Stress Wave Propagation in Cracked Geological Solids Using Finite Difference Scheme

2018 ◽  
Vol 09 (01) ◽  
pp. 1750009
Author(s):  
P. A. Kakavas ◽  
N. A. Kalapodis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Scheme ◽  
Analytical Solutions ◽  
Stress Wave Propagation ◽  
The Finite Element Method ◽  
The Finite Difference Method

The aim of this study is the numerical computation of the wave propagation in crack geological solids. The finite difference method was applied to solve the differential equations involved in the problem. Since the problem is symmetric, we prefer to use this technique instead of the finite element method and/or boundary elements technique. A comparison of the numerical results with analytical solutions is provided.

HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION

2001 ◽  
Vol 09 (02) ◽  
pp. 671-680 ◽  
Author(s):  
W. A. MULDER
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Wave Equation ◽  
Finite Elements ◽  
Finite Difference Method ◽  
Seismic Wave Propagation ◽  
The Finite Element Method ◽  
Efficient Scheme ◽  
The Finite Difference Method

The finite-element method (FEM) with mass lumping is an efficient scheme for modeling seismic wave propagation in the subsurface, especially in the presence of sharp velocity contrasts and rough topography. A number of numerical simulations for triangles are presented to illustrate the strength of the method. A comparison to the finite-difference method shows that the added complexity of the FEM is amply compensated by its superior accuracy, making the FEM the more efficient approach.

scholarly journals The optimal dimensions of the domain for solving the single-band Schrödinger equation by the finite-difference and finite-element methods

2014 ◽  
Vol 11 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Dusan Topalovic ◽  
Stefan Pavlovic ◽  
Nemanja Cukaric ◽  
Milan Tadic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Element Methods ◽  
Ground State ◽  
Difference Method ◽  
Grid Size ◽  
The Finite Element Method ◽  
The Finite Difference Method

The finite-difference and finite-element methods are employed to solve the one-dimensional single-band Schr?dinger equation in the planar and cylindrical geometries. The analyzed geometries correspond to semiconductor quantum wells and cylindrical quantum wires. As a typical example, the GaAs/AlGaAs system is considered. The approximation of the lowest order is employed in the finite-difference method and linear shape functions are employed in the finite-element calculations. Deviations of the computed ground state electron energy in a rectangular quantum well of finite depth, and for the linear harmonic oscillator are determined as function of the grid size. For the planar geometry, the modified P?schl-Teller potential is also considered. Even for small grids, having more than 20 points, the finite-element method is found to offer better accuracy than the finite-difference method. Furthermore, the energy levels are found to converge faster towards the accurate value when the finite-element method is employed for calculation. The optimal dimensions of the domain employed for solving the Schr?dinger equation are determined as they vary with the grid size and the ground-state energy.

Finite-Difference Method Appliance to the Computation of Ground Additional Stress and Settlement of Storage Tank

2011 ◽  
Vol 243-249 ◽  
pp. 2638-2642
Author(s):  
Xu Dong Cheng ◽  
Wen Shan Peng ◽  
Lei Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Storage Tank ◽  
Three Dimensional ◽  
Additional Stress ◽  
The Finite Element Method ◽  
The Finite Difference Method

This paper adopts the Finite-difference method to research the distribution of ground additional stress and distortion in differently isotropic and non-isotropic foundation conditions, and uses the Finite-difference method to compare with the Finite-element method and the three-dimensional settlement method used by the code. Through comparative analysis, the reliability and superiority of Finite-difference method used for calculating ground additional stress and settlement are justified.

scholarly journals The finite difference versus the finite element method for the solution of boundary value problems

1984 ◽  
Vol 29 (2) ◽  
pp. 267-288
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
The Finite Element Method ◽  
Discretization Schemes ◽  
The Finite Difference Method ◽  
Element Method

In this lecture we describe, discuss and compare the two classes of methods most commonly used for the numerical solution of boundary value problems for partial differential equations, namely, the finite difference method and the finite element method. For both of these methods an extensive development of mathematical error analysis has taken place but individual numerical analysts often express strong prejudices in favor of one of them. Our purpose is to try to convey our conviction that this attitude is both historically unjustified and inhibiting, and that familiarity with both methods provides a wider range of techniques for constructing and analyzing discretization schemes.

Study and Simulate the Air Pollution Based on the Finite Difference Method

2012 ◽  
Vol 518-523 ◽  
pp. 2820-2824
Author(s):  
Yi Ni Guo ◽  
Yan Zhang ◽  
Jian Wang ◽  
Ye Huang
Keyword(s):  
Finite Element Method ◽  
Air Pollution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
The Finite Element Method ◽  
Liquid Diffusion ◽  
Continuous Problems ◽  
The Finite Difference Method ◽  
The Difference

The finite difference method that is the finite element method is used to solve the plane continuous problems. In this article, the theory and method of the finite difference method, as well as the application on the boundary problem are introduced. By analyzing the potential flew field equation and liquid diffusion equation, they are discreted using the difference method and the numerical analysis under certain boundary condition is conducted. In air pollution, the smoke in the diffusion is typical planar continuous problems. In this paper, the finite difference method is used to analyse and simulate the spread of the smoke.

The role and application of entropy terms for acoustic wave modeling by the finite‐difference method

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1457-1465 ◽  
Author(s):  
M. A. Dablain
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Acoustic Wave Propagation ◽  
Central Difference ◽  
Central Difference Scheme ◽  
One Dimensional ◽  
The Finite Difference Method

The significance of entropy‐like terms is examined within the context of the finite‐difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central‐difference scheme, and (2) the Lax‐Wendroff two‐step scheme. Numerical results are presented comparing the short‐wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one‐dimensional source is used.

Sharpening of metal sheets during electrochemical polishing. Theory and experiments

1984 ◽  
Vol 49 (5) ◽  
pp. 1267-1276
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference Method ◽  
The Finite Element Method ◽  
Electrochemical Polishing ◽  
Electrochemical Parameters ◽  
Metal Sheets ◽  
The Finite Difference Method ◽  
Shape Changes ◽  
Theory And Experiments

The electrochemical polishing with simultaneous shape changes of anodes was studied. A theory was derived based on the knowledge of basic electrochemical parameters and the solution of the Laplace equation. To this purpose, the finite element method and the finite difference method with a double transformation of the inter-electrode region were employed. Only the former method proved well and can therefore be recommended for different geometries.

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