2026-09-21T08:05:55Zhttps://repository.rice.edu/server/oai/request

oai:repository.rice.edu:1911/195502024-01-11T20:56:52Zcom_1911_8299col_1911_13110

Spanos, Pol D. Rao, Vallabhajosyula Ravi Shankar 2009-06-04T08:47:06Z 2009-06-04T08:47:06Z 2000 Rao, Vallabhajosyula Ravi Shankar. "A wavelet-based numerical scheme for stochastic mechanics." (2000) Diss., Rice University. <a href="https://hdl.handle.net/1911/19550">https://hdl.handle.net/1911/19550</a>. https://hdl.handle.net/1911/19550 THESIS M.E. 2000 RAO 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. 117 p. application/pdf eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. Applied mechanics Mechanical engineering A wavelet-based numerical scheme for stochastic mechanics Thesis Text Mechanical Engineering Engineering Rice University Doctoral Doctor of Philosophy open.access