scholarly journals Solving the complete-electrode direct model of ERT using the boundary element method and the method of fundamental solutions

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
T. E. Dyhoum ◽  
D. Lesnic ◽  
R. G. Aykroyd
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Stable Solution ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Direct Model ◽  
Complete Electrode Model ◽  
Simply Connected ◽  
The Mathematical Model ◽  
Element Method

This paper discusses solving the forward problem for electrical resistance tomography (ERT). The mathematical model is governed by Laplace's equation with the most general boundary conditions forming the so-called complete electrode model (CEM). We examine this problem in simply-connected and multiply - connected domains (rigid inclusion, cavity and composite bi-material). This direct problem is solved numerically using the boundary element method (BEM) and the method of fundamental solutions (MFS). The resulting BEM and MFS solutions are compared in terms of accuracy, convergence and stability. Anticipating the findings, we report that the BEM provides a convergent and stable solution, whilst the MFS places some restrictions on the number and location of the source points.

A Methodology Based on Structural Finite Element Method-Boundary Element Method and Acoustic Boundary Element Method Models in 2.5D for the Prediction of Reradiated Noise in Railway-Induced Ground-Borne Vibration Problems

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Dhananjay Ghangale ◽  
Aires Colaço ◽  
Pedro Alves Costa ◽  
Robert Arcos
Keyword(s):  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Noise Analysis ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Noise And Vibration ◽  
Model Soil ◽  
Acoustic Bem ◽  
Element Method

This work is focused on the analysis of noise and vibration generated in underground railway tunnels due to train traffic. Specifically, an analysis of noise and vibration generated by train passage in an underground simple tunnel in a homogeneous full-space is presented. In this methodology, a two-and-a-half-dimensional coupled finite element and boundary element method (2.5D FEM-BEM) is used to model soil–structure interaction problems. The noise analysis inside the tunnel is performed using a 2.5D acoustic BEM considering a weak coupling. The method of fundamental solutions (MFS) is used to validate the acoustic BEM methodology. The influence of fastener stiffness on vibration and noise characteristic inside a simple tunnel is investigated.

scholarly journals Coupling the BEM/TBEM and the MFS for the Numerical Simulation of Wave Propagation in Heterogeneous Fluid-Solid Media

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
António Tadeu ◽  
Igor Castro
Keyword(s):  
Wave Propagation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Transient Analysis ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Cpu Time ◽  
Solid Media ◽  
Full Domain ◽  
Element Method

This paper simulates wave propagation in an elastic medium containing elastic, fluid, rigid, and empty heterogeneities, which may be thin. It uses a coupling formulation between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS). The full domain is divided into subdomains, which are handled separately by the BEM/TBEM or the MFS, to overcome the specific limitations of each of these methods. The coupling is enforced by applying the prescribed boundary conditions at all medium interfaces. The accuracy, efficiency, and stability of the proposed algorithms are verified by comparing the results with reference solutions. The paper illustrates the computational efficiency of the proposed coupling formulation by computing the CPU time and the error. The transient analysis of wave propagation in the presence of a borehole driven in a cracked medium is used to illustrate the potential of the proposed coupling formulation.

Failure Analysis of Anisotropic Plates by the Boundary Element Method

2014 ◽  
Vol 30 (6) ◽  
pp. 561-570 ◽  
Author(s):  
A. Sahli ◽  
S. Boufeldja ◽  
S. Kebdani ◽  
O. Rahmani
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Integration ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Anisotropic Plates ◽  
Second Derivatives ◽  
Dynamic Formulation ◽  
Derivatives Of ◽  
Element Method

AbstractThis paper presents a dynamic formulation of the boundary element method for stress and failure criterion analyses of anisotropic thin plates. The elastostatic fundamental solutions are used in the formulations and inertia terms are treated as body forces. The radial integration method (RIM) is used to obtain a boundary element formulationithout any domain integral for general anisotropic plate problems. In the RIM, the augmented thin plate spline is used as the approximation function. A formulation for transient analysis is implemented. The time integration is carried out using the Houbolt method. Integral equations for the second derivatives of deflection are developed and all derivatives of fundamental solutions are computed analytically. Only the boundary is discretized in the formulation. Numerical results show good agreement with results available in literature as well as finite element results.

scholarly journals A comparative study of the direct boundary element method and the dual reciprocity boundary element method in solving the Helmholtz equation

2007 ◽  
Vol 49 (1) ◽  
pp. 131-150 ◽  
Author(s):  
Song-Ping Zhu ◽  
Yinglong Zhang
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Frequency Domain ◽  
Boundary Element ◽  
Fundamental Solutions ◽  
Numerical Accuracy ◽  
Keywords And Phrases ◽  
Direct Boundary Element Method ◽  
Accurate Numerical Solution ◽  
Element Method

In this paper, we compare the direct boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) for solving the direct interior Helmholtz problem, in terms of their numerical accuracy and efficiency, as well as their applicability and reliability in the frequency domain. For BEM formulation, there are two possible choices for fundamental solutions, which can lead to quite different conclusions in terms of their reliability in the frequency domain. For DRBEM formulation, it is shown that although the DBREM can correctly predict eigenfrequencies even for higher modes, it fails to yield a reasonably accurate numerical solution for the problem when the frequency is higher than the first eigenfrequency. 2000 Mathematics subject classification: primary 65N38; secondary 35Q35. Keywords and phrases: the dual reciprocity boundary element method (DRBEM), Helmholtz equation, irregular frequencies.

A Fast Multipole Boundary Element Method Based on Legendre Series for Three-Dimensional Potential Problems

2012 ◽  
Vol 468-471 ◽  
pp. 426-429
Author(s):  
Chun Xiao Yu ◽  
Hai Yuan Yu ◽  
Yi Ming Chen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Multipole Expansion ◽  
Fundamental Solutions ◽  
Fast Multipole ◽  
Legendre Series ◽  
Truncation Errors ◽  
Potential Problems ◽  
Element Method

Vectorization expressions of a Fast Multipole Boundary Element Method (FM-BEM) based on Legendre series are presented for three-dimensional (3-D) potential problems. The formulas are applied to the expression of fundamental solutions for the Boundary Element Method(BEM). Truncation errors of the multipole expansion and local expansion are deduced and analyzed. It shows that the errors can be controlled by truncation terms.

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