The volume integral equation method in magnetostatic problem

Volume Integral Equation Method in Problems of

Preface In our course we will consider the volume integral equations in the following form) () () () () () (x f dy y u y b y x y x K x u x a Q m = − − + ∫ , 3 ≤ m. Many important classes of the wave scattering problems can be described by equations of this form; for example, this is the case for problems of electromagnetic and acoustic scattering on 3D transparent bodies. The corresponding inte...

A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena

The analysis of elastic wave propagation and scattering is an important issue in fields such as earthquake engineering, nondestructive testing, and exploration for energy resources. Since the 1980s, the boundary integral equation method has played an important role in the analysis of both forward and inverse scattering problems. For example, Colton and Kress (1998) presented a survey of a vast ...

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

The Boundary Integral Equation Method

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...