TY - JOUR
T1 - The Method of Fundamental Solutions for Optical Fluorescence
AU - Karageorghis , Andreas
AU - Lesnic , Daniel
JO - Annals of Applied Mathematics
VL - 2
SP - 219
EP - 238
PY - 2025
DA - 2025/06
SN - 41
DO - http://doi.org/10.4208/aam.OA-2025-0010
UR - https://global-sci.org/intro/article_detail/aam/24149.html
KW - Optical fluorescence, method of fundamental solutions, elliptic equations.
AB - <p style="text-align: justify;">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.</p>