Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies - Softcover

Ramm, Alexander G.

Softcover

ISBN 10: 0387906827 ISBN 13: 9780387906829

Verlag: Springer, 2013

Inhaltsangabe

Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var­ ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad­ vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal­ culation of multiple integrals. Of special interest is the case of inte­ grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.

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Über die Autorin bzw. den Autor

Alexander G. Ramm, Ph.D., was born in Russia, immigrated to the U.S. in 1979, and is a U.S. citizen. He is Professor of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics. He is an author of 690 research papers, 16 monographs, and an editor of 3 books. He has lectured in many universities throughout the world, presented approximately 150 invited and plenary talks at various conferences, and has supervised 11 Ph.D. students. He was Fulbright Research Professor in Israel and in Ukraine, distinguished visiting professor in Mexico and Egypt, Mercator professor, invited plenary speaker at the 7th PACOM, won the Khwarizmi international award, and received other honors. Recently he solved inverse scattering problems with non-over-determined data and the many-body wave-scattering problem when the scatterers are small particles of an arbitraryshape; Dr. Ramm used this theory to give a recipe for creating materials with a desired refraction coefficient, gave a solution to the refined Pompeiu problem and proved the refined Schiffers conjecture.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2013
• Sprache: Englisch
• ISBN 10: 0387906827
• ISBN 13: 9780387906829
• Einband: Taschenbuch
• Anzahl der Seiten: 140
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