𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A NON-SINGULAR BOUNDARY INTEGRAL EQUATION FOR ACOUSTIC PROBLEMS

✍ Scribed by B.-U. Koo; B.-C. Lee; J.-G. Ih

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
547 KB
Volume
192
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

✦ Synopsis

A weakly singular boundary integral equation and a non-singular one are derived for acoustic problems. By using the one-dimensional wave propagation mode, the degree of the singularities appearing in the conventional boundary integral equation can be reduced. Since the strong singularity is removed in the weakly singular equation, the jump term of the field pressure expression in the very vicinity of the boundary disappears. It is shown that the weak singularity can be also removed for a smooth boundary in the non-singular representation, and thus special treatments for singular integral are no longer needed. In order to test the proposed method, several simple problems have been solved by employing the triangular element with standard Gaussian quadrature integration points. The results obtained show the accuracy of the method in the near field as well as on the boundary.

πŸ“œ SIMILAR VOLUMES

A singular function boundary integral me
A singular function boundary integral method for the Laplace equation
✍ Georgiou, Georgios C. ;Olson, Lorraine ;Smyrlis, Yiorgos S. πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 464 KB πŸ‘ 2 views

The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic expansion. The essential boundary conditions are weakly enforced by means of app

Free-Boundary Problem for a Singular Dif
Free-Boundary Problem for a Singular Diffusion Equation
✍ P.Y.H. Pang; H.Y. Wang; J.X. Yin πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 120 KB

In this paper, we study the free-boundary problem associated with a singular diffusion equation. An entropy equality derived by the authors for BV solutions in an earlier paper is used in its formulation. Existence, uniqueness, and regularity results are obtained.

Non-singular direct formulation of bound
Non-singular direct formulation of boundary integral equations for potential flows
✍ W. S. Hwang; Y. Y. Huang πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 85 KB πŸ‘ 2 views

This paper presents a general direct integral formulation for potential flows. The singularities of Green's functions are desingularized theoretically, using a subtracting and adding back technique, so that Gaussian quadrature or any other numerical integration methods can be applied directly to eva

A local boundary integral equation metho
A local boundary integral equation method for potential problems
✍ R. T. Fenner; J. O. Watson πŸ“‚ Article πŸ“… 1988 πŸ› John Wiley and Sons 🌐 English βš– 710 KB

Boundary integral equation (boundary element) methods have the advantage over other commonly used numerical methods that they do not require values of the unknowns at points within the solution domain to be computed. Further benefits would be obtained if attention could be confined to information at