scholarly journals EFFICIENT CALCULATION OF THE BEM INTEGRALS ON ARBITRARY SHAPES WITH THE FFT

2018 ◽  
Vol 16 (3) ◽  
pp. 405 ◽  
Author(s):  
Justus Benad
Keyword(s):  
Boundary Element Method ◽  
High Resolution ◽  
Boundary Element ◽  
Fourier Transformation ◽  
Fast Fourier Transformation ◽  
Numerical Techniques ◽  
Low Resolution ◽  
Boundary Integrals ◽  
Efficient Calculation ◽  
Arbitrary Shapes

This paper builds upon the results of a recent study which illustrates how the Fast Fourier Transformation (FFT) can be used to accelerate the Boundary Element Method (BEM) for arbitrary shapes. In the present work, we further deepen this understanding and focus especially on implementation details in order to calculate the boundary integrals with the FFT. Different numerical techniques are compared for an exemplary shape. Also, additions to the concept are mentioned such as the introduction of a high-resolution grid close to the boundary and a low-resolution grid farther away.

The efficient calculation of the normal matrix in least-squares refinement of macromolecular structures

1999 ◽  
Vol 55 (4) ◽  
pp. 700-703 ◽  
Author(s):  
Dale E. Tronrud
Keyword(s):  
Fourier Transformation ◽  
Matrix Method ◽  
Fourier Transforms ◽  
Optimization Procedure ◽  
Computer Time ◽  
Normal Matrix ◽  
Fast Fourier Transformation ◽  
Great Cost ◽  
Full Matrix ◽  
Efficient Calculation

The optimization procedure with the greatest power of convergence is the full-matrix method. This method has not been utilized to a great extent in macromolecular refinement because of the great cost of both calculating and inverting the `normal' matrix. This paper describes an algorithm that can calculate this matrix in a relatively short amount of computer time. The procedure requires two Fourier transforms, which can be performed with the fast-Fourier transformation (FFT) algorithm, as well as a large number of simple function products.

A Boundary Element Method Without Internal Cells for Two-Dimensional and Three-Dimensional Elastoplastic Problems

2001 ◽  
Vol 69 (2) ◽  
pp. 154-160 ◽  
Author(s):  
X.-W. Gao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Initial Stresses ◽  
Boundary Integrals ◽  
Transformation Technique ◽  
Weakly Singular ◽  
Simple Boundary ◽  
Singular Domain ◽  
Element Method

In this paper, a new and simple boundary element method without internal cells is presented for the analysis of elastoplastic problems, based on an effective transformation technique from domain integrals to boundary integrals. The strong singularities appearing in internal stress integral equations are removed by transforming the domain integrals to the boundary. Other weakly singular domain integrals are transformed to the boundary by approximating the initial stresses with radial basis functions combined with polynomials in global coordinates. Three numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

Fast Calculation of Far-Field Sound Directivity Based on Fast Multipole Boundary Element Method

2020 ◽  
Vol 28 (04) ◽  
pp. 1950024
Author(s):  
Takayuki Masumoto ◽  
Yosuke Yasuda ◽  
Naohisa Inoue ◽  
Tetsuya Sakuma
Keyword(s):  
Boundary Element Method ◽  
High Resolution ◽  
Boundary Element ◽  
Conventional Method ◽  
Numerical Results ◽  
Computational Time ◽  
Fast Method ◽  
Far Field ◽  
Fast Multipole ◽  
Element Method

A fast method for calculating sound radiation/reflection directivities at high resolution in the infinite far field is proposed with the use of the fast multipole boundary element method (FMBEM). This method calculates directivities using direction-dependent coefficients called outgoing coefficients, which are obtained in the calculation process of the matrix-vector products in the FMBEM. Since the outgoing coefficients are generally calculated for a large number of directions high-resolution directivities can be easily obtained with extremely small computational cost and minor modifications in the FMBEM program codes. It is confirmed via comparison with the numerical results using the conventional method that the proposed method can calculate directivities at infinity. Numerical results also show that the computational time for the proposed method is significantly shorter than that for the conventional method with no addition of the required memory.

scholarly journals 2-D Numerical Wave Tank by Boundary Element Method Using Different Numerical Techniques

2013 ◽  
Vol 1 (1) ◽  
Author(s):  
Farid Habashi Aliabadi ◽  
Parviz Ghadimi ◽  
Seyed Reza Djeddi ◽  
Abbas Dashtimanesh
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Wave Tank ◽  
Numerical Techniques ◽  
Wave Tank ◽  
Numerical Wave ◽  
Element Method

scholarly journals CALCULATION OF THE IMPROPER INTEGRALS FOR FOURIER BOUNDARY ELEMENT METHOD

2013 ◽  
Vol 3 (3) ◽  
pp. 7-10
Author(s):  
Edyta Łukasik ◽  
Beata Pańczyk ◽  
Jan Sikora
Keyword(s):  
Partial Differential Equations ◽  
Boundary Element Method ◽  
Differential Equations ◽  
Boundary Element ◽  
Numerical Approach ◽  
Numerical Techniques ◽  
Matrix Coefficients ◽  
Improper Integrals ◽  
Galerkin Boundary Element Method ◽  
Element Method

The traditional Boundary Element Method (BEM)  is a collection of numerical techniques for solving some partial differential equations. The classical BEM produces a fully populated coefficients matrix. With Galerkin Boundary Element Method (GBEM) is possible to produce a symmetric coefficients matrix. The Fourier BEM is a more general numerical approach. To calculate the final matrix coefficients it is necessary to find the improper integrals.  The article presents the method for calculation of such integrals.

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