A Well-Conditioned Hypersingular Boundary Element Method for Electrostatic Potentials in the Presence of Inhomogeneities within Layered Media

2016 ◽  
Vol 19 (4) ◽  
pp. 970-997 ◽  
Author(s):  
Brian Zinser ◽  
Wei Cai
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Layered Media ◽  
Dielectric Materials ◽  
Electrostatic Potentials ◽  
Iterative Solvers ◽  
Condition Numbers ◽  
Janus Particle ◽  
Integral Equation Formulation ◽  
Element Method

AbstractIn this paper, we will present a high-order, well-conditioned boundary element method (BEM) based on Müller's hypersingular second kind integral equation formulation to accurately compute electrostatic potentials in the presence of inhomogeneity embedded within layered media. We consider two types of inhomogeneities: the first one is a simple model of an ion channel which consists of a finite height cylindrical cavity embedded in a layered electrolytes/membrane environment, and the second one is a Janus particle made of two different semi-spherical dielectric materials. Both types of inhomogeneities have relevant applications in biology and colloidal material, respectively. The proposed BEM gives condition numbers, allowing fast convergence of iterative solvers compared to previous work using first kind of integral equations. We also show that the second order basis converges faster and is more accurate than the first order basis for the BEM.

Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis

1987 ◽  
Vol 109 (1) ◽  
pp. 15-21 ◽  
Author(s):  
A. F. Seybert ◽  
C. Y. R. Cheng
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Transmission Loss ◽  
Radiation Condition ◽  
Boundary Integral ◽  
Exterior Problems ◽  
Integral Equation Formulation ◽  
Element Method

This paper is concerned with the application of the Boundary Element Method (BEM) to interior acoustics problems governed by the reduced wave (Helmholtz) differential equation. The development of an integral equation valid at the boundary of the interior region follows a similar formulation for exterior problems, except for interior problems the Sommerfeld radiation condition is not invoked. The boundary integral equation for interior problems does not suffer from the nonuniqueness difficulty associated with the boundary integral equation formulation for exterior problems. The boundary integral equation, once obtained, is solved for a specific geometry using quadratic isoparametric surface elements. A simplification for axisymmetric cavities and boundary conditions permits the solution to be obtained using line elements on the generator of the cavity. The present formulation includes the case where a node may be placed at a position on the boundary where there is not a unique tangent plane (e.g., at an edge or a corner point). The BEM capability is demonstrated for two types of classical interior axisymmetric problems: the acoustic response of a cavity and the transmission loss of a muffler. For the cavity response comparison data are provided by an analytical solution. For the muffler problem the BEM solution is compared to data obtained by a finite element method analysis.

Fast Multipole Boundary Element Method for 3-Dimension Acoustic Radiation Problem

2011 ◽  
Vol 130-134 ◽  
pp. 80-85
Author(s):  
Bing Rong Zhang ◽  
Jian Chen ◽  
Li Tao Chen ◽  
Wu Zhang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Acoustic Radiation ◽  
Cell Structure ◽  
Level Structure ◽  
Iterative Solvers ◽  
Influence Coefficient ◽  
Fast Multipole ◽  
Element Method

In order to reduce computational complexity and memory requirements using conventional boundary element method (CBEM) for large scale acoustical analysis, a fast solving algorithm called the Fast Multipole BEM (FMBEM) based on the fast multipole algorithm and GMRES iterative solver is developed without composing the dense influence coefficient matrices. The multipole level structure is introduced to accelerate the solution of large-scale acoustical problems, by employing a concept of cells clustering boundary elements and hierarchical cell structure. To further improve the efficiency of the FMBEM with iterative solvers, a block diagonal matrix method is used in the system of equations as the left pre-conditioner. Numerical examples are presented to further demonstrate the efficiency, accuracy and potentials of the fast multipole BEM for solving large-scale acoustical problems.

A topology optimisation of 3 dielectric materials with the boundary element method

2016 ◽  
Vol 2016.12 (0) ◽  
pp. 2205
Author(s):  
Yusuke MATSUDA ◽  
Hiroshi ISAKARI ◽  
Toru TAKAHASHI ◽  
Toshiro MATSUMOTO
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Dielectric Materials ◽  
Topology Optimisation ◽  
Element Method

BOUNDARY ELEMENT SOLUTION OF A BODY'S EXTERIOR ACOUSTIC FIELD NEAR ITS INTERNAL EIGENVALUES

1993 ◽  
Vol 01 (03) ◽  
pp. 335-353 ◽  
Author(s):  
R. A. MARSCHALL
Keyword(s):  
Integral Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Value ◽  
Practical Implementation ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Value Decomposition ◽  
Element Method ◽  
Helmholtz Integral

A relatively straightforward Boundary Element Method (BEM) for the numerical solution of the exterior Helmholtz problem is specified in a tutorial fashion. The algorithm employs the Combined Helmholtz Integral Equation Formulation (CHIEF) and then Singular Value Decomposition (SVD) to solve the resulting system. Its accuracy and convergence characteristics are examined, and compared to the simplest boundary element method for exterior acoustics, the Helmholtz Integral Equation Formulation or HIEF. Boundary element and auxiliary (CHIEF) point requirements to obtain BEM solutions of a desired accuracy are described. This particular CHIEF algorithm is found to largely avoid the numerical difficulties of the HIEF technique while retaining theoretical and practical implementation simplicity.

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