Publication Abstracts
Doicu and Mishchenko 2020
Doicu, A., and , 2020: An overview of the null-field method. II: Convergence and numerical stability. Phys. Open, 3, 100019, doi:10.1016/j.physo.2020.100019.
In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.
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BibTeX Citation
@article{do01300f,
author={Doicu, A. and Mishchenko, M. I.},
title={An overview of the null-field method. II: Convergence and numerical stability},
year={2020},
journal={Physics Open},
volume={3},
pages={100019},
doi={10.1016/j.physo.2020.100019},
}
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RIS Citation
TY - JOUR ID - do01300f AU - Doicu, A. AU - Mishchenko, M. I. PY - 2020 TI - An overview of the null-field method. II: Convergence and numerical stability JA - Phys. Open JO - Physics Open VL - 3 SP - 100019 DO - 10.1016/j.physo.2020.100019 ER -
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