The cavity of a particular electron accelerator is analysed thanks to boundary integral equations. Electrons are accelerated several times in the median plane of a single coaxial cavity resonating on its fundamental TEMj mode. The geometry of the conductors is modified to improve the shunt impedance. The proper frequency of the new resonator is calculated thanks to Green's function associated t...

Acoustic scattering by three-dimensional obstacles is considered, using boundary integral equations, null-field equations and the T-matrix. Connections between these techniques are explored. It is shown that solving a boundary integral equation by a particular Petrov–Galerkin method leads to the same algebraic system as obtained from the null-field equations. It is also emphasised that the T-ma...

‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...

Multigrid methods are typically used to solve partial differential equations, i.e., they approximate the inverse of the corresponding partial differential operators. At least for elliptic PDEs, this inverse can be expressed in the form of an integral operator by Green's theorem. This implies that multigrid methods approximate certain integral operators , so it is straightforward to look for var...

The aim of the talk is to present an advanced implementation of a direct spacetime Galerkin boundary element method for the discretization of retarded potential boundary integral equations related to Dirichlet-Neumann 2D wave propagation problems defined on multi-domains. This technique, recently introduced for the case of a single-domain [1, 2, 4], is based on a natural energy identity satisfi...

A Regular Indirect Boundary Element formulation is developed following a weighted residual approach. In this formulation, the fictitious source density, which appears in the integral equations of the method, is distributed on a surface which is exteriorly separated from the physical field boundary of the problem. This approach does not require the evaluation of singular integrals and produces u...

Low Reynolds number uid ow past a cylindrical body of arbitrary shape in an unbounded, two-dimensional domain is a singular perturbation problem involving an innnite logarithmic expansion in the small parameter ", representing the Reynolds number. We apply a hybrid asymptotic-numerical method to compute the drag coeecient, C D , and lift coeecient, C L , to within all logarithmic terms. The hyb...

The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for twoand three-dimensional structures, respectively. ...

We study the hand p{versions of the Galerkin boundary element method for integral equations of the rst kind in 2D and 3D which result from the scattering of time harmonic acoustic waves at hard or soft scatterers. We derive an abstract a{posteriori error estimate for indeenite problems which is based on stable multilevel decompositions of our test and trial spaces. The Galerkin error is estimat...

A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. For hypersingular integral equations in 2D with positive-order Sobolev space, we analyze the mathematical relation between the h − h/2error estimator from [18], the two-level error estimator from [22], and the averaging error estimator from [7]. All of these a posteriori error e...