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Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies (Paperback, Softcover reprint of the original 1st ed. 1982)
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Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies (Paperback, Softcover reprint of the original 1st ed. 1982)
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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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