Integral boundary conditions for evolution problems have various applications in chemical engineering, thermoelasticity, underground water flow and population dynamics, see for example [16, 17, 24]. In fact, boundary value problems involving integral boundary conditions have received considerable attention, see for instance, [3, 10], [12]–[15], [18, 19, 26] and the references therein. In a rece...

This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and...

We propose a discrete collocation method for the boundary integral equations which arise from solving Laplace's equation u = 0. The Laplace's equation is deened on connected regions D in R 3 with a smooth boundary S. The piecewise polynomial interpolation in the parametrization variables along with the collocation method is used, and a numerical integration scheme for collocation integrals is g...

We develop a simple, efficient numerical method of boundary integral type for solving an elliptic partial differential equation in a three-dimensional region using the classical formulation of potential theory. Accurate values can be found near the boundary using special corrections to a standard quadrature. We treat the Dirichlet problem for a harmonic function with a prescribed boundary value...

The main purpose of this paper is to develop a fast numerical method for solving the first kind boundary integral equation, arising from the two-dimensional interior Dirichlet boundary value problem for the Helmholtz equation with a smooth boundary. This method leads to a fully discrete linear system with a sparse coefficient matrix. We observe that it requires a nearly linear computational cos...

MKT0000528 › With recent improvements in the efficiency of integral equation solutions it is now possible to combine the integral equation procedure with the finite element method (FEM) in a hybrid Finite Element Boundary Integral approach (FEBI) [1]. In electromagnetics the FEM is a general purpose technique that solves for volumetric electric fields and can be used to accurately characterize ...

A boundary element method has been developed for the analysis of 3D eddy current problems. This method is based on the boundary integral equation formulation with equivalent electric and magnetic currents and electric charge as unknowns. Linear shape functions, defined parametrically over a quadrilateral element, have been selected for the Galerkin’s method.

Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for doublyconnected domain problems, the eccentric and annular membranes, are studied analytically and numerically in this paper. For the mathematical analysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions...

We consider the initial boundary value problem for the heat equation in a region with in nite and nite boundaries (direct problem) and the related problem to reconstruct the nite boundary from Cauchy data on the in nite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an approximate solution of the inverse problem w...

The boundary integral equation (BIE) method was first proposed by Yan and Sakurai [2000], which is used to extrapolate the nonlinear force-free magnetic field in the solar atmosphere. Recently, Yan and Li [2006] improved the BIE method and proposed the direct boundary integral equation (DBIE) formulation, which represents the nonlinear force-free magnetic field by direct integration of the magn...