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| The Method of Fundamental Solutions forOptical Fluorescence |
| Andreas Karageorghis,Daniel Lesnic |
| (Department of Mathematics and Statistics, University of Cyprus/ Πανεπιστ?μιο
Κ?πρου, P.O.Box 20537, 1678 Nicosia/Λευκωσ?α, Cyprus/Κ?προ?;Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK) |
| DOI： |
| Abstract: |
| In this paper, we develop the method of fundamental solutions
(MFS) for solving boundary value problems in the field of optical fluorescence.
The governing system of diffusion–absorption equations for the excitation and
emission fluences is transformed into a single fourth–order partial differential
equation whose fundamental solution can be expressed as the difference of two
fundamental solutions of the complex Helmholtz equation. The numerically obtained results confirm the accuracy of the MFS when compared with an available
analytical solution. Numerical results are also provided for a physical application in optical fluorescence. Furthermore, extensions to three dimensions along
with numerical verification are performed. |
| Key words: Optical fluorescence, method of fundamental solutions, elliptic equations. |