Computation and visualization of cuspidal waveforms for modular group using GridMathematica

Spectral studies on the eigenfunctions of Laplace-Beltrami operator on a cusp manifold are known to contain both discrete and continuous eigenvalues. The discrete eigenfunctions are usually called Maass cusp forms where their eigenvalues are not known analytically. The aims of this report were to co...

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Main Authors:	Chan, Kar Tim, Hishamuddin Zainuddin, Molladavoudi, Saeid
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2013
Online Access:	http://journalarticle.ukm.my/6160/ http://journalarticle.ukm.my/6160/ http://journalarticle.ukm.my/6160/1/14_Chan_Kar_Tim.pdf

id	ukm-6160
recordtype	eprints
spelling	ukm-61602016-12-14T06:40:31Z http://journalarticle.ukm.my/6160/ Computation and visualization of cuspidal waveforms for modular group using GridMathematica Chan, Kar Tim Hishamuddin Zainuddin, Molladavoudi, Saeid Spectral studies on the eigenfunctions of Laplace-Beltrami operator on a cusp manifold are known to contain both discrete and continuous eigenvalues. The discrete eigenfunctions are usually called Maass cusp forms where their eigenvalues are not known analytically. The aims of this report were to compute the eigenvalues λ = r2 + 1/4 for the modular group, PSL(2,Z) numerically and visualize the waveforms using GridMathematica. At the same time, we compared the performance of parallel programming (GridMathematica) and normal programming (Mathematica). This serves to show the feasibility and advantages of using the parallel version of commercially available software for complex computations of Maass cusp forms. In our computer search for 33 eigenvalues in the r-interval [9, 30.4], we found that the performance of the parallel programme is about six times faster than the normal programme. Universiti Kebangsaan Malaysia 2013-05 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/6160/1/14_Chan_Kar_Tim.pdf Chan, Kar Tim and Hishamuddin Zainuddin, and Molladavoudi, Saeid (2013) Computation and visualization of cuspidal waveforms for modular group using GridMathematica. Sains Malaysiana, 42 (5). 655 -660. ISSN 0126-6039 http://www.ukm.my/jsm/
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	Spectral studies on the eigenfunctions of Laplace-Beltrami operator on a cusp manifold are known to contain both discrete and continuous eigenvalues. The discrete eigenfunctions are usually called Maass cusp forms where their eigenvalues are not known analytically. The aims of this report were to compute the eigenvalues λ = r2 + 1/4 for the modular group, PSL(2,Z) numerically and visualize the waveforms using GridMathematica. At the same time, we compared the performance of parallel programming (GridMathematica) and normal programming (Mathematica). This serves to show the feasibility and advantages of using the parallel version of commercially available software for complex computations of Maass cusp forms. In our computer search for 33 eigenvalues in the r-interval [9, 30.4], we found that the performance of the parallel programme is about six times faster than the normal programme.
format	Article
author	Chan, Kar Tim Hishamuddin Zainuddin, Molladavoudi, Saeid
spellingShingle	Chan, Kar Tim Hishamuddin Zainuddin, Molladavoudi, Saeid Computation and visualization of cuspidal waveforms for modular group using GridMathematica
author_facet	Chan, Kar Tim Hishamuddin Zainuddin, Molladavoudi, Saeid
author_sort	Chan, Kar Tim
title	Computation and visualization of cuspidal waveforms for modular group using GridMathematica
title_short	Computation and visualization of cuspidal waveforms for modular group using GridMathematica
title_full	Computation and visualization of cuspidal waveforms for modular group using GridMathematica
title_fullStr	Computation and visualization of cuspidal waveforms for modular group using GridMathematica
title_full_unstemmed	Computation and visualization of cuspidal waveforms for modular group using GridMathematica
title_sort	computation and visualization of cuspidal waveforms for modular group using gridmathematica
publisher	Universiti Kebangsaan Malaysia
publishDate	2013
url	http://journalarticle.ukm.my/6160/ http://journalarticle.ukm.my/6160/ http://journalarticle.ukm.my/6160/1/14_Chan_Kar_Tim.pdf
first_indexed	2023-09-18T19:46:08Z
last_indexed	2023-09-18T19:46:08Z
_version_	1777405912854560768

Computation and visualization of cuspidal waveforms for modular group using GridMathematica

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