We identify the coefficients of the transport equation in N dimensions grad c.grad h+c Delta h=d delta h/ delta t+f by solving a differential system of the form grad c+ca=b. The assignment of c at one point only yields a unique solution, found by integration along arbitrary paths. This arbitrariness guarantees a good control of the error, notwithstanding the ill-posedness of the problem. For N=2, the hypotheses allowing for this identification are satisfied when one knows two stationary potentials with non-overlapping equipotential lines and a third non-stationary one-this last needed only for determining d. The theory is applied to a numerical synthetic example, for various grid sizes or for noisy data. Notwithstanding the minimal a priori information required for the coefficients, we are able to compute these at a large number of nodes with good precision. For the sake of completeness, we give other results on identification.

Minimal a priori assignment in a direct method for determining phenomenological coefficients uniquely / G. Parravicini, M. Giudici, G. Morossi, G. Ponzini. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 11:3(1995), pp. 009.616-009.629.

Minimal a priori assignment in a direct method for determining phenomenological coefficients uniquely

G. Parravicini;M. Giudici;
1995

Abstract

We identify the coefficients of the transport equation in N dimensions grad c.grad h+c Delta h=d delta h/ delta t+f by solving a differential system of the form grad c+ca=b. The assignment of c at one point only yields a unique solution, found by integration along arbitrary paths. This arbitrariness guarantees a good control of the error, notwithstanding the ill-posedness of the problem. For N=2, the hypotheses allowing for this identification are satisfied when one knows two stationary potentials with non-overlapping equipotential lines and a third non-stationary one-this last needed only for determining d. The theory is applied to a numerical synthetic example, for various grid sizes or for noisy data. Notwithstanding the minimal a priori information required for the coefficients, we are able to compute these at a large number of nodes with good precision. For the sake of completeness, we give other results on identification.
Settore GEO/12 - Oceanografia e Fisica dell'Atmosfera
Settore FIS/06 - Fisica per il Sistema Terra e Il Mezzo Circumterrestre
INVERSE PROBLEMS
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/177574
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 21
social impact