scispace - formally typeset

Integral equation

About: Integral equation is a(n) research topic. Over the lifetime, 41607 publication(s) have been published within this topic receiving 768093 citation(s). more

More filters

01 Jan 1947-
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. more

7,401 citations

01 Jan 1989-
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. more

5,482 citations

Journal ArticleDOI
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. more

5,170 citations

Journal ArticleDOI
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. more

4,499 citations

Network Information
Related Topics (5)
Boundary value problem

145.3K papers, 2.7M citations

92% related
Electric-field integral equation

4.4K papers, 79.5K citations

91% related
Basis function

15.6K papers, 405.6K citations

90% related
Green's function

4.9K papers, 78.8K citations

90% related
Maxwell's equations

13.7K papers, 262K citations

90% related
No. of papers in the topic in previous years

Top Attributes

Show by:

Topic's top 5 most impactful authors

Weng Cho Chew

189 papers, 11K citations

Eric Michielssen

103 papers, 2.9K citations

Khosrow Maleknejad

87 papers, 2K citations

Tapan K. Sarkar

80 papers, 2.5K citations

Balasubramaniam Shanker

61 papers, 974 citations