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Compact Moving Mesh Method for Gas Dynamics Equations

Thesis Info

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Author

Ch. , Maqbool Ahmad

Program

PhD

Institute

University of Engineering and Technology

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2011

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/622

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725749620

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The objective of this dissertation is to develop fourth order compact moving mesh method. This method is a hybrid of compact method and moving mesh method. The usual second order method becomes less suitable due to the increase of number of grid points to achieve the required accuracy. In this method, only three nodes are needed to yield a fourth order accuracy whereas other methods would have required five nodes and more computational effort to achieve the same accuracy. Compact moving mesh method is used to solve one dimensional gas dynamics equations. Compact method and moving mesh method are also reviewed in this dissertation. The results obtained by using compact moving mesh method are compared with the results determined by using second order finite difference method for gas dynamics equations.
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Non-Uniform and Uniform Discrete Multitone Transceivers for the Dsl and the Power Line Channels

Discrete Multitone (DMT) modulation is a popular multicarrier technique adopted for wireline communication, which offers computationally inexpensive channel equalization, based on cyclic prefix, in addition to bit and power loading. A cyclic prefix is pre-appended in multicarrier modulated (MCM) techniques, that helps mitigate the inter-symbol interference due to mul- tipath effect. For channel equalization, a single tap per subcarrier is sufficient to compensate for the channel distortion in the frequency domain, provided the cyclic prefix length is of the order of the channel. This formulates a Zero-Forcing frequency domain equalizer, which com- pensates the channel attenuation with an inverse channel response. However, this method has the shortcoming of enhancing channel noise, where the channel is of low magnitude, in the high frequency range. It has been observed through the studies on channel measurements that most channels display the characteristics similar to that of a lowpass filter. Therefore, the cyclic prefix (CP) based equalization in MCM techniques enhances channel noise, which in turn increases the bit error rate and also reduces the post equalization signal-to-noise ratio (SNR). In this thesis, as a solution to this problem, hybrid DMT modulation techniques, that is the Uniform and Non-Uniform DMT modulation are proposed and implemented for the DSL and the power line channels. The performance analysis of the proposed modulation techniques in the DSL channel and for the various categories of the power line channel is presented. Since the Non-Uniform and Uniform modulation techniques are hybrid techniques, and their structures are a combination of wavelet filter banks and conventional DMT systems, therefore, the effect of inter-channel crosstalk and its relation with the filter’s order is also investigated. Computational complexity of the hybrid modulation techniques is also derived, and it is found to be greater than that of the conventional DMT system. Moreover, different methods are adopted for quantization of channel noise enhancement. A reconstruction error is derived to ascertain the quantity of channel noise enhancement in different subbands of the communication channel and also for this purpose, post equalization SNR is computed. A modified Non-Uniform DMT transceiver was proposed and implemented for the DSL channel. It is depicted through simulation results that the Non- Uniform DMT modulation shows some improvement in the post equalization SNR, and its modified form gives better performance, however at the cost of reduced data rate. The Uniform DMT modulation technique is proposed with a power-allocation algorithm for different sub- channels of the DSL and the power line channels. The Uniform DMT modulation performance evaluation through simulation results shows significant improvement in SNR in comparison with the conventional DMT system, at the cost of greater computational complexity, for the various DSL and power line channels.