| 1. |
- Lundengård, Karl, 1987-, et al.
(author)
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An Examination of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Channel-Base Currents
- 2015
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In: 12TH INTERNATIONAL CONFERENCE ON APPLIED ELECTROMAGNETICS PES2015. - : Faculty of Electronic Engineering (Niš). - 9788661251443
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Conference paper (peer-reviewed)abstract
- A multi-peaked version of the analytically extendedfunction (AEF) intended for approximation of multi-peaked light-ning current waveforms will be presented along with some of itsbasic properties. A general framework for estimating the parame-ters of the AEF using the Marquardt least-squares method(MLSM) for a waveform with an arbitrary (finite) number ofpeaks as well as a given charge transfer and specific energy willalso be described. This framework is used to find parameters forsome common single-peak wave-forms and some advantages anddisadvantages of the approach will be discussed.
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| 2. |
- Lundengård, Karl, 1987-, et al.
(author)
-
Estimation of Parameters for the Multi-peaked AEF Current Functions
- 2015
-
In: ASMDA 2015 Proceedings. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180058 ; , s. 623-636
-
Conference paper (peer-reviewed)abstract
- Examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is performed in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as one-peaked Standard IEC 62305 lightning currents.
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| 3. |
- Lundengård, Karl, 1987-, et al.
(author)
-
Optimization of the determinant of the Vandermonde matrix on the sphere and related surfaces
- 2015
-
In: ASMDA 2015 Proceedings. - : ISAST: International Society for the Advancement of Science and Technology. - 9786185180058 ; , s. 637-648
-
Conference paper (peer-reviewed)abstract
- The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Gröbner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.
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