Integral equation

Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

Abstract: Time--Varying and Time--Harmonic Electromagnetic Fields. Electrical Properties of Matter. Wave Equation and Its Solutions. Wave Propagation and Polarization. Reflection and Transmission. Auxiliary Vector Potentials, Contruction of Solutions, and Radiation and Scattering Equations. Electromagnetic Theorems and Principles. Rectangular Cross--Section Waveguides and Cavities. Circular Cross--Section Waveguides and Cavities. Spherical Transmission Lines and Cavities. Scattering. Integral Equations and the Moment Method. Geometrical Theory of Diffraction. Greena s Functions. Appendices. Index.

Abstract: We present a new integral equation formulation of the polarizable continuum model (PCM) which allows one to treat in a single approach dielectrics of different nature: standard isotropic liquids, intrinsically anisotropic medialike liquid crystals and solid matrices, or ionic solutions. The present work shows that integral equation methods may be used with success also for the latter cases, which are usually studied with three-dimensional methods, by far less competitive in terms of computational effort. We present the theoretical bases which underlie the method and some numerical tests which show both a complete equivalence with standard PCM versions for isotropic solvents, and a good efficiency for calculations with anisotropic dielectrics.

Abstract: The electric field integral equation (EFIE) is used with the moment method to develop a simple and efficient numerical procedure for treating problems of scattering by arbitrarily shaped objects. For numerical purposes, the objects are modeled using planar triangular surfaces patches. Because the EFIE formulation is used, the procedure is applicable to both open and closed surfaces. Crucial to the numerical formulation is the development of a set of special subdomain-type basis functions which are defined on pairs of adjacent triangular patches and yield a current representation free of line or point charges at subdomain boundaries. The method is applied to the scattering problems of a plane wave illuminated flat square plate, bent square plate, circular disk, and sphere. Excellent correspondence between the surface current computed via the present method and that obtained via earlier approaches or exact formulations is demonstrated in each case.