Loading [MathJax]/jax/output/HTML-CSS/config.js
Volume 41, Issue 2
The Method of Fundamental Solutions for Optical Fluorescence

Andreas Karageorghis & Daniel Lesnic

Ann. Appl. Math., 41 (2025), pp. 219-238.

Published online: 2025-06

Export citation
  • 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.

  • AMS Subject Headings

65N80, 65N38

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAM-41-219, author = {Karageorghis , Andreas and Lesnic , Daniel}, title = {The Method of Fundamental Solutions for Optical Fluorescence}, journal = {Annals of Applied Mathematics}, year = {2025}, volume = {41}, number = {2}, pages = {219--238}, 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.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2025-0010}, url = {http://global-sci.org/intro/article_detail/aam/24149.html} }
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 -

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.

Karageorghis , Andreas and Lesnic , Daniel. (2025). The Method of Fundamental Solutions for Optical Fluorescence. Annals of Applied Mathematics. 41 (2). 219-238. doi:10.4208/aam.OA-2025-0010
Copy to clipboard
The citation has been copied to your clipboard