Integral Equations and Iteration Methods in Electromagnetic Scattering
By: Yu V. Shestopalov (editor)Hardback
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The analysis of scattering of electromagnetic waves in inhomogeneous three-dimensional bounded media is extremely important from both theoretical and practical viewpoints, and constitutes the core family of problems in electromagnetics. In this monograph the following fundamental topics relating to these problems are considered: mathematical problems and methods related to the scattering of electromagnetic waves by inhomogeneous three-dimensional anisotropic bodies and their reduction to volume singular integral equations; iteration techniques for solving linear operator equations; and efficient methods for solving volume integral equations that employ iteration procedures. Nowadays, volume singular integral equations are widely used as an efficient tool of numerical solution to the problems of complicated three-dimensional structures. Analysis of integral equations and corresponding scattering problems, including nonclassical ones, is performed in the general formulation. The necessary and sufficient conditions that provide fulfilment of the Noether property of operators and sufficient conditions for the Fredholm property are obtained.
Existence and uniqueness theorems for scattering problems considered in both classical and nonclassical settings are proved. Much attention is given to iteration techniques and development of corresponding computational algorithms. This monograph will be of interest to researchers in electromagnetics, integral equations, iteration methods and numerical analysis both in academia and industry.
Iteration methods for solving linear equations; the Jacobi method; minimal residual method; multistep minimal residual method; quasi-minimal residual methods; numerical implementation of iteration methods; iteration method of increasing the accuracy of the solution; comparison of iteration methods; singular equations in electromagnetic scattering; initial equations; analysis of integral equations; classical solutions to the scattering problems; generalized solution of the scattering problems; analysis of other classes of scattering problems; methods and algorithms for solution to the problems of scattering by three-dimensional structures; application of the Jacobi method for the scattering problems of the quasistatic wavelength range; substantiation of applicability of MRM and QMRM for the problems of scattering by a transport body; algorithms of numerical solution and peculiarities of their utilization; application of MRM for solving other families of scattering problems; appendix.
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- ID: 9789067643368
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