cretization of certain boundary integral equations on a very general class of two-dimensional domains with corner points. The resulting quadrature rules allow for the rapid high accuracy solution of Laplace’s equation and the Helmholtz equation on such domains. Our approach can be adapted to many other boundary value problems as well as to the case of surfaces with singularities in three dimens...

Free space Green's functions are derived for graded materials in which the thermal conductivity varies exponentially in one coordinate. Closed form expressions are obtained for the steady state di usion equation, in two and three dimensions. The corresponding boundary integral equation formulations for these problems are derived, and the three-dimensional case is solved numerically using a Gale...

Abstract: A theory is derived for plasmons in two-dimensional (2D) materials by using three-dimensional (3D) plasmon theory, which was reported previously in the random phase approximation under high frequency conditions. When the 3D local electron density is expressed by the 2D local electron density n2D multiplied by the delta function in the thickness direction, a self-consistent integral eq...

We propose a rigorous full-vector integral-equation formulation for analyzing modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic mode field is completely determined by the y-component electric and magnetic field functions on the interfaces between sl...

Reports and Memoranda No. 3447* August, z964 Summary. Existing methods of calculating the incompressible turbulent boundary layer have been critically examined and the results that they give compared with a large amount of published experimental data. The investigation has shown that different methods of calculating shape-factor development give, in general, widely different results and are in ...

In this paper, we present a method for solving the rst kind Abel integral equation. In thismethod, the rst kind Abel integral equation is transformed to the second kind Volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. By using Sidi's sinm - transformation and modied Navot-Simpson'sintegration rule, an algorithm for solving this...

Method. G. H. Rawitscher, I. Koltracht and R. A. Gonzales Physics and Mathematics Departments, University of Connecticut, Storrs, CT 06268, USA A new spectral type method for solving the one dimensional quantummechanical Lippmann-Schwinger integral equation in configuration space is described. The radial interval is divided into partitions, not necessarily of equal length. Two independent local...

infiltration is a complex process that changed by initial moisture and water head on the soil surface. the main objective of this study was to estimate the coefficients of infiltration equations, kostiakov-lewis, philip and horton, and evaluate the sensitivity of these equations and their coefficients under various initial conditions (initial moisture soil) and boundary (water head on soil surf...

In this paper, we will present composite boundary elements (CBE) for classical Fredholm boundary integral equations. These new boundary elements allow the low-dimensional discretisation of boundary integral equation where the minimal number of degrees of freedom is independent of the, possibly, huge number of charts which are necessary to describe a complicated surface. The applications are thr...

In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎ ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then...