The use of Gaussian elimination with backsubstitution for matrix inversion in scattering theories is discussed. Within the framework of the T-matrix method (the state-of-the-art code by Mishchenko is freely available at http://www.giss.nasa.gov/∼crmim), it is shown that the domain of applicability of Mishchenko’s fortran 77 (F77) code can be substantially expanded in the direction of strongly absorbing particles where the current code fails to converge. Such an extension is especially important if the code is to be used in nanoplasmonic or nanophotonic applications involving metallic particles. At the same time, convergence can also be achieved for large nonabsorbing particles, in which case the non–Numerical Algorithms Group option of Mishchenko’s code diverges. Computer F77 implementation of Mishchenko’s code supplemented with Gaussian elimination with backsubstitution is freely available at http://www.wave-scattering.com.

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Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Sphere in Vacuum^{a}

Calculations are shown as a function of radius AXI and refractive index MRR + i*MRI for a fixed incidence wavelength of LAM = 100.
G.w.b., Gaussian elimination with backsubstitution.
Indicates that nearly singular matrices were encountered during the calculation. n.c., the calculation did not converge.

Table 2

Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Prolate Spheroid with an Aspect Ratio 2 in Vacuuma^{a}

Calculations are shown as a function of the equal-volume-sphere radius AXI and refractive index MRR + i*MRI. Light incidence at the vacuum wavelength of LAM = 100 was fixed at the angle THET0 = 30°.
G.w.b., Gaussian elimination with backsubstitution.
Albedo returned larger than 1.
Indicates that nearly singular matrices were encountered during the calculation. n.c., the calculation did not converge.

Tables (2)

Table 1

Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Sphere in Vacuum^{a}

Calculations are shown as a function of radius AXI and refractive index MRR + i*MRI for a fixed incidence wavelength of LAM = 100.
G.w.b., Gaussian elimination with backsubstitution.
Indicates that nearly singular matrices were encountered during the calculation. n.c., the calculation did not converge.

Table 2

Comparison of the Total Extinction Efficiency as Calculated by Mishchenko’s Code with Three Different Inversion Techniques for the Case of a Prolate Spheroid with an Aspect Ratio 2 in Vacuuma^{a}

Calculations are shown as a function of the equal-volume-sphere radius AXI and refractive index MRR + i*MRI. Light incidence at the vacuum wavelength of LAM = 100 was fixed at the angle THET0 = 30°.
G.w.b., Gaussian elimination with backsubstitution.
Albedo returned larger than 1.
Indicates that nearly singular matrices were encountered during the calculation. n.c., the calculation did not converge.