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...

We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method has optimal complexity with respec...

AbstructIn basic electrostatics, the formula for the capacitance of parallel-plate capacitors is derived, for the case that the spacing between the electrodes is very small compared to the length or width of the plates. However, when the separation is wide, the formula for very small separation does not provide accurate results. In our previously published papers, we use the boundary element me...

Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp we have implemented a complete operator algebra that depends on knowledge of the domain, ...

We analyze the h-p version of the bem for mixed Dirichlet Neumann problems of the Laplacian in polyhedral domains. Based on a regularity analysis of the solution in count-ably normed spaces we show that the boundary element Galerkin solution of the h-p version converges exponentially fast on geometrically graded meshes.