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Title:
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A wavelet-based numerical scheme for stochastic mechanics |
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Author:
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Rao, Vallabhajosyula Ravi Shankar |
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Advisor:
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Spanos, Pol D. |
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Degree:
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Doctor of Philosophy thesis |
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Abstract:
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Uncertainty is an inherent part of many physical systems. This is often ignored to simplify mathematical models thereby leading to a deterministic treatment of the system. Incorporation of the uncertainty into the model, particularly in the presence of strong correlation across scales is a difficult task for the conventional modeling techniques. This work studies a biorthogonal wavelet framework for the representation of random fields. It is shown that such a representation scheme leads to significantly decorrelated wavelet coefficients. The amount of decorrelation obtained is an improvement over that achieved with orthonormal wavelet basis functions. It is shown that a biorthogonal dual wavelets with sufficient number of vanishing moments and corresponding to a low primal order perform better than Daubechies wavelets at this task. These observations are used in pursuing the development of Wavelet based Galerkin and Petrov-Galerkin schemes for one-dimensional and two-dimensional stochastic mechanics problems. |
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Citation:
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Rao, Vallabhajosyula Ravi Shankar. "A wavelet-based numerical scheme for stochastic mechanics." Doctoral Thesis, Rice University, ETD http://hdl.handle.net/1911/19550. |
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Citable link to this page:
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http://hdl.handle.net/1911/19550 |
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Date:
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2000 |
