Table 1.
Explicit -integration Exponential Factors
, relation | Source | |
| | |
| | |
| | |
| | |
Table 2.
FAZIMFLAL Regions Defined by the Conditions (note that , , and are discretized on the same grid )
Region | Jacobian | | | | Integration domain |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
Table 3.
FAZIMFLAL Path Integrals According to the Region of the Source Point
Region | Path Integral |
| |
| |
| |
| |
| |
| |
Table 4.
Area of the -th Elemental Region
Region | Area |
| |
| |
| |
| |
| |
| |
Table 5.
Area and Spectral Density Truncation Error in the -th Elemental Region
Region | Area | Error formula |
| | |
| | |
| | |
| | |
| | |
| | |
Table 6.
Passive Illustration Physical Parameters
Parameter | Value |
Disk radius | |
Disk thickness | |
Cap thickness | |
Percent dopant | 5 |
Total doped sites | |
Excited state fraction | 0.10 |
Excited state lifetime | |
Fluorescence wavelength | |
Absorption coefficient | 0 |
Absorption cross-section | |
Emission cross-section | |
Integral emission cross-section | |
Pump source | |
Pump radius | |
Table 7.
Passive Case: Performance Summary Versus (run times are for the MATLAB and implementations of the grid area’s generation and the fluorescence/error estimate computation; the reported error is the maximum relative error over the observation grid points)
| Implementation | Grid setup [sec] | Solution [sec] | Actual error [%] | Estimated error [%] |
101 | MATLAB | 15.05 | 2.27 | 14.22 | 1.36 |
101 | | 3.33 | 0.0938 | 14.21 | 1.36 |
201 | MATLAB | 59.41 | 8.70 | 9.04 | 0.759 |
201 | | 3.32 | 0.223 | 9.04 | 0.759 |
401 | MATLAB | 270.66 | 35.16 | 4.45 | 0.404 |
401 | | 12.39 | 1.33 | 4.44 | 0.404 |
801 | MATLAB | 2312.07 | 148.98 | 2.68 | 0.209 |
801 | | 49.26 | 5.02 | 2.67 | 0.209 |