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.

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.

Inverse Identification of Heat Boundary Conditions for 2-D Anisotropic Coating Structures

2011 ◽  
Vol 130-134 ◽  
pp. 1825-1828
Author(s):  
Huan Lin Zhou ◽  
Hu Sha Han ◽  
Chang Zheng Cheng ◽  
Zhong Rong Niu
Keyword(s):  
Boundary Element Method ◽  
Singular Value Decomposition ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Singular Integrals ◽  
Singular Value ◽  
Thin Body ◽  
Ill Posed ◽  
Value Decomposition ◽  
Element Method

The singular value decomposition is employed to identify heat boundary conditions for 2-D anisotropic coating structures. The boundary element method is applied to analyzing the model. The nearly singular integrals in the boundary element method for thin body problems are dealt with by the analytical integral formulas. The ill-posed system is treated by the truncated singular value decomposition technique. Numerical example demonstrates the effectiveness and accuracy of the present algorithm.

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.

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