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Numerical algorithms for the basic problem
Published in E.V. Chizhonkov, Mathematical Aspects of Modelling Oscillations and Wake Waves in Plasma, 2019
included as factors in the right-hand sides of ak(η) and integrals YYY (k, l, s), YZZ (k, l, s), which are coefficients of the system (8.39), was carried out using the DQAG program from the QUADPACK package [156], part of the library SLATEC [128]. In order to test the program, we checked the orthonormal relations on the segment [0, 1] with the weight function ρ for the basis functions Yk(ρ) and Zk(ρ) constructed above. The calculations showed that for 1 ≤ k ≤ 300 the absolute deviations of the tested relations do not exceed the value of 0.6 · 10−13.
A highly accurate analytical solution for the surface fields of a short vertical wire antenna lying on a multilayer ground
Published in Waves in Random and Complex Media, 2018
To test the correctness of the developed theory, formulas (32)–(33) are applied to the calculation of the electric field components produced by the unit-moment dipole source on the top surface of a two-layer conducting medium. The electromagnetic parameters of the two layers are assumed to be mS/m, S/m, , and . The results of the simulations, shown in Figures 3–6, are compared with those arising from numerically evaluating (1)–(3). Numerical integration of the field integrals is carried out using Quadpack library contained in the Slatec mathematical libraries.
Multidual Sensitivity Method in Ray-Tracing Transport Simulations
Published in Nuclear Science and Engineering, 2021
Matthew R. Balcer, Harry Millwater, Jeffrey A. Favorite
This work applied the multidual differentiation method to a relatively simple ray-tracing code. However, the methodology is general and should be equally applicable to other nuclear applications. The numerical accuracy along with minimal modifications to existing codes make this method attractive for practical applications. The multidual transformation of many types of code is possible. For example, multidual differentiation was implemented in the QUADPACK adaptive numerical integration library in this work, so that the integrand and limits of integration can accept multidual numbers.