Using multiple-precision arithmetic to prevent low-frequency breakdowns in the diagonalization of the green's function

Date

2014-08-28

Author

Ergül, Özgür Salih

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

120
views

0
downloads

Multiple-precision arithmetic (MPA) is used to prevent low-frequency breakdowns in the diagonalization of the Green's function that is required to implement the multilevel fast multipole algorithm (MLFMA). The breakdown problem is considered at a numerical level, where rounding errors are reduced by increasing the precision as much as required. Using MPA seems to provide a direct solution to low-frequency breakdowns of the standard diagonalization, which may lead to straightforward implementations of broadband MLFMA.

Subject Keywords

Composite structures, Addition theorem, Error analysis, Algorithm, MLFMA, Electromagnetics, Objects

URI

https://hdl.handle.net/11511/55826

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Low-frequency multilevel fast multipole algorithm using an approximate diagonalization of the Green's function Ergül, Özgür Salih (2014-08-23) We present an approximate diagonalization of the Green's function to implement a stable multilevel fast multipole algorithm (MLFMA) for low-frequency problems. The diagonalization is based on scaled spherical functions, leading to stable computations of translation operators at all distances and for all frequencies. Similar to the conventional diagonalization, shift operators are expressed in terms of complex exponentials, while radiated and incoming fields are expanded in terms of scaled plane waves. Even ...
Stabilization of the Fast Multipole Method for Low Frequencies Using Multiple-Precision Arithmetic Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2014-08-23) We stabilize a conventional implementation of the fast multipole method (FMM) for low frequencies using multiple-precision arithmetic (MPA). We show that using MPA is a direct remedy for low-frequency breakdowns of the standard diagonalization, which is prone to numerical errors at short distances with respect to wavelength. By increasing the precision, rounding errors are suppressed until a desired level of accuracy is obtained with plane-wave expansions. As opposed to other approaches in the literature, u...
Optimal Control of Diffusion Convection Reaction Equations Using Upwind Symmetric Interior Penalty Galerkin SIPG Method Karasözen, Bülent; Yücel, Hamdullah (2012-05-01) We discuss the numerical solution of linear quadratic optimal control problem with distributed and Robin boundary controls governed by diffusion convection reaction equations. The discretization is based on the upwind symmetric interior penalty Galerkin (SIPG) methods which lead to the same discrete scheme for the optimize-then-discretize and the discretize-then-optimize.
Error Control of MLFMA within a Multiple-Precision Arithmetic Framework Kalfa, Mert; ERTÜRK, VAKUR BEHÇET; Ergül, Özgür Salih (2018-07-13) We present a new error control scheme that provides the truncation numbers as well as the required digits of machine precision for the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems. When combined with a multiple-precision arithmetic framework, the proposed method can be used to solve low-frequency problems that would otherwise experience overflow issues. Numerical results...
Approximate Chernoff Fusion of Gaussian Mixtures Using Sigma-Points Gunay, Melih; Orguner, Umut; Demirekler, Mübeccel (2014-07-10) Covariance intersection (CI) is a method used for consistent track fusion with unknown correlations. The well-known generalization of CI to probability density functions is known as Chernoff fusion. In this paper, we propose an approximate approach for the Chernoff fusion of Gaussian mixtures based on a sigma-point approximation of the underlying densities. The resulting general density fusion rule yields a closed form cost function and an analytical fused density for Gaussian mixtures. The proposed method ...

Citation Formats

Ö. S. Ergül, “Using multiple-precision arithmetic to prevent low-frequency breakdowns in the diagonalization of the green’s function,” 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55826.