Application of a new composite BIE for 3-D acoustic problems
نویسندگان
چکیده
Applications of a new and efficient composite BIE formulation for 3-D acoustic problems are studied in this paper, based on an improved weakly-singular form of the hypersingular boundary integral equation (HBIE). This new form of the HBIE involves only tangential derivatives of the density function and thus its discretization using the boundary element method (BEM) is easier to perform. C continuous (conforming) quadratic elements are employed in the discretization of this weakly-singular form of the HBIE, as compared with using nonconforming and/or C continuous boundary elements which were advocated earlier. Numerical examples of both scattering and radiation problems with various geometries are presented in this paper to demonstrate the accuracy and versatility of this improved composite BIE for 3-D acoustics.
منابع مشابه
A weakly singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems
The composite boundary integral equation (BIE) formulation, using a linear combination of the conventional BIE and the hypersingular BIE, emerges as the most effective and efficient formula for acoustic wave problems in an exterior medium which is free of the well-known fictitious eigenfrequency difficulty. The crucial part in implementing this formulation is dealing with the hypersingular inte...
متن کاملDirectly Derived Non-Hyper-Singular Boundary Integral Equations for Acoustic Problems, and Their Solution through Petrov-Galerkin Schemes
Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r−2) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity...
متن کاملHypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions
A weakly singular form of the hypersingular boundary integral equation (BIE) (traction equation) for 3-D elastic wave problems is developed in this paper. All integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements, regular quadrature and collocation procedures used for conventional BIEs are sufficient for the discretization of the or...
متن کاملA Boundary Meshless Method for Neumann Problem
Boundary integral equations (BIE) are reformulations of boundary value problems for partial differential equations. There is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. In this paper, the Neumann problem is reformulated to a BIE, and then moving least squares as a meshless method is describe...
متن کاملNon-Hyper-Singular Boundary Integral Equations for Acoustic Problems, Implemented by the Collocation-Based Boundary Element Method
The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integr...
متن کامل