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The scattering support
Author(s) -
Kusiak Steven,
Sylvester John
Publication year - 2003
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3038
Subject(s) - obstacle , convex hull , inverse scattering problem , mathematics , scattering , regular polygon , helmholtz equation , inverse , inverse problem , set (abstract data type) , convex analysis , mathematical analysis , convex optimization , computer science , physics , geometry , optics , boundary value problem , programming language , political science , law
We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce the convex scattering support of a far field, a set which will be a subset of the convex hull of the support of any source which can produce it. We give several theorems which explain how to compute the convex scattering support and how to relate it to the actual support of a source, medium, or obstacle. © 2003 Wiley Periodicals, Inc.