A Boundary Integral Equation Related to the Ahlfors Map

The Boundary Integral Equation Method

Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method.

For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are...

Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu,...

A General Boundary Integral Equation Approach to Eddy Current Crack

Eddy current techniques have been widely used in the NDE inspection of aircraft engine components. Depending on the flaw characteristics and specimen composition, various EC probe designs have been employed to achieve the maximum probability of detection (POD). Traditionally, the effectiveness of a probe design for a given inspection is determined experimentally. In particular, parameterssuch a...

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...