linking the values of the unknown functions at certain points sufficiently close to each other.

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21

Lugo Jiménez, Abdul Abner, Guelvis Enrique Mata Díaz, and Bladismir Ruiz. "A comparative analysis of methods: mimetics, finite differences and finite elements for 1-dimensional stationary problems." Selecciones Matemáticas 8, no. 1 (June 30, 2021): 1–11. http://dx.doi.org/10.17268/sel.mat.2021.01.01.

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Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since such problems present complex geometries, boundary or initial conditions, or involve non-linear differential equations. Currently, the number of problems that are modeled with partial differential equations are diverse and these must be addressed numerically, so that the results obtained are more in line with reality. In this work, a comparison of the classical numerical methods such as: the finite difference method (FDM) and the finite element method (FEM), with a modern technique of discretization called the mimetic method (MIM), or mimetic finite difference method or compatible method, is approached. With this comparison we try to conclude about the efficiency, order of convergence of these methods. Our analysis is based on a model problem with a one-dimensional boundary value, that is, we will study convection-diffusion equations in a stationary regime, with different variations in the gradient, diffusive coefficient and convective velocity.

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22

Anguelov, Roumen, and Jean M. S. Lubuma. "Nonstandard finite difference method by nonlocal approximation." Mathematics and Computers in Simulation 61, no. 3-6 (January 2003): 465–75. http://dx.doi.org/10.1016/s0378-4754(02)00106-4.

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23

Junk, Michael, and Zhaoxia Yang. "Asymptotic analysis of finite difference methods." Applied Mathematics and Computation 158, no. 1 (October 2004): 267–301. http://dx.doi.org/10.1016/j.amc.2003.08.097.

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24

Cimen, Erkan, and Musa Cakir. "Convergence analysis of finite difference method for singularly perturbed nonlocal differential-difference problem." Miskolc Mathematical Notes 19, no. 2 (2018): 795. http://dx.doi.org/10.18514/mmn.2018.2302.

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25

Cangiani, Andrea, Gianmarco Manzini, and Alessandro Russo. "Convergence Analysis of the Mimetic Finite Difference Method for Elliptic Problems." SIAM Journal on Numerical Analysis 47, no. 4 (January 2009): 2612–37. http://dx.doi.org/10.1137/080717560.

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26

Marn, Jure, Marjan Delic, and Zoran Zunic. "Non-Newtonian Fluid Flow Analysis with Finite Difference and Finite Volume Numerical Models." Applied Rheology 11, no. 6 (December 1, 2001): 325–35. http://dx.doi.org/10.1515/arh-2001-0019.

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Abstract Suitability of finite difference method and finite volume method for computation of incompressible non newtonian flow is analyzed. In addition, accuracy of numerical results depending of mesh size is assessed. Both methods are tested for driven cavity and compared to each other, to results from available literature and to results obtained using commercial code CFX 4.3.

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27

Shigeyama, Haruhisa, A. Toshimitsu Yokobori Jr., Toshihito Ohmi, and Takenao Nemoto. "Analysis of Stress Induced Voiding Using by Finite Element Analysis Coupled with Finite Difference Analysis." Defect and Diffusion Forum 326-328 (April 2012): 632–40. http://dx.doi.org/10.4028/www.scientific.net/ddf.326-328.632.

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In this paper, the vacancy migration in Cu interconnect of large scale integration caused by stress induced voiding was calculated using the α multiplication method. Then, the effect of weight coefficient, α, on stress induced vacancy diffusion analysis was investigated and the validity of the α multiplication method was verified. Furthermore, the method of the vacancy diffusion analysis coupled with thermal stress analysis which can consider the history of thermal stress due to temperature changes was proposed. The results of the vacancy diffusion analysis coupled with the thermal stress analysis were compared with the analytical results of the vacancy migration without the effect of history of thermal stress. As a result, the maximum site of vacancy accumulation was found to be qualitatively in good agreement between them. However, the quantitative value of maximum vacancy concentration obtained by the vacancy diffusion analysis coupled with thermal stress analysis was found to be much higher and the vacancy distribution is found to be much more localized.

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28

Cook, Robert D., and Xianrui Huang. "Continuous stress fields by the finite element-difference method." International Journal for Numerical Methods in Engineering 22, no. 1 (January 1986): 229–40. http://dx.doi.org/10.1002/nme.1620220117.

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29

FUJIOKA, Ryosuke, Naoto MITSUME, Tomonori YAMADA, and Shinobu YOSHIMURA. "HYBRID ANALYSIS OF PEDESTRIAN FLOW BY FINITE DIFFERENCE METHOD AND PARTICLE METHOD." Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM)) 75, no. 2 (2019): I_195—I_201. http://dx.doi.org/10.2208/jscejam.75.2_i_195.

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30

Effati Daryani, Mohamadbagher, Hadi Bahadori, and Khalil Effati Daryani. "Soil Probabilistic Slope Stability Analysis Using Stochastic Finite Difference Method." Modern Applied Science 11, no. 4 (January 24, 2017): 23. http://dx.doi.org/10.5539/mas.v11n4p23.

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The paper contrasts results obtained by the partially factored limit state design method and a more advanced Random Finite Difference Method (RFDM) in a benchmark problem of slope stability analysis with variable undrained shear strength. Local Average Subdivision method was used to simulate the non-Gaussian random variables. The key difference between the methods is that RFDM takes into account spatial variability of soil parameters allowing slope failure to occur naturally along the path of least resistance. The probabilistic method leads to predictions of the "probability of slope failure" as opposed to the more traditional "factor of safety" measure of slope safety in the limit state design method; however, they give significant different results depending on the level of the variability. Analyses conducted using Monte Carlo Simulation show that the same partial factor can have very different levels of risk depending on the degree of uncertainty of the mean value of the soil shear strength. Calibration studies show the partial factor necessary to achieve target probability values.

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31

Wallace, Jon W., and Michael A. Jensen. "Analysis of optical waveguide structures by use of a combined finite-difference/finite-difference time-domain method." Journal of the Optical Society of America A 19, no. 3 (March 1, 2002): 610. http://dx.doi.org/10.1364/josaa.19.000610.

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32

Annunziato, Mario. "A FINITE DIFFERENCE METHOD FOR PIECEWISE DETERMINISTIC PROCESSES WITH MEMORY." Mathematical Modelling and Analysis 12, no. 2 (June 30, 2007): 157–78. http://dx.doi.org/10.3846/1392-6292.2007.12.157-178.

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In this paper the numerical approximation of solutions of Liouville‐Master Equation for time‐dependent distribution functions of Piecewise Deterministic Processes with memory is considered. These equations are linear hyperbolic PDEs with non‐constant coefficients, and boundary conditions that depend on integrals over the interior of the integration domain. We construct a finite difference method of the first order, by a combination of the upwind method, for PDEs, and by a direct quadrature, for the boundary condition. We analyse convergence of the numerical solution for distribution functions evolving towards an equilibrium. Numerical results for two problems, whose analytical solutions are known in closed form, illustrate the theoretical finding.

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33

., K. Soren. "STABILITY ANALYSIS OF OPEN PIT SLOPE BY FINITE DIFFERENCE METHOD." International Journal of Research in Engineering and Technology 03, no. 05 (May 25, 2014): 326–34. http://dx.doi.org/10.15623/ijret.2014.0305062.

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34

OHNAKA, Itsuo, and Keizo KOBAYASHI. "Flow analysis during solidification by the direct finite difference method." Transactions of the Iron and Steel Institute of Japan 26, no. 9 (1986): 781–89. http://dx.doi.org/10.2355/isijinternational1966.26.781.

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35

Kim Chi Kyung. "Structural Stability Analysis of Circular Arches using Finite Difference Method." Journal of Risk Management 21, no. 2 (December 2010): 125–41. http://dx.doi.org/10.21480/tjrm.21.2.201012.005.

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36

Min, Bog-Ki, Chun-Hong Park, and Sung-Chong Chung. "Thermal Analysis of Ballscrew Systems by Explicit Finite Difference Method." Transactions of the Korean Society of Mechanical Engineers A 40, no. 1 (January 1, 2016): 41–51. http://dx.doi.org/10.3795/ksme-a.2016.40.1.041.

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37

Khalaj-Amirhosseini, Mohammad. "ANALYSIS OF LOSSY INHOMOGENEOUS PLANAR LAYERS USING FINITE DIFFERENCE METHOD." Progress In Electromagnetics Research 59 (2006): 187–98. http://dx.doi.org/10.2528/pier05091201.

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38

Huang, W., C. Xu, S. T. Chu, and S. K. Chaudhuri. "The finite-difference vector beam propagation method: analysis and assessment." Journal of Lightwave Technology 10, no. 3 (March 1992): 295–305. http://dx.doi.org/10.1109/50.124490.

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39

TSURU, Hideo, and Kunikazu Hirosawa. "739 Noise Analysis by Finite Difference Method and Boundary Integral." Proceedings of the Dynamics & Design Conference 2006 (2006): _739–1_—_739–6_. http://dx.doi.org/10.1299/jsmedmc.2006._739-1_.

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40

Guo, Shangping, Feng Wu, Sacharia Albin, and Robert S. Rogowski. "Photonic band gap analysis using finite-difference frequency-domain method." Optics Express 12, no. 8 (2004): 1741. http://dx.doi.org/10.1364/opex.12.001741.

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41

YU. SHAHVERDIAN, A. "THE FINITE-DIFFERENCE METHOD OF ONE-DIMENSIONAL NONLINEAR SYSTEMS ANALYSIS." Fractals 08, no. 01 (March 2000): 49–65. http://dx.doi.org/10.1142/s0218348x0000007x.

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The paper introduces one-dimensional analogy of Poincare "section" method. It reduces the one-dimensional nonlinear system orbit's study to consideration of some special conjugate orbit's "asymptotical" intersections with a thin arithmetical space of zero Lebesgue measure. The application of this approach to analysis of the logistic map orbits, earthquake time-series, and the sequences of fractional parts, is considered. Through computational study of these time-series, the existence of some Cantor sets, to which the conjugate orbits are attracted, is established. A fractal dynamical system, describing these different systems from a unified point of view, is introduced. The inner differential Cantorian structure of brain activity and time flow is discussed.

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42

Reineix, A., T. Monediere, and F. Jecko. "Ferrite analysis using the finite-difference time-domain (FDTD) method." Microwave and Optical Technology Letters 5, no. 13 (December 1992): 685–86. http://dx.doi.org/10.1002/mop.4650051311.

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43

Yamauchi, Junji, Takashi Ando, and Hisamatsu Nakano. "Propagating beam analysis by alternating-direction implicit finite-difference method." Electronics and Communications in Japan (Part II: Electronics) 75, no. 9 (1992): 54–62. http://dx.doi.org/10.1002/ecjb.4420750906.

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44

Grinenko, A., P. D. Wilcox, C. R. P. Courtney, and B. W. Drinkwater. "Acoustic radiation force analysis using finite difference time domain method." Journal of the Acoustical Society of America 131, no. 5 (May 2012): 3664–70. http://dx.doi.org/10.1121/1.3699204.

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45

Yang, Xiao-Dong, Wei Zhang, Li-Qun Chen, and Ming-Hui Yao. "Dynamical analysis of axially moving plate by finite difference method." Nonlinear Dynamics 67, no. 2 (April 23, 2011): 997–1006. http://dx.doi.org/10.1007/s11071-011-0042-2.

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46

Goyal, Priyanka, Soumya Gupta, Gurjit Kaur, and Brajesh Kumar Kaushik. "Performance analysis of VCSEL using finite difference time domain method." Optik 156 (March 2018): 505–13. http://dx.doi.org/10.1016/j.ijleo.2017.11.201.

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47

Yan, Zhi-xin, Jian Duan, Ping Jiang, Zi-zhen Liu, Hong-liang Zhao, and Wen-gui Huang. "Finite difference method for dynamic response analysis of anchorage system." Journal of Central South University 21, no. 3 (March 2014): 1098–106. http://dx.doi.org/10.1007/s11771-014-2042-0.

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48

Beirão da Veiga, L., K. Lipnikov, and G. Manzini. "Convergence analysis of the high-order mimetic finite difference method." Numerische Mathematik 113, no. 3 (May 28, 2009): 325–56. http://dx.doi.org/10.1007/s00211-009-0234-6.

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49

Yuan, Yirang. "The upwind finite difference fractional steps method for nonlinear coupled systems." Numerical Methods for Partial Differential Equations 23, no. 5 (2007): 1037–58. http://dx.doi.org/10.1002/num.20208.

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50

Lin, Yuan, Xuejun Gao, and MingQing Xiao. "A high-order finite difference method for 1D nonhomogeneous heat equations." Numerical Methods for Partial Differential Equations 25, no. 2 (March 2009): 327–46. http://dx.doi.org/10.1002/num.20345.

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