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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30080/1/30080.pdf |
| _version_ | 1825947636693204992 |
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| author | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid |
| author_facet | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid |
| author_sort | Chan, Kar Tim |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T08:16:26Z |
| format | Article |
| id | upm.eprints-30080 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:16:26Z |
| publishDate | 2013 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| record_format | dspace |
| spelling | upm.eprints-300802018-10-17T02:39:07Z http://psasir.upm.edu.my/id/eprint/30080/ Computation and visualization of cuspidal waveforms for modular group using GridMathematica Chan, Kar Tim Zainuddin, Hishamuddin 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. Penerbit Universiti Kebangsaan Malaysia 2013 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/30080/1/30080.pdf Chan, Kar Tim and Zainuddin, Hishamuddin and Molladavoudi, Saeid (2013) Computation and visualization of cuspidal waveforms for modular group using GridMathematica. Sains Malaysiana, 42 (5). pp. 655-660. ISSN 0026-6039 http://www.ukm.my/jsm/english_journals/vol42num5_2013/contentsVol42num5_2013.html |
| spellingShingle | Chan, Kar Tim Zainuddin, Hishamuddin Molladavoudi, Saeid Computation and visualization of cuspidal waveforms for modular group using GridMathematica |
| title | 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_short | Computation and visualization of cuspidal waveforms for modular group using GridMathematica |
| title_sort | computation and visualization of cuspidal waveforms for modular group using gridmathematica |
| url | http://psasir.upm.edu.my/id/eprint/30080/1/30080.pdf |
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