An inverse source problem for the stationary diffusion–advection–decay equation

Autor:	Nilson C. Roberty, Denis Mota de Sousa
Rok vydání:	2011
Předmět:	Applied Mathematics Mathematical analysis General Engineering Plane wave Synthetic data Computer Science Applications Algebraic equation Nonlinear system symbols.namesake Reciprocity (electromagnetism) Helmholtz free energy Collocation method symbols Fourier series Mathematics
Zdroj:	Inverse Problems in Science and Engineering. 20:891-915
ISSN:	1741-5985 1741-5977
DOI:	10.1080/17415977.2011.609466
Popis:	In this work we consider a source reconstruction problem for stationary diffusion–advection–decay equation from boundary data. Making a change of variable, we obtain an equivalent modified Helmholtz source problem. Some continuation solutions in the unitary disk are then presented. We also present a variational formulation based in the reciprocity functional formulation. Test functions are plane waves. Considering characteristic sources with star-shaped support in this variational formulation, we obtain a non-linear system of integral equations that must be solved to reconstruct this class of sources. This non-linear problem is then investigated with truncated Fourier series representation and then solved by collocation method. The system of nonlinear algebraic equations which approximates the solution is solved using the Levenberg–Marquardt method. Synthetic data are produced by the finite-element method. We present some numerical reconstructions for an unidimensional and a bidimensional model.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f3b733d59a74b8de8e771a754efc4b11 https://doi.org/10.1080/17415977.2011.609466 Zobrazit plný text záznamu