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On the reconstruction of heat and acoustic sources from boundary measurements

TítuloOn the reconstruction of heat and acoustic sources from boundary measurements
Publication TypeUnpublished
Year of Publication2012
AuthorsMartins NFM
Series TitlePreprint
Palavras-chavefundamental solutions, Inverse source problems, Laplace and Helmholtz boundary value problems, plane waves.
AbstractWe address the identification and reconstruction of source functions in inverse boundary value problems for the Helmholtz and Laplace problems. We introduce particular affine/linear classes of sources and address the identification and reconstruction is such classes. In order to solve these inverse problems we propose a new numerical method that relies on solving several Helmholtz/Laplace boundary value problems. We establish a connection between these particular classes and full identification results using many boundary measurements. The developed methods are theoretically justified and illustrated with several numerical examples.
URLhttp://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/18_12.pdf