Predefined exponential basis set for half-bounded multi domain spectral method

Fahhad Alharbi

doi:10.1109/nusod.2009.5297216

Predefined exponential basis set for half-bounded multi domain spectral method

Fahhad Alharbi^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

A fast and efficient multi-domain spectral method (MDSM) based on wide range non-orthogonal predefined exponential basis set is presented. This method works extremely well for semi-infinite differential problems. It spans wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to approximate different exponentially decaying functions and compared with Laguerre basis method. Also for comparison purpose, it is used to analyze arbitrary quantum wells (QW) and optical waveguides. The comparisons exhibit the accuracy and the efficiency of the presented method. In the analytical limit, the relative error in the quantized energy level of the studied QW is in the order of 10^-12 with very small number of bases.

Original language	English
Title of host publication	9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009
Publisher	IEEE Computer Society
Pages	77-78
Number of pages	2
ISBN (Print)	9781424441808
DOIs	https://doi.org/10.1109/nusod.2009.5297216
State	Published - 2009
Externally published	Yes

Publication series

Name	9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009

ASJC Scopus subject areas

Computational Theory and Mathematics
Electrical and Electronic Engineering
Electronic, Optical and Magnetic Materials
Computational Mathematics

Access to Document

10.1109/nusod.2009.5297216

Cite this

Alharbi, F. (2009). Predefined exponential basis set for half-bounded multi domain spectral method. In 9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009 (pp. 77-78). Article 5297216 (9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009). IEEE Computer Society. https://doi.org/10.1109/nusod.2009.5297216

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title = "Predefined exponential basis set for half-bounded multi domain spectral method",

abstract = "A fast and efficient multi-domain spectral method (MDSM) based on wide range non-orthogonal predefined exponential basis set is presented. This method works extremely well for semi-infinite differential problems. It spans wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to approximate different exponentially decaying functions and compared with Laguerre basis method. Also for comparison purpose, it is used to analyze arbitrary quantum wells (QW) and optical waveguides. The comparisons exhibit the accuracy and the efficiency of the presented method. In the analytical limit, the relative error in the quantized energy level of the studied QW is in the order of 10-12 with very small number of bases.",

author = "Fahhad Alharbi",

year = "2009",

doi = "10.1109/nusod.2009.5297216",

language = "English",

isbn = "9781424441808",

series = "9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009",

publisher = "IEEE Computer Society",

pages = "77--78",

booktitle = "9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009",

address = "United States",

}

Alharbi, F 2009, Predefined exponential basis set for half-bounded multi domain spectral method. in 9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009., 5297216, 9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009, IEEE Computer Society, pp. 77-78. https://doi.org/10.1109/nusod.2009.5297216

Predefined exponential basis set for half-bounded multi domain spectral method. / Alharbi, Fahhad.
9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009. IEEE Computer Society, 2009. p. 77-78 5297216 (9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Predefined exponential basis set for half-bounded multi domain spectral method

AU - Alharbi, Fahhad

PY - 2009

Y1 - 2009

N2 - A fast and efficient multi-domain spectral method (MDSM) based on wide range non-orthogonal predefined exponential basis set is presented. This method works extremely well for semi-infinite differential problems. It spans wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to approximate different exponentially decaying functions and compared with Laguerre basis method. Also for comparison purpose, it is used to analyze arbitrary quantum wells (QW) and optical waveguides. The comparisons exhibit the accuracy and the efficiency of the presented method. In the analytical limit, the relative error in the quantized energy level of the studied QW is in the order of 10-12 with very small number of bases.

AB - A fast and efficient multi-domain spectral method (MDSM) based on wide range non-orthogonal predefined exponential basis set is presented. This method works extremely well for semi-infinite differential problems. It spans wide range of exponential decay rates with multi scaling and does not suffer from zero crossing. These two conditions are necessary for many physical problems. For comparison, the method is used to approximate different exponentially decaying functions and compared with Laguerre basis method. Also for comparison purpose, it is used to analyze arbitrary quantum wells (QW) and optical waveguides. The comparisons exhibit the accuracy and the efficiency of the presented method. In the analytical limit, the relative error in the quantized energy level of the studied QW is in the order of 10-12 with very small number of bases.

UR - https://www.scopus.com/pages/publications/73449100459

U2 - 10.1109/nusod.2009.5297216

DO - 10.1109/nusod.2009.5297216

M3 - Conference contribution

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SN - 9781424441808

T3 - 9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009

SP - 77

EP - 78

BT - 9th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2009

PB - IEEE Computer Society

ER -

Predefined exponential basis set for half-bounded multi domain spectral method

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ASJC Scopus subject areas

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