The Local Point Interpolation–Boundary Element Method: Application to 3D Stationary Thermo-Piezoelectricity

2016 ◽  
Vol 13 (01) ◽  
pp. 1650003 ◽  
Author(s):  
Richard Kouitat Njiwa
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Thermal Conduction ◽  
Linear Equations ◽  
Point Collocation ◽  
Simple Strategy ◽  
Local Point ◽  
Radial Point Interpolation ◽  
Point Interpolation ◽  
Element Method

This paper presents a simple strategy allowing to adapt well-established isotropic BEM approach for the solution of multi-physics problems with anisotropic material parameters. The method is based on the partition of the primary kinematical fields into complementary and particular parts. The isotropic linear equations for the complementary fields are solved by the conventional boundary element method. The particular fields are obtained by a point collocation of a strong form differential equation. Adopting local radial point interpolation, the effectiveness of the approach is proved by considering various examples of stationary thermal conduction, thermos-elasticity and thermos-piezoelectricity.

scholarly journals Spherical Indentation of a Micropolar Solid: A Numerical Investigation Using the Local Point Interpolation–Boundary Element Method

2021 ◽  
Vol 2 (3) ◽  
pp. 581-590
Author(s):  
Gaël Pierson ◽  
M’Barek Taghite ◽  
Pierre Bravetti ◽  
Richard Kouitat Njiwa
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Interpolation Method ◽  
Poisson Ratio ◽  
Young Modulus ◽  
Contact Radius ◽  
Spherical Indentation ◽  
Local Point ◽  
Point Interpolation ◽  
Element Method

The load-penetration curve in elastic nanoindentation of an elastic micropolar flat by a diamond spherical punch is analyzed. The presented results are obtained by a specifically developed numerical tool based on a judicious combination of the conventional boundary element method and strong form local point interpolation method. The results show that the usual linear relationship between the material depression and the square of the radius of the contact area is also valid in this case of micropolar elastic material. It is also shown that the relation between the indentation stress (applied load over the contact surface) and the indentation strain (ratio of contact radius by the punch radius) is linear. The proportionality coefficient which is none other than the indentation stiffness varies with the coupling factor of the micropolar elastic medium. A relation between the indentation stiffness of a micropolar solid and that of a conventional solid with the same Young modulus and Poisson ratio is derived.

Boundary Element Method for Horizontally Polarized Shear Wave Scattering by an Elliptical Cavity in Orthotropic Graded Saturated Porous Media

2014 ◽  
Vol 638-640 ◽  
pp. 412-415
Author(s):  
Jun Qiao Liu ◽  
Hui Qin Duan ◽  
Xing Li
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Shear Wave ◽  
Wave Scattering ◽  
Mass Density ◽  
Linear Equations ◽  
Boundary Surface ◽  
Dirac Delta ◽  
Elliptical Cavity ◽  
Element Method

The shear wave scattering due to an elliptical cavity in an infinitely long strip of orthotropic graded saturated porous (OGSP) media is studied with the boundary element method (BEM). The shear modulus and the mass density of the OGSP are assumed to have exponential forms. Using Biot's theory, the governing equations are developed for OGSP. The fundamental function is obtained by separating variables in terms of the Dirac delta function. A system of linear equations describing the displacement on the ellipse is obtained by applying the linear BEM. The numerical results for the normalized boundary surface displacements in the scattering field are presented with different OGSP coefficients. The effects of many parameters are evaluated with numerical examples. These results are expected to have great technical interest for determining boundary stability when elastic waves interact with OGSP cavities.

The Stability and the Computed Speed of Application Boundary Element Method to Compute the Electric Potential of One Hundred and Fifty-Needle Electrodes

2013 ◽  
Vol 437 ◽  
pp. 245-248
Author(s):  
An Ling Wang ◽  
Fu Ping Liu
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Current Density ◽  
Electric Potential ◽  
Linear Equations ◽  
Discrete Equations ◽  
Linear Current ◽  
The Stability ◽  
Computing Method ◽  
Element Method

According to the electric potential of one hundred and fifty-needle electrodes (OONE), the discrete equations based on the indetermination linear current density were established by the boundary element integral equations (BEIE) The non-uniform distribution of the current flowing from one hundred and fifty-needle electrodes was imaged by solving a set of linear equations. Then, the electric potential generated by OONE at any point can be determined through the boundary element method (BEM). The time of program running and stability of computing method are examined by an example. It demonstrates that the algorithm possesses a quick speed and the steady computed results. It means that this method has an important referenced significance for computing the potential generated by OONE, which is a fast, effective and accurate computing method.

scholarly journals VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method

2016 ◽  
Author(s):  
Chunxiao Yu ◽  
Cuihuan Ren ◽  
Xueting Bai
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Linear Equations ◽  
Iteration Algorithm ◽  
Fast Multipole ◽  
Minimal Residual Method ◽  
Generalized Inverse Matrix ◽  
Selection Of ◽  
Element Method

To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector rm+1 on rm is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.

Laser welding of dissimilar metals aided by unsteady thermal conduction boundary element method analysis

2005 ◽  
Vol 19 (9) ◽  
pp. 687-696 ◽  
Author(s):  
Y Miyashita ◽  
Y Mutoh ◽  
M Akahori ◽  
H Okumura ◽  
I Nakagawa ◽  
...  
Keyword(s):  
Boundary Element Method ◽  
Laser Welding ◽  
Boundary Element ◽  
Thermal Conduction ◽  
Dissimilar Metals ◽  
Method Analysis ◽  
Element Method
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