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...

The aim of the present paper is to associate a new symmetric boundary integral method to well known symmetric domain methods with the purpose of improving solutions of multi-eld problems with coupled boundary and domain methods. From a single-eld variational principle for a 3D linear, elastodynamic state a three-eld hybrid principle is developed by Hamiltons principle and decoupling displacemen...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

The optical eld in a weakly guiding homogeneous waveguide satis es scalar Helmholtz equations in both the core and cladding, and transmission conditions on the boundary. The transverse wavenumbers of the two scalar Helmholtz equations for the core and cladding are di erent and both of them depend on the propagation constants in the longitudinal direction of the waveguide. Two di erent systems o...

We provide a new method to study the classical Dirichlet problem for Laplace's equation on a convex polyhedron. This new approach was motivated by Fokas' unified method for boundary value problems. The central object in this approach is the global relation: an integral equation which couples the known boundary data and the unknown boundary values. This integral equation depends holomorphically ...

Fredholm integral equations arise naturally in the context of ordinary and partial differential equations: Two-point boundary value problems can be reformulated as Fredholm integral equations, whose kernels are continuous but have finite jump discontinuities in their derivatives. Two-dimensional elliptic boundary problems can be reformulated as Fredholm integral equations with kernels that have...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one t...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to ch...

This paper presents to the solutions of the acoustic problem using dual reciprocity boundary element method (DRBEM). The acoustic propagates inside the silencer and its sound can be formulated by the three dimensional (3D) Helmholtz equation. The form of the equation is which can be solved by the integral form on the boundary. The conventional boundary element method (BEM) is not suitable for s...

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...