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Thursday, August 6, 2020 | History

2 edition of Treatment of singularities in the numerical solution of scattering problems. found in the catalog.

Treatment of singularities in the numerical solution of scattering problems.

Soheir Takla Meleika Abdelmessih

Treatment of singularities in the numerical solution of scattering problems.

by Soheir Takla Meleika Abdelmessih

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  • 1 Currently reading

Published in [Toronto] .
Written in English

    Subjects:
  • Cylinders,
  • Electric waves -- Scattering,
  • Integral equations -- Numerical solutions

  • Edition Notes

    ContributionsToronto, Ont. University.
    The Physical Object
    Paginationv, 101 leaves.
    Number of Pages101
    ID Numbers
    Open LibraryOL18702156M

    The two-part treatment begins by examining the boundary-value problem without singularities. Topics include particular solutions of the system without singularities, the spectrum and scattering matrix for the boundary-value problem without singularities, Parseval's equality, and the inverse problem. A very common approach to solve a nonlinear inverse scattering problem are x-point iterations, which produce a sequence of linear inverse scattering problems with solutions that converge, un-der some suitable assumptions, to a solution of the nonlinear problem. One such approximation technique is the Born approximation, see e.g. [7, 35].

    () A Riemann–Hilbert problem for the finite-genus solutions of the KdV equation and its numerical solution. Physica D: Nonlinear Phenomena , () Boundary Value Problems for the Elliptic Sine-Gordon Equation in a Semi-strip. This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions.

    Treatment of the finite element method for an unbounded field problem was proposed by McDonald and Wexler in Their method is superior to others, because it can exclude the singularities of Green's functions. This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex .


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Treatment of singularities in the numerical solution of scattering problems by Soheir Takla Meleika Abdelmessih Download PDF EPUB FB2

The book covers topics related to the subject, which includes low-frequency electromagnetic scattering; the uniform asymptomatic theory of electromagnetic edge diffraction; analyses of problems involving high frequency diffraction and imperfect half planes; and multiple scattering of waves by periodic and random distribution.

treatment of singularities in scattering from perfectly conducting polygonal cylinders—a numerical technique Article in Canadian Journal of Physics 45(3). a novel integra tion method for weak singularity arising in 2-d scattering problems of the paper and added nicely to the presentation and read- ability of the paper.

The problem related to the integration of the GF singularity on arbitrary shaped domains is solved through a hybrid numerical-analytical technique based on an original integral transformation and. In spite of its conceptional simplicity, some problems regarding the choice and the distribution of discrete sources, the elaboration of stable numerical algorithms for amplitude determination, the evaluation of the accuracy of results and the solution of scattering problems for domains with geometrical singularities, have to be solved.

solution of elliptic boundary value problems is presented in Ref. [11]. Material on the MFS may also be found in the recent books by Golberg and Chen [19] and Kolodziej [20]. In this paper, we describe the development of the MFS and related methods for the numerical solution of scattering and radiation problems in fluids and solids.

We also. The first coherent treatment of the subject in nearly two decades-an important working resource for researchers and a superior graduate-level text Variational Principles and the Numerical Solution of Scattering Problems is designed to serve as both a professional guide and a self-contained graduate-level text.

Singularities Treatment in Solving Volume Electric The electromagnetic scattering problems from arbitrary analytical solution compared to the numerical one. Suppose that the surface of integration is the triangle shown in Figure 3 that has the. A family of scattering problems is defined, that is, the classical problem (which follows from Maxwell’s equations) and the so-called “regularized problem” obtained by adding a regularizing term in Maxwell’s equations.

These problems are shown to be well posed and to have the same solution. An integral representation technique is described. In spite of its conceptional simplicity, some problems regarding the choice and the distribution of discrete sources, the elaboration of stable numerical algorithms for amplitude determination, the evaluation of the accuracy of results and the solution of scattering problems for domains with geometrical singularities, have to be solved.

The discrete sources method is an efficient and powerful tool for solving a large class of boundary-value problems in scattering theory. A variety of numerical methods for discrete sources now exist.

In this book, the authors unify these formulations in the context of the so-called discrete sources method. The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed.

A brief review of the developments and applications in all areas of the MFS over the last five years is also given. This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure.

We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar Laplace operator, namely the interior Neumann problem. Numerical solution of electromagnetic scattering problems by the surface integral methods leads to numerical integration of singular integrals in the Method of Moments.

The heavy numerical cost of a straightforward numerical treatment of these integrals can be avoided by a more efficient and accurate approach based on the singularity.

Models of electromagnetic scattering problems based on discrete sources method. Singularities of wave fields and numerical methods of solving the boundary-value problems for Helmholtz equations. Yasuura's method, its relation to the fictitious-source methods, and its advancements in the solution of 2-D problems.

A numerical method for the computation of the singular behavior of the solution of the Laplace equation is proposed. Numerical Treatment of Vertex Singularities and Intensity Factors for Mixed Boundary Value Problems for the Laplace Equation in $\mathbb{R}^3 $ The finite element method with anisotropic mesh grading for elliptic problems.

By using a complete set of poroelastodynamic spherical wave potentials (SWPs) representing a fast compressional wave P I, a slow compressional wave P II, and a shear wave S with 3 vectorial potentials (not all are independent), a solution scheme based on the method of fundamental solution (MFS) is devised to solve 3‐D wave scattering and dynamic stress concentration problems.

() Local solutions to high-frequency 2D scattering problems. Journal of Computational Physics() Numerical evaluation of the two-dimensional partition of unity boundary integrals for Helmholtz problems.

Search within book. Front Matter. Pages I-IX. PDF. Finite element methods for the solution of problems with rough input data. Babuška, J. Osborn. Pages The treatment of singularities in orthonormalization methods for numerical conformal mapping.

Papamichael. Pages. Book Description. As a satellite conference of the International Mathematical Congress and part of the celebration of the th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, Numerical investigation on three treatments for eliminating the singularities of acoustic fundamental solutions in the singular boundary method Zhuo-Jia Fu, Wen Chen & Wenzhen Qu College of Mechanics and Materials and State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, P.

R. China Abstract. Numerical methods such as the close-coupling, R-matrix and Kohn variational methods have been around for decades, but more recently they have been applied to the treatment of the time-dependent.