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.  

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 Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

The Boundary Element Method to Solve the 2D Elastic Stress and Displacement Problem

2011 ◽  
Vol 117-119 ◽  
pp. 1774-1778
Author(s):  
Zhong Ping Yang ◽  
Nan Cong
Keyword(s):  
Differential Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Stress ◽  
Basic Solution ◽  
Displacement Problem ◽  
Numerical Example ◽  
Elastic Mechanics ◽  
Element Method

With the balance of elastic mechanics differential equation and basic solution(Kelvin solution) As the foundation introduced the boundary element method for calculating the stress and displacement of elastomer. With a numerical example of the algorithm proved. The results show that the method can be more accurate solving 2 D elastic stress and displacement problem.

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