Evaluation of terrain effects in AEM surveys using the boundary element method

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 272-278 ◽  
Author(s):  
Guimin Liu ◽  
Alex Becker
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Scale Model ◽  
Mountainous Areas ◽  
Secondary Field ◽  
Topographic Features ◽  
Terrain Effects ◽  
Audio Range ◽  
Element Method

In mountainous areas, electromagnetic terrain effects are readily observed in the course of VLF (14–20 kHz) measurements made on the surface and constitute a serious source of geological noise that affects the collected data. One may, therefore, inquire whether similar effects will be observed during the course of conventional helicopter‐towed electromagnetic (HEM) surveys as the frequency of the newer systems is increased beyond the lower regions of the audio range. To answer the question, we have evaluated the terrain effects that would be observed with a conventional HEM system in a number of simple cases. The operating frequency chosen for most of the numerical simulations was 8 kHz, while the topographic features investigated were taken to be two‐dimensional. The calculations were done using the boundary element method of solving the appropriate integral equations. Accuracy of the numerical solutions was shown to vary from 1 percent for a half space to 10 percent for a shallow valley where the verification was done on a laboratory scale model. For the models investigated, the amplitude of the computed secondary fields shows a distinct correlation with the overflown topography. Surprisingly, however, the phase of the secondary field remains invariant and so may be reliably used to compute the resistivity of the terrain below the aircraft.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

scholarly journals Simulation of Partial and Supercavitating Flows around Axisymmetric and Quasi-3D Bodies by Boundary Element Method Using Simple and Reentrant Jet Models at the Closure Zone of Cavity

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
M. Nouroozi ◽  
M. Pasandidehfard ◽  
M. H. Djavareshkian
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Navier Stokes Equations ◽  
Short Time ◽  
Element Method

A fixed-length Boundary Element Method (BEM) is used to investigate the super- and partial cavitating flows around various axisymmetric bodies using simple and reentrant jet models at the closure zone of cavity. Also, a simple algorithm is proposed to model the quasi-3D cavitating flows over elliptical-head bodies using the axisymmetric method. Cavity and reentrant jet lengths are the inputs of the problem and the cavity shape and cavitation number are some of the outputs of this simulation. A numerical modeling based on Navier-Stokes equations using commercial CFD code (Fluent) is performed to evaluate the BEM results (in 2D and 3D cases). The cavitation properties approximated by the present research study (especially with the reentrant jet model) are very close to the results of other experimental and numerical solutions. The need for a very short time (only a few minutes) to reach the desirable convergence and relatively good accuracy are the main advantages of this method.

Boundary Element Method Analysis for the Bioheat Transfer Equation

1992 ◽  
Vol 114 (3) ◽  
pp. 358-365 ◽  
Author(s):  
Cho Lik Chan
Keyword(s):  
Steady State ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Conjugate Problem ◽  
Bioheat Transfer ◽  
Bioheat Equation ◽  
Method Analysis ◽  
Good Agreement ◽  
Element Method

In this paper, the boundary element method (BEM) approach is applied to solve the Pennes (1948) bioheat equation. The objective is to develop the BEM formulation and demonstrate its feasibility. The basic BEM formulations for the transient and steady-state cases are first presented. To demonstrate the usefulness of the BEM approach, numerical solutions for 2-D steady-state problems are obtained and compared to analytical solutions. Further, the BEM formulation is applied to model a conjugate problem for an artery imbedded in a perfused heated tissue. Analytical solution is possible when the conduction in the x-direction is negligible. The BEM and analytical results have very good agreement.

MULTISCALE BOUNDARY ELEMENT METHOD FOR LAPLACE EQUATION

2016 ◽  
Vol 78 (3-2) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Munira Ismail ◽  
Nor Atirah Izzah Zulkefli ◽  
Yeak Su Hoe
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Laplace Equation ◽  
Numerical Solutions ◽  
New Technique ◽  
Fortran Compiler ◽  
Numerical Example ◽  
Comparison Results ◽  
Speed Up ◽  
Element Method

In this paper, the multiscale boundary element method is applied to solve the Laplace equation numerically. The new technique is the coupling of the multiscale technique and the boundary element method in order to speed up the computation. A numerical example is given to illustrate the efficiency of the proposed method. The computed numerical solutions by the proposed method will be compared with the solutions obtained by the conventional boundary element method with the help of Fortran compiler. By comparison, results show that the new technique use less iterations to arrive at the solutions.  

A Boundary Element Method Based on the Hierarchical Matrices and Multipole Expansion Theory for Acoustic Problems

2018 ◽  
Vol 15 (03) ◽  
pp. 1850009 ◽  
Author(s):  
Xiujuan Liu ◽  
Haijun Wu ◽  
Weikang Jiang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Multipole Expansion ◽  
Hierarchical Matrices ◽  
Low Rank ◽  
Scale Model ◽  
Degenerate Kernel ◽  
Set Up ◽  
Element Method

The coefficient matrices of conventional boundary element method (CBEM) are dense and fully populated. Special techniques such as hierarchical matrices (H-matrices) format are required to extent its ability of handling large-scale problems. Adaptive cross approximation (ACA) algorithm is a widely adopted algorithm to obtain the H-matrices. However, the accuracy of the ACA boundary element method (ACABEM) cannot be adjusted by changing the tolerance [Formula: see text] when it exceeds a certain value. In this paper, the degenerate kernel approximation idea for the low-rank matrices is developed to build a fast BEM for acoustic problems by exploring the multipole expansion of the kernel, which is referred as the multipole expansion H-matrices boundary element method (ME-H-BEM). The newly developed algorithm compresses the far-field submatrices into low rank submatrices with the expansion terms of Green’s function. The obtained H-matrices are applied in conjunction with the generalized minimal residual method (GMRES) to solve acoustic problems. Numerical examples are carefully set up to compare the accuracy, efficiency as well as memory consumption of the CBEM, ACABEM, fast multipole boundary element method (FMBEM) and ME-H-BEM. The results of a pulsating sphere indicate that the ME-H-BEM keeps both storage and operation logarithmic-linear complexity of the H-matrices format as the ACABEM does. Moreover, the ME-H-BEM can achieve better convergence and higher accuracy than the ACABEM. For the analyzed complicated large-scale model, the ME-H-BEM with appropriate number of expansion terms has an advantage in terms of efficiency as compared with the ACABEM. Compared with the FMBEM, the ME-H-BEM is easier to be implemented.

ANALYSIS OF RING CRACKS IN CERAMIC ROLLING ELEMENTS USING THE BOUNDARY ELEMENT METHOD

Tribologia ◽  
2019 ◽  
Vol 285 (3) ◽  
pp. 51-59
Author(s):  
Waldemar KARASZEWSKI
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Contact Point ◽  
High Hardness ◽  
Ceramic Materials ◽  
Rolling Contact ◽  
Numerical Calculations ◽  
Three Dimensional Model ◽  
Element Method

Ceramic materials have been increasingly used in bearing systems for over a dozen years. This is due to the specific properties of ceramic materials, such as high hardness, corrosion resistance, the possibility of use in aggressive chemical environments, as well as due to the lower specific weight as compared to steel materials. However, the use of ceramic materials imposes many limitations. The main disadvantages include surface cracks and a low fracture toughness value. The paper presents a numerical analysis of crack propagation in silicon nitride balls. The directions of propagation were analysed for the cracks that are most commonly found on the surface of the commercially available ceramic balls. The directions were analysed along the crack front and considering the location of the crack in relation to the contact point of the balls in the rolling contact. The numerical calculations are based on a three-dimensional model of the ring crack. Numerical calculations were carried out using the boundary element method. Numerical solutions were compared with the results of experimental research.

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