Severe loss of precision in calculations of T-matrix integrals

A severe loss of precision is unravelled in the numerical calculation of surface integrals that appear in the Extended Boundary Condition Method (EBCM), to calculate the T-matrix elements of axisymmetric particles. We systematically study the occurrence of numerical cancellations for three basic particle shapes, namely cylinders, spheroids, and offset spheres, with typical sizes, aspect ratios and materials often studied as benchmark examples in the literature. The cancellations are evidenced both for spheroids and offset spheres, and are particularly pronounced in the latter case. The resulting loss of precision is independent from the commonly asserted problems of matrix inversion. We show that the origin of these severe cancellations can be further studied and understood by numerical investigations of the scaling of the integrands and integrals with respect to the particle size parameter. This allows us to develop a detailed mathematical proof of these cancellations. The results suggest that the EBCM method, in its usual formulation, suffers important numerical instabilities which reduce the domain of convergence for specific particle shapes that are commonly used for testing and benchmarking the method.

► A numerical loss of precision in T-matrix integrals is demonstrated. ► An analytic proof of cancellations is provided. ► This highlights a new source of numerical instability in addition to matrix inversion.