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 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 ...

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...

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, ...

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

in this paper, shielding effectiveness (se) of a perforated enclosure with imperfectly conducting walls is evaluated. to this end, first, an accurate numerical technique based on method of moments (mom) ispresented. in this method, lossy metallic walls of the enclosure are replaced by equivalent electric surfacecurrent sources. then, the impedance boundary condition on the imperfectly conductin...

This paper investigates the buckling of finite isotropic rectangular plates with circular cutout under uniaxial and biaxial loading. The complex potential method is used to calculate the pre-buckling stress distribution around the cutout in the plate with finite dimensions. To satisfy the in-plane boundary conditions, the generalized complex-potential functions are introduced and a new method b...

We present several coupled finite and boundary element formulations for the vibro-acoustic simulation of completely immersed bodies such as submarines. All formulations are based on the different use of standard boundary integral equations. In addition to the well known symmetric coupling we discuss two different approaches which are based on the weakly singular boundary integral equation only.

in this article, a transversely isotropic linear elastic half-space with depth wise isotropy axis of material containing a cylindrical cavity of finite length is considered to be under the effect of an arbitrary torsion force applied on the wall of the cavity. to this end, the equation of equilibrium has been written in a cylindrical coordinate system, by dividing the involved domain to two reg...