We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singula...

To predict the sound field in an acoustic problem, the well-known non-uniqueness problem has to be solved. In a departure from the common approaches used in the prior literature, the weak-form of the Helmholtz differential equation, in conjunction with vector test-functions, is utilized as the basis, in order to directly derive non-hyper-singular boundary integral equations for the velocity pot...

The structural-acoustic optimization shows high potential in minimization of radiated noise especially for thin shell geometries. Acoustic design sensitivity analysis can provide information on how the geometry change affects the acoustic performance of the given structure, so it is an important step of the acoustic design and optimization processes. But the sensitivity analysis of the structur...

The construction of geometry models of heart-torso is critical for solving the forward and inverse problems of magnetoand electro-cardiography (MCG/ECG). Boundary element method (BEM) is a commonly used numerical approach for the solution of these problems and it requires the modeling of interfaces between various tissue regions. In this study, a new BEM (h-adaptive type) has been applied to th...

Narrow, open-circuited aluminum electrodes can provide controllable, weak reflectivity necessary for many applications such as surface acoustic wave (SAW) tags and dispersive delay lines (DDLs). We show, using finiteand boundary element method (FEM-BEM) based simulations and experiments, that a reflectivity of 0.3% per wavelength can be achieved easily and controlled by varying the electrode wi...

In this paper we describe the theory and code implementation of a tool to obtain the time-dependent pressure distribution on a marine structure using the results from a boundary element method code (BEM). Here, we present a case study of a floating wave energy converter (WEC) in regular waves. The results are verified by comparison with open-source codes and then used to run a structural simula...

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of openboundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. PACS. 41.20.Cv Electrostatics; Poisson and Laplace equatio...

In this chapter we investigate local errors and condition numbers in the BEM. The results of these investigations are important in guiding adaptive meshing strategies and solvability of linear systems in BEM. We show that the local error for the BEM with constant or linear elements decreases quadratically with the boundary element mesh size. We also investigate better ways of treating boundary ...

We present cubature methods for the approximation of surface integrals arising from Galerkin discretizations of 3-D boundary integral equations. This numerical integrator is fully implicit in the sense that the form of the kernel function, the surface parametrization, the trial and test space, and the order of the singularity of the kernel functions are not used explicitly. Different kernels ca...

It is well known that BEM/BIEM result in degenerate scale for two-dimensional Laplace problem subjected to the Dirichlet boundary condition. In such a case, nontrivial boundary flux exist even the trivial boundary potential is given. It is proved that the unit logarithmic capacity in the Riemann conformal mapping with respect to the unit circle results in a null field for the interior domain. T...