Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for +publisher:"Purdue University" +contributor:("Peijun Li"). Showing records 1 – 3 of 3 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters


Purdue University

1. Homan, Andrew J. Applications of microlocal analysis to some hyperbolic inverse problems.

Degree: PhD, Mathematics, 2015, Purdue University

This thesis compiles my work on three inverse problems: ultrasound recovery in thermoacoustic tomography, cancellation of singularities in synthetic aperture radar, and the injectivity and stability of some generalized Radon transforms. Each problem is approached using microlocal methods. In the context of thermoacoustic tomography under the damped wave equation, I show uniqueness and stability of the problem with complete data, provide a reconstruction algorithm for small attenuation with complete data, and obtain stability estimates for visible singularities with partial data. The chapter on synthetic aperture radar constructs microlocally several infinite-dimensional families of ground reflectivity functions which appear microlocally regular when imaged using synthetic aperture radar. Finally, based on a joint work with Hanming Zhou, we show the analytic microlocal regularity of a class of analytic generalized Radon transforms, using this to show injectivity and stability for a generic class of generalized Radon transforms defined on analytic Riemannian manifolds. Advisors/Committee Members: Plamen Stefanov, Plamen Stefanov, Antônio Sá Barreto, Peijun Li, Kiril Datchev.

Subjects/Keywords: Mathematics

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Homan, A. J. (2015). Applications of microlocal analysis to some hyperbolic inverse problems. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/473

Chicago Manual of Style (16th Edition):

Homan, Andrew J. “Applications of microlocal analysis to some hyperbolic inverse problems.” 2015. Doctoral Dissertation, Purdue University. Accessed October 25, 2020. https://docs.lib.purdue.edu/open_access_dissertations/473.

MLA Handbook (7th Edition):

Homan, Andrew J. “Applications of microlocal analysis to some hyperbolic inverse problems.” 2015. Web. 25 Oct 2020.

Vancouver:

Homan AJ. Applications of microlocal analysis to some hyperbolic inverse problems. [Internet] [Doctoral dissertation]. Purdue University; 2015. [cited 2020 Oct 25]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/473.

Council of Science Editors:

Homan AJ. Applications of microlocal analysis to some hyperbolic inverse problems. [Doctoral Dissertation]. Purdue University; 2015. Available from: https://docs.lib.purdue.edu/open_access_dissertations/473


Purdue University

2. Chen, Yi. Local polynomial chaos expansion method for high dimensional stochastic differential equations.

Degree: PhD, Mathematics, 2016, Purdue University

Polynomial chaos expansion is a widely adopted method to determine evolution of uncertainty in dynamical system with probabilistic uncertainties in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the efficiency brought by PC expansion compared to sampling-based Monte Carlo experiments, but still suffered from relatively high simulation cost when facing high dimensional random inputs. We propose a localized polynomial chaos expansion method that employs a domain decomposition technique to approximate the stochastic solution locally. In a relatively lower dimensional random space, we are able to solve subdomain problems individually within the accuracy restrictions. Sampling processes are delayed to the last step of the coupling of local solutions to help reduce computational cost in linear systems. We perform a further theoretical analysis on combining a domain decomposition technique with a numerical strategy of epistemic uncertainty to approximate the stochastic solution locally. An establishment is made between Schur complement in traditional domain decomposition setting and the local PCE method at the coupling stage. A further branch of discussion on the topic of decoupling strategy is presented at the end to propose some of the intuitive possibilities of future work. Both the general mathematical framework of the methodology and a collection of numerical examples are presented to demonstrate the validity and efficiency of the method. Advisors/Committee Members: Dongbin Xiu, Suchuan Dong, Dongbin Xiu, Peijun Li, Guang Lin.

Subjects/Keywords: Applied sciences; Generalized polynomial chaos; Stochastic differential equations; Uncertainty quantification; Applied Mathematics

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chen, Y. (2016). Local polynomial chaos expansion method for high dimensional stochastic differential equations. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/744

Chicago Manual of Style (16th Edition):

Chen, Yi. “Local polynomial chaos expansion method for high dimensional stochastic differential equations.” 2016. Doctoral Dissertation, Purdue University. Accessed October 25, 2020. https://docs.lib.purdue.edu/open_access_dissertations/744.

MLA Handbook (7th Edition):

Chen, Yi. “Local polynomial chaos expansion method for high dimensional stochastic differential equations.” 2016. Web. 25 Oct 2020.

Vancouver:

Chen Y. Local polynomial chaos expansion method for high dimensional stochastic differential equations. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2020 Oct 25]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/744.

Council of Science Editors:

Chen Y. Local polynomial chaos expansion method for high dimensional stochastic differential equations. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/744

3. He, Ying. Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems.

Degree: PhD, Mathematics, 2013, Purdue University

This dissertation focuses on the development of high-order numerical methods for acoustic and electromagnetic scattering problems, and nonlinear fluid-structure interaction problems. For the scattering problems, two cases are considered: 1) the scattering from a doubly layered periodic structure; and 2) the scattering from doubly layered, unbounded rough surface. For both cases, we first apply the transformed field expansion (TFE) method to reduce the two-dimensional Helmholtz equation with complex scattering surface into a successive sequence of the transmission problems with a plane interface. Then, we use Fourier-Spectral method in the periodic structure problem and Hermite-Spectral method in the unbounded rough surface problem to reduce the two-dimensional problems into a sequence of one-dimensional problems, which can then be efficiently solved by a Legendre-Galerkin method. In order for TFE method to work well, the scattering surface has to be a sufficiently small and smooth deformation of a plane surface. To deal with scattering problems from a non-smooth surface, we also develop a high-order spectral-element method which is more robust than the TFE method, but is computationally more expensive. We also consider the non-linear fluid-structure interaction problem, and develop a class of monolithic pressure-correction schemes, based on the standard pressure-correction and rotational pressure-correction schemes. The main advantage of these schemes is that they only require solving a pressure Poisson equation and a linear coupled elliptic equation at each time step. Hence, they are computationally very efficient. Furthermore, we prove that the proposed schemes are unconditionally stable. Advisors/Committee Members: Jie Shen, Jie Shen, Patricia Bauman, Peijun Li, Robert Skeel.

Subjects/Keywords: applied sciences; fourier-spectral method; hermite-spectral method; acoustic scattering problems; electromagnetic scattering problems; Applied Mathematics

…127 4.3 4.4 4.5 4.6 4.7 x ABSTRACT He, Ying Ph.D., Purdue University, December 2013… 

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

He, Y. (2013). Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/148

Chicago Manual of Style (16th Edition):

He, Ying. “Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems.” 2013. Doctoral Dissertation, Purdue University. Accessed October 25, 2020. https://docs.lib.purdue.edu/open_access_dissertations/148.

MLA Handbook (7th Edition):

He, Ying. “Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems.” 2013. Web. 25 Oct 2020.

Vancouver:

He Y. Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems. [Internet] [Doctoral dissertation]. Purdue University; 2013. [cited 2020 Oct 25]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/148.

Council of Science Editors:

He Y. Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems. [Doctoral Dissertation]. Purdue University; 2013. Available from: https://docs.lib.purdue.edu/open_access_dissertations/148

.