The complex variable boundary-element method is routinely used to determine the complex potential, h 1⁄4 / þ iw, at any position, z 1⁄4 xþ iy, internal to the flow domain. We reverse this mapping by exactly determining the complex position for specified complex potentials––in effect solving for zðhÞ instead of hðzÞ. Direct calculation of the physical location, 1⁄2x; y , of potential, 1⁄2/;w , i...

Recently, Mastroianni and Monegato derived error estimates for a numerical approach to evaluate the integral ∫ b a ∫ 1 −1 f(x, y) x− y dxdy, where (a, b) ≡ (−1, 1) or (a, b) ≡ (a,−1) or (a, b) ≡ (1, b) and f(x, y) is a smooth function (see G. Mastroianni and G. Monegato, Error estimates in the numerical evaluation of some BEM singular integrals, Math. Comp. 7

The spatial density of false measurements is known as clutter density in signal and data processing of targets. It is unknown in practice and its knowledge has a significant impact on the effective processing of target information. This paper presents in the first time a number of theoretically solid estimators for clutter density based on conditional mean, maximum likelihood, and method of mom...

We analyze an adaptive boundary element method for Symm’s integral equation in 2D and 3D which incorporates the approximation of the Dirichlet data g into the adaptive scheme. We prove quasi-optimal convergence rates for any H-stable projection used for data approximation.

The radiation efficiency of an acoustically thick circular cylindrical shell has been examined by calculations using the boundary element method for three different boundary conditions, and by conducting experiments using point excitation with the boundary conditions being free at both ends. Both the numerical and experimental results indicate that the radiation efficiency attains a value of un...

The mixed Dirichlet-Neumann problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in 2 and 3 dimensions. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called the "method of interior boundaries", because additional boundaries are introduced inside scattering bodies, where the Neumann ...

In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze computing results according to diverse precision requirement. Against the malpractice exists in the above process, a new method of error estimation was suggested on H-R adaptive boundary element method in this paper. Based on the discrete meshes that are generated for the process ...

The weak Neumann problem for the Poisson eqution is studied on Lipschitz domain with compact boundary using the direct integral equation method. The domain is bounded or unbounded, the boundary might be disconnected. The problem leads to a uniquely solvable integral equation in H(∂Ω). It is proved that we can get the solution of this equation using the successive approximation method. AMS class...

In the tutorial 3, we presented other examples on the derivation of the boundary integral equation in the direct form. Mainly, elasticity and plate in bending problems were discussed. In this tutorial, we will discuss the definitions and the methods of derivation of fundamental solutions. The use of such solution within the boundary element method was discussed in the former tutorial. A table p...