Second-kind integral solvers for TE and TM problems of diffraction by open arcs
نویسندگان
چکیده
[1] We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of weighted versions of the classical integral operators associated with the Dirichlet and Neumann problems (TE and TM polarizations, respectively) together with a generalization to the open-arc case of the well known closed-surface Calderón formulae. When used in conjunction with spectrally accurate discretization rules and Krylov-subspace linear algebra solvers such as GMRES, the new second-kind TE and TM formulations for open arcs produce results of high accuracy in small numbers of iterations—for low and high frequencies alike.
منابع مشابه
A generalized Calderón formula for open-arc diffraction problems: theoretical considerations
We deal with the general problem of scattering by open-arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form Ñ S̃[φ] = f , where Ñ and S̃ are first-kind integral operators whose composition gives rise to a generalized Calderón formula of the form ÑS̃ = J̃τ 0 +K̃ in a weighted, periodized Sobolev space. (Here J̃τ 0 is a co...
متن کاملHigh-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures
This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet and Neumann open-surface problems. In the two-dimensional case, a rigorous proof is presented, establishing that the new weighted formulations ...
متن کاملNumerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets
In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...
متن کاملTheory of block-pulse functions in numerical solution of Fredholm integral equations of the second kind
Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...
متن کاملDegenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...
متن کامل