Boundary element methods for potential problems

Boundary element methods for potential problems with nonlinear boundary conditions

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

Finite Element and Boundary Element Methods for Transient Acoustic Problems

The paper focuses on the numerical treatment of transient acoustic problems using finite element (FE) and boundary element (BE) methods. The FE method relies on a pressure formulation and the use of an implicit integration schemes for solving the related second-order differential system. The procedure is shown on cavity (interior) problems but can be extended to exterior problems using the DtN ...

Boundary element methods for high frequency scattering problems

where n is the outward normal, Φ(x,y) = i 4H (1) 0 (k|x − y|) is the fundamental solution to the two-dimensional Helmholtz equation, and the coupling parameter η 6= 0 ensures that the integral equation has a unique solution for all k. The conventional approach to solving this boundary integral equation, applying a Galerkin method in which ∂u/∂n is approximated by piecewise polynomials, suffers ...

Developments in Boundary Element Methods for Time-dependent Problems

The Cell Boundary Element Methods for Multiscale Elliptic Problems

ABSTRACT In this paper we consider the following elliptic problem: L (u ) = −∇ · (a ∇u ) = f on Ω, (1a) u = 0 on ∂Ω. (1b) Here, and in what follows, set a (x) = a(y) where y = x and Ω is a convex polygonal domain or a smooth boundary. We assume that the conductivity a is an I-periodic, symmetric tensor. Localized problem for each K ∈ Kh: −∇ · a ∇u = f in K, [(a ∇u ) · ν] = 0 on ep = ∂K ∩ ∂K ′, ...