The accurate evaluation of nearly singular boundary integrals is an important issue in BEM. Several techniques have been developed in recent years, with various degree of success, but it should be stressed that the boundary geometry is depicted essentially by using lower-order elements in those approaches. However, a high level of the geometry approximation in BEM is desired in many application...

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work,...

Simulating wave propagation in 3D configurations is becoming a very active area of research. Themain advantage of the BEM is that only the domain boundaries are discretized. As a result, thismethod is well suited to dealing with unbounded domains. However, the standard BEM leadsto fully-populated matrices, which results in high computational costs in CPU time and mem-ory require...

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress ten...

The direct electro/magnetoencephalographic (E/MEG) problem consists of simulating the electromagnetic field produced by neuronal sources on the cortex. We compare two different methods for the resolution of this problem, from the point of view of computational complexity and accuracy. First, the finite element method (FEM), based on the discretization of the PDE in the entire head volume. Secon...

We consider the Galerkin boundary element method (BEM) for weaklysingular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related s...

The self-noise generated by a flat plate immersed in low Mach number flow is predicted using a hybrid RANS-BEM technique. A Reynolds Averaged Navier-Stokes (RANS) simulation is performed of the turbulent flow over the flat plate. The predicted flow field data, such as mean velocity, turbulent kinetic energy and turbulent dissipation rate, is then processed using a statistical noise model and co...